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Design Results of RC Members Subjected toBending Shear and Torsion Using ACI 31808
and BS 811097 Building Codes
Ali S Alnuaimi
1
Iqbal I Patel
2
and Mohammed C Al-Mohsin
3
Abstract In this research a comparative study was conducted on the amount of required reinforcement using American Concrete Institute
(ACI) and British Standards Institution (BSI) building codes The comparison included design cases of rectangular beam sections subjected to
combined loads of bending shear and torsion and punching shear at slabndashcolumn connections In addition the study included comparison of
the differencesin the amount of reinforcement requiredowing to different codesrsquo factors of safety for design loads It wasfound thatthe BScode
requires less reinforcement than the ACI code does for the same value of design load However when the load safety factors are included in
calculating the design loads the values of the resulting design loads become different for each code and in this case the ACI was found to
require less reinforcement than the BS Thepunching shear strength of 1047298at slabndashcolumnconnections calculated using theACI code was found to
be more than that calculated using the BS code for the same geometry material and loading conditions The minimum area of 1047298exural
reinforcementrequired by ACI was found to be greater than by BS while the opposite was found for the minimum area of shear reinforcement
In case both codesunify the load safetyfactors while keeping the otherdesign equations as they are now the BS code will have preference over
the ACI code owing to lower reinforcement requirements which leads to cheaper construction while maintaining safety The study showedthat both codes are good choices for design in Oman Because SI units are becoming more and more enforced internationally material that is
available in Oman is conversant more toward SI units to unify the knowledge of design among municipality and site engineers it is
recommended to use the BS code as a 1047297rst choice until a national code is established DOI 101061(ASCE)SC1943-55760000158 copy 2013
American Society of Civil Engineers
CE Database subject headings Reinforced concrete Design Bending Comparative studies
The structural design codes for RC ACI 31808 [American Con-
crete Institute (ACI) 2008] and BS 811097 [British StandardsInstitution (BSI) 1997] are based on the limit state design How-
ever these designcodes differ on thedesignequations especiallyfor
shear and torsion They also differ on the factors of safety for
material and loads Because there is no national structural design
code in Oman a question about the most appropriate code in terms
of safety economy and suitability to the environment in Oman is
always asked Knowledge of main features of and differences be-
tween the ACI 318 and BS 8110 codes is deemed a necessity
Although both ACI 318 and BS 8110 codes agree on the live load
factor ofsafety tobe 16the factorof safetyfor the deadload inACI
is 12 whereas in BS it is14 17 greaterSubsequently this resultsin a larger value of ultimate (design) load which in turn affects theamount of reinforcement and concrete The material strength re-
duction factor f inthe ACI 318 is090 for 1047298exure and075 forshear and torsion whereas in BS 8110 the material partial safety factor is067for 1047298exure and 08for shear and torsion Further unlike the ACI318 code where the reinforcement design strength is As f y the BS8110 design strength is 095 As f y The limit of maximum strain inconcrete in ACI 318 is 0003 whereas in BS 8110 the limit is00035 Appendix I shows that the ACI 318 considers the materialand geometry in de1047297ning the minimum area of longitudinal re-inforcement Asmin whereas BS 8110 is based on geometry onlyThere is no differentiation between the sizes of bw and b in con-sidering the Asmin in ACI318 whereas BS 8110 hasdifferent valuesfor Asmin when bw=b 04 and bw=b$ 04 ACI 318 considers theeffective depth d in calculating the geometry whereas BS 8110considers the total depth h The ACI 318 equation
V c frac14
016
ffiffiffiffi f c9
q thorn 17r
V ud
M u
bd 029
ffiffiffiffi f c9
q bd
(Section 11221) assumes that shear strength of concrete is pro-portional to the square root of concrete cylindercompressive strengthwhereas the BS 8110 equation
V c frac14
079g m
100 As
bwd
1=3400
d
1=4 f cu
25
1=3
bwd
(Section 3454) assumes that the shear strength is proportional tothe cubic rootof cube concrete compressive strength The maximum
1Associate Professor Dept of Civil and Architectural Engineering
College of Engineering Sultan Qaboos Univ PO Box 33 PC 123Muscat Oman (corresponding author) E-mail alnuaimisqueduom
alnuaimiasmgmailcom 2Structural Engineer Muscat Municipality PO Box 79 PC 100
Muscat Oman3Assistant Professor Civil Engineering Dept College of Engineering
Univ of Buarimi PO Box 890 PC 512 Buraimi OmanNote This manuscript was submitted on December 6 2011 approved
on November 28 2012 published online on December 1 2012 Discus-
sion period open until April 1 2014 separate discussions must be sub-mitted for individual papers This paper is part of the Practice Periodical
on Structural Design and Constructi on Vol 18 No 4 November 1
spacing between stirrups fortorsional reinforcement in ACI 318 is thesmaller of ph=8 or 300 mm whereas BS 8110 speci1047297es the maximum spacing as the least of 08 x 1 y1eth095 f yvTHORN Asvt =T u x 1 y1=2 or 200 mm
As per Jung and Kim (2008) the response of structural concreteto the actions of bending moment is quite well understood andconsequently design procedures andprovisionsfor bendingmomentarereasonably effective and consistent between different codes Jung andKim also stated ldquoMany of shear design code provisions are principallyempirical vary greatly from code to code and do not provide uniform factors of safety against failurerdquo
Sharma and Inniss (2006) found that the slab punching shear capacity vc in ACI 318 is calculated from the concrete compressivestrength as 033
ffiffiffiffi f c9p
without any consideration to the effect of longitudinal reinforcement whereas in BS 8110
vc frac14 079g m
ffiffiffiffiffiffiffiffi400
d
4
r ffiffiffiffiffiffiffiffiffiffiffiffi100 As
bwd
3
r ffiffiffiffiffi f cu
25
3
r
which takes account of the longitudinal reinforcement in addition toconcrete strength
Subramanian (2005) pointed out that in BS 8110 the critical sectionfor checking the punching shear is 15d from edge of load pointwhereas in ACI 318 the critical section for checking punching shear is
05d from edge of load pointBari (2000) reviewed the shear strength of slabndashcolumn con-nections and concluded that the BS code predicts smaller shear strength than ACI for values of r less than 12 and larger strengthfor values of r greater than 12 However this limit may vary for differentcolumnshapes concretestrengths and effectivedepths Barialso concluded that with a ratio of column side length of 25 to 5 theBS code predictsgreater strength than theACI code whereas for ratioranges between 1 and 25 ACI predicts more shear strength than BS
Ngo (2001) stated ldquoDepending on method used the criticalsection forchecking punching shear in slabs is usually situated between05 to 2 times the effective depth from edge of load or the reactionrdquoHeconcluded that the punching shear strength values that are speci1047297ed indifferent codes vary with concrete compressive strength f c9 and are
usually expressed in terms of eth f c9THORN
n
In ACI 318 the punching shear strength is expressed as proportional to ffiffiffiffi
f c9p
whereas in BS 8110punching shear strength is assumed to be proportional to
ffiffiffiffiffi f cu
3p
Chiu et al (2007) carried out a parametric study based on ACI
31805(ACI 2005) and found that torsional strength decreases as theaspect ratio (longer dimensionshorter dimension) of specimenincreases
Bernardo and Lopes (2009) analyzed several codes of practice re-garding torsion andconcluded that the ACIcode hasclauses that imposemaximum and minimum amounts of torque reinforcement (for bothtransverse and longitudinal bars) The equations for minimum amount of reinforcement are however mainly empirical and sometimes lead toquestionable solutions namely negative minimum longitudinal rein-forcement or disproportional longitudinal reinforcement and stirrups
According to Ameli and Ronagh (2007) the area used in shear 1047298ow calculation is determined differently in different codes whichresults in different torsional shear strengths Taking the centers of longitudinal bars or center-to-center of stirrups for the calculation of this area will result in different sizes of area
Alnuaimi and Bhatt (2006) reported that ldquomost researchersbelieve that the shear stress owing to direct shear is resisted by thewhole width of cross section while the torsional shear stress isresisted by the outer skin of concrete section They differ howeveron the thickness of outer skinrdquo
Based on the literature it is clear that some research works havebeen carried out on the comparison between ACI and BS codes
However the comparisons were limited to few parameters and donot touch the effects of these differences on the amount of rein-forcement No study was found in the literature on the preference of design codes for structural design in Oman or the rest of the Gulf states In this research an intensive comparison work was carriedout to 1047297nd out the effects of design results on the amount of rein-forcement using ACI and BS codes Effects of different parameterswere studied including M u=V u ratio load safety factors requiredlength for transverse reinforcement minimum 1047298exural and shear re-inforcement etc A recommendation on a preferred code is presented
Design Equations
Bending
The design procedures in ACI 31808 and BS 811097 are based onthe simpli1047297ed rectangular stress block as given in ACI 31808ndash102and BS 811097ndash344 respectively The area of required 1047298exuralreinforcement in ACI 31808ndash1034 is given as
The design provision for torsional cracking strength of RC solidbeam in ACI 31808ndash1151 is speci1047297ed as
T cr frac14 ffiffiffiffi
f c9p
3
A2
cp
Pcp
(9)
If T u fT cr =4 no torsional reinforcement is neededThe torsional strength of a member is given by ACI 31808ndash
11535 as
T n frac14 2 At Ao f yv
s cot u (10)
where Ao 5 085 Aoh and u5 45 for RC memberIn BS 8110ndash285 (BSI 1985)ndash2441 the torsional shear stress
vt for rectangular beam is computed as
vt frac14 2T u
h2min
hmax2
hmin
3
(11)
The minimum torsion stress vt min below which torsion in thesection can be ignored based on BS 8110ndash285ndash246 is given for different grades of concrete as
vt min frac14 0067 ffiffiffiffiffi
f cu
p 04 N=mm 2 (12)
If v t vt min then torsional resistance is to be provided by closed
stirrups and longitudinal barsBased on ACI 31808ndash11537 the required longitudinal re-
inforcement is calculated as
Al frac14 At
sPh
f yv
f yl
cot 2u (13)
ACI 31808ndash11553 speci1047297es the minimum longitudinal torsionalreinforcement as
Al min frac14 042 ffiffiffiffi
f c9p
Acp
f yl
2
At
s
Ph
f yv
f yl
(14)
where At =s 0175bw= f yvIn addition ACI 31808ndash11562 restricts the maximum spacing
between bars of the longitudinal reinforcement required for torsion
to 300 mm The longitudinal bars shall be inside the closed stirrups
and at least one bar is required in each corner Longitudinal bar
diameter shall not be less than 10 mmThe required longitudinal reinforcement due to torsion is given
in BS 8110ndash
285ndash
248 as
Al frac14 Asvt f yveth x 1 thorn y1THORNsv f y
(15)
BS 8110ndash285ndash249 states that the longitudinal torsion reinforce-
ment shall be distributedevenly around theperimeter of stirrups The
clear distance between these bars should not exceed 300 mm Lon-
gitudinal bar diameter shall not be less than 12 mmThe required stirrups (by assuming u5 45) is given by ACI
31808ndash11535 as
At
sfrac14 T u
17f Aoh f yv
(16)
For pure torsion the minimum amount of closed stirrup is speci1047297edby ACI 31808ndash11552 as the greater result of the following
At min frac14 larger of
266664
2 At min
s frac14 0062
ffiffiffiffi f c9
q bw
f yv
2 At min
s$ 035
bw
f yv
377775 (17)
ACI 31808ndash11561 speci1047297es the maximum spacing of stirrups as
the smaller of ph=8 or 300 mmThe shear reinforcement made of closed stirrups is calculated
based on BS 8110ndash285ndash247 as
Asvt
S v frac14 T
u08 x 1 y1
095 f yv
(18)
S v should not exceed the least of x 1 y1=2 or 200 mmTo prevent crushing of surface concrete of solid section ACI
31808ndash11531 restricts the cross-sectional dimension as ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiV u
bwd
2
thorn
T uPh
17 A2oh
2v uut f
V c
bwd thorn 066
ffiffiffiffi f c9
q (19)
where V c 5 017 ffiffiffiffiffiffiffiffiffi
f c9bd p
PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013 215
For section dimensions check in BS 8110ndash285ndash245 thecomputed torsional shear stress vt should not exceed the followinglimit for sections with larger center-to-center dimensions of closedlink less than 550 mm
vt vtu y1
550 (20)
In no case should the sum of the shear stresses resulting from shear force and torsion (vtu 5 vs 1 vt ) exceed the maximum shear stress
speci1047297
ed by Eq (8) If a combination of applied shear stress vs andtorsional stress vt exceeds this limit the section should be resized
Design Results and Discussions
Here design results of rectangular beams with different load com-binations and spandepth ratios are presented The ACI 31808 andBS 811097 codes were used in the design and results were judgedbased on the amount of longitudinal and transverse reinforcement requirements The characteristic cube compressive strength of con-crete was 30N=mm 2 and the cylinder compressive strength was24 N=mm 2 with concrete density of 24 kN=m 3 and the charac-teristic yield strength of the longitudinal and transverse reinforce-ment was 460 N=mm 2
Design for Combined Bending Moment and Shear Force Using ACI 31808 and BS 811097
Tables 1ndash3 and Table 4 show the design results of three groups of simply supported beams and one group of two-span continuousbeams respectively In beam numbering the 1047297rst letter denotes thetype of member considered eg B means beam the second letter denotes the variable eg R means spandepth ratio the third letter denotes thetype of loading eg W means uniformly distributedloadThe 1047297rst numeral represents the value of R and the second numeralrepresents the value of W The beam cross-sectional dimension was
selected to be 3503 700 mm with effective depth of 625 mm Dif-ferent ultimate design uniformly distributed load values were used asshownin the caption of each table It wasassumedthat 50 of bottom longitudinal bars are curtailed at 01 L from support and transversestirrups were used for shear reinforcement ie no bent-up barsconsidered to resist shear The spandepth ratio was varied among eachgroup resulting in different M u=V u ratios The design was carried out using the ACI and BS codes for the same ultimate design load values
It is clear that the two codes gave almost the same results for bendingreinforcement with minimal effect of M u=V u ratio changesgiving a maximum difference of 26 in the case of single-spansimply supported beams and 084 in the case of the continuousbeams However theresults differ largelyon theshear reinforcement with the change of M u=V u ratio using ACI and BS codes as can be
Table 1 Simply Supported Beams with Ultimate Design UDL of 75 kN=m
seen for a typical beam in Fig 1 The differences become pronouncedwith the increase of M u=V u ratio leading to continually divergingcurves In most cases it wasfound that theBS requires less transversereinforcement than the ACI For the given geometry and loads thedifferences reached up to 181 in thecaseof simplysupported beamsand 314 in the case of continuous beams Further the length from the face of support to the point beyond which only minimum shear reinforcement is required was also investigated andis presented in thepenultimate columns of Tables 1ndash4 It was found that the length that needs shear reinforcement required by BS is less than that required
by ACI The differences become more pronounced with increaseof M u=V u ratio For the given geometry and loads the differencesreached up to 1108 in the case of simply supported beams and1533 in the case of continuous beams This indicates that with theincrease of loads the BS code becomes more economical on thetransverse reinforcement
Table 5 shows comparisonbetween theACI and BS resultson theshear strength capacity of concrete using
vc frac14
016
ffiffiffiffi f c9
q thorn 17r
V ud
M u
029
ffiffiffiffi f c9
q
as extracted from Eq (3) in the case of ACI code and Eq (4) in thecase of BS code for different values of r ranging from 02 to 20
In the ACI the values of V ud = M u were varied from 0 to 10 and inthe case ofBS the value of 400=d wastaken as constant equal to 1 It is obvious that the above equations lead to highly different resultsInitially when reinforcement ratio r is 02 vc of BS is less by
about60 than that of ACI for all values of V ud = M uAsthe V ud = M uandor r increases the concrete shear capacity increases Fig 2shows that the nonlinear curve resulting from the BS equation crossesthe linearly diverging curves made by the ACI equation for variablevalues of V ud = M u at different points The1047297rst crossing point occurredat r 5 08 with V ud = M u 5 0 The succeeding crosses occurredsequentially with the increased V ud = M u curves It isalsoclear that theBS rate of increasein shear capacity is more rapid than that of the ACIAppendix II shows formulation of both ACI and BS code equationsfor required shear reinforcement to produce two similar equations with
differences in the empirical values It can be seen that even in the casewhen vc in ACI is equal to vc in BS as shown in the crosses of Fig 2the values of spacing between stirrups S as shown by the resultingequations in Appendix II will be different and the ACI code requiresapproximately 26 more shear reinforcement than the BS code Thisdifference is attributed to differences in material safety factors
Design for Torsion Using ACI 31808 and BS 811097
Here 5003 700-mm beams with effective depth of 625 mm weresubjected to pure twisting moment Table 6 shows the design resultsof 1047297xed beams subjected to ultimate design torsion using ACI andBS codes In beam numbering the 1047297rst letter denotes the type of member eg B means beam the second letter denotes the variable
eg L means span and the numeral gives the value of L It is clear thatthe requiredlongitudinalreinforcement by ACI is 192 larger than that required by BS for most of the beams (ie BL6 BL8 andBL10) Because BL4 needs minimum steel in the ACI approach this
Table 4 Two Span Continuous Beam with Ultimate Design UDL of 60 kN=m
beam was not considered in the comparison The transverse re-inforcement required by ACI is approximately 19 larger than that required by BS This shows that BS is more economical than ACI inthe case of design for torsion in RC rectangular solid beams
Appendix I shows a comparison between the ACI and BS torsionequations that lead to required transverse and longitudinal reinforce-ment It is clear that the area of the shear 1047298ow Aoh is taken as 085 x 1 y1
in ACI whereas in BS it is taken as 08 x 1 y1 Further owing to dif-ferences in material safety factors ACI required about 19 moretransverse torsional reinforcement than BS Regarding longitudinal
reinforcementthederivedEqs(2)and(4)inAppendix I look identical inboth codes but since longitudinal reinforcement is dependent on theamount of transverse reinforcement the same difference of 19 that was found above for transverse reinforcement is carried to longitudinalreinforcement
DesignforCombinedBendingMomentShearForceand Twisting Moment Using ACI 31808 and BS 811097
Tables 7 and 8 show the design results of longitudinal reinforcement fortwo groupsof 1047297xed end beams withdifferent uniformly distributedload values and torsional moment of 125 kNm =m as shown in thecaption of each table The beam size considered was 400 3 700mm
with effective depth of 625 mm and design results were calculatednearthe supportIn beam numbering the1047297rstletter denotes thetypeof member considered eg B meansbeamthe second letter denotes thevariable eg R means spandepth ratio the third letter denotes thetype of loading eg W means uniformly distributed load The 1047297rst numeral represents the value of R and the second numeral representsthevalue of W It is clear that therequired topreinforcementfor ACIislarger than that for BS with a maximum difference of 84 for thegiven loads and beam geometry The bottom and face reinforcement required by ACIis largerby about 193than that required by BSNo
major changes were found in the longitudinal reinforcementdue to theincrease of L =d or M u=T u ratios However the results differ largely onthe transverse reinforcementwith the change of V u=T u ratio using ACIand BScodes ascanbe seenin Fig 3ItcanbeseenthattheACIcurveis linear whereas the BS curve is nonlinear The differences becomepronounced with increase of V u=T u ratio leading to continually di-verging curves In most cases it was found that BS requires lesstransverse reinforcement than ACI For the given geometry and loadsthe difference reached up to 193
Impactof Load SafetyFactors on DesignLoad Using ACI 31808 and BS 811097
In this section simply supported RC beams of 200-3 700-mm
cross section 625-mm effective depth and 6-m effective span withuniformly distributedlive anddead loads weredesignedusingthe ACIandBS codesThe live load waskeptconstant at 5 kN=m for all beamswhile the dead load values were varied from 20 to 40 kN=m The liveload was kept constant because the factor of safety for the live load isthe same inboth ACI and BScodes ie 16 It was assumed that50of bottom bars are curtailedat 01 L from thecenter of supportTable9shows theeffects of theACI andBS code factors of safety on requiredreinforcement In the beam numbering the1047297rst letterdenotes the typeof member eg B means a beam the second letter denotes thevariable eg R is the ratio of dead load to live load (DLLL) and thenumeral gives the value of R It is clear that because of the different values of dead load factors of safety 12 in ACI and 14 in BS thedifferences in design bending moments and shear forces between
the results from ACI and BS are linearly increasing with the increaseof the dead load For the given service loads the factored (ultimate)
design load usingBS waslarger than that forACI having a maximum
difference of 143 As a result to these load differences therequiredlongitudinal and transverse reinforcements are differing with maxi-mum of 165 for bending and 600 for shear reinforcementsrespectively The results for the1047298exural reinforcement indicates slight
diversion due to the effect of increasing dead load while the requiredshear reinforcement shows convergence on the required transversereinforcement with the increase of the DLLL ratio Beams BR4 andBR5 required minimum stirrups in ACIand hence are notconsidered in
the discussion It is interesting to notice that as seen in Tables 1ndash4 for
the ultimate design loading the difference in 1047298exural reinforcement using ACIandBS is negligible Forservice loadinghowever shown inTable 9 the required 1047298exural reinforcement for BS was larger than for ACI with differences varying from 99 to 165 This difference isattributed to thedifferentload safetyfactors that areused in ACIandBSfor dead and live load combinations Similarly as seen in Tables 1ndash4for the ultimate design loading the shear reinforcement required by BSis less compared with ACI whereas for service loading (Table 9) theresultis reversed This reversal of resultis also attributed to thedifferent load safety factors used in ACI and BS codes for the dead load
Punching Shear Strength (at SlabndashColumn Connection) Using ACI 31808 and BS 811097
Here a parametric study of punching shear capacity at slabndashcolumnconnection using ACI and BS codes was carried out with different column aspect ratios percentagesof 1047298exural reinforcement and slabthicknesses The characteristic cube and cylindrical compressivestrengths were taken as 35 and 28 N=mm 2 respectively and thecharacteristic yield strength of reinforcementwas taken as 460N=mm 2
Table 6 Fixed Beams with Ultimate Design Torsion
Beam
number
Span
(m)
T u
(kNm)
Al
(mm 2)Difference
in Al ()
At =s
(mm 2=mm)Difference
in At =s ()ACI BS ACI BS
BL4 4 50 min 583 mdash 068 057 193
BL6 6 75 1043 875 192 102 086 186
BL8 8 100 1391 1167 192 136 114 193
BL10 10 125 1738 1458 192 17 143 189
Table 7 Fixed End Beams with Ultimate Design UDL of 100 kN=m and Torsion of 125kNm =m
From Eqs (4) and (7) it can be seen that unlike BS 8110 ACI 318does not consider dowel action of 1047298exural reinforcement in thecalculation of shear capacity Fig 4 shows punching shear strengthof a 250-mm-thick slab with effective depth of 220 mm at interior column having r 5 10 with column sizes of 3003 3003003 600 3003 900 and 3003 1200 mm resulting in different aspectratios usingACI andBS codesThe concrete cube compressivestrength f cu was 35 Nmm 2 with concrete cylinder compressivestrength as 08 f cu and steel yield strength of 460 N=mm 2 It can beseen that punching shearstrength forACI is larger than for BS for all
aspect ratios This means that for the same ultimate design punchingshear force ACI requires less slab thickness than BS The largest difference is368 when column aspect ratio is 2 It canalsobe seenthat in BS code punching shear strength increases linearly ascolumn aspect ratio increases whereas in ACI code the curve isnonlinear having a larger rate of increase of punching shear strengthbetween column aspect ratio of 1 and 2 than between 2 and 4 Fig 5shows punching shear strength of 250-mm-thick slab at interior columnof size 3003 300 mm with different percentages of 1047298exural re-inforcement ranging between 015 and 3 using ACI and BS codesThe material strengths and effective depths of slab were the same as inthe previous slab It can be seen that in ACI code the punching shear strength is constant at 773 kN without any effect of the percentage of 1047298exural reinforcement whereas in BS code punching shear strength
increases with increase of reinforcement TheBS curve is nonlinear and
it crosses the ACI horizontal line at r 5 17 This shows that with thegiven data untilr 5 17 ACI leads to largerpunching shear strengththan BS with the largest difference of 1314 when r 5 015
Fig 6 shows punching shear strengthof slabat interiorcolumnof size3003 300 mm with area of 1047298exural reinforcement As 5 2 050 mm 2
with varying depth The material strengths were the same as in theprevious slab The effective depth of each slab is 35 mm less than theoverall thickness It can be seen that ACIestimates more punchingshear strength than BS The differences with the given data ranged between148 and 233 Both ACI and BS curves vary linearly with increase of
depth however the rate ofincreaseinthe ACIresults ismorethan inBSleading to diverging curves This shows that the difference in V c usingboth codes increases as depth increases
Comparison for Minimum Area of Flexural Reinforcement Using ACI 31808 and BS 811097
The equations of minimum required 1047298exural reinforcement basedon the ACI and BS codes are shown in Appendix I Fig 7 was de-veloped based on those equations for different values of f c9 which istakenas08 f cu Thebeamcross-sectional dimension is 3503 700 mm with effective depth of 625 mm The yield strength of reinforcement was taken as 460 N=mm 2 It can be seen that the minimum area of 1047298exural reinforcement required by ACI is much larger than that re-
quired by BS The BS curve is constant with all grades of concrete
Table 9 Parametric Study to Compare Steel Required for Bending and Shear with DL 1 LL Combination Using ACI and BS
while the ACI curve changes from being constant for concretegrades of 30ndash40 N=mm 2 to nonlinear for concrete grades larger than40 N=mm 2 The difference is constant at the value of 106 for theconcrete strengths of 30ndash40 N=mm 2 then it increases with the in-crease in the concrete strength The maximum difference for thegiven beam geometry and concrete strengths was 1335
Comparison for Minimum Area of Shear Reinforcement Using ACI 31808 and BS 811097
Fig 8 was developed based on Eqs (5) and (6) for different values of f c9 which is taken as 08 f cu The beam cross-sectional dimension is3503 700 mm with effective depth of 625 mm The yield strengthof reinforcement was taken as 460 N=mm 2 It can be seen that theminimum area of shear reinforcement required by BS is larger thanrequired by ACI The BS curve is constant for all grades of concretewhereas theACI curveis constant forconcretegrades of 30ndash40 N=mm 2
then reduces linearly for grades larger than 40 N=mm 2 The dif-ference is constant at the value of 185 for the concrete strengths
between 30 and 40 N=mm 2 then decreases with the increase in theconcretestrength Theminimum difference forthegiven beamgeometryand concrete strengths was 67 at concrete grade of 50 N=mm 2
Concluding Remarks and Recommendations
In this research design results of rectangular RC beams subjected to
bending shear and torsion and punching shear at the slabndashcolumnconnection using ACI 31808 and BS 811097 were comparedConclusions can be drawn as follows
Design for Combined Bending Moment Twisting Moment and Shear Force
bull Therequired 1047298exural reinforcementsfor thesame designbendingmoment using ACI and BS codes are almostthe same regardlessof M u=V u ratio
bull In most cases the required shear reinforcement by ACI code islargerthan that by BS code forthesame design load This difference
Fig 5 Punching shear strength versus percentage of r using ACI and BS codes
Fig 6 Punching shear strength versus slab thickness using ACI and BS codes
PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013 221
becomes morepronounced with the increase of M u=V u ratio It wasfound that empirical equations of shear capacity in BS and ACIcodes have led to highlydifferent results It wasalso established that owing to differences in material safety factors ACI equations leadto more required shear reinforcement than BS
bull The beam length that needs shear reinforcement (beyond whichonly minimum shear reinforcement is needed) required by BS
code is shorter than that for ACI code The difference becomesmore pronounced with the increase of M u=V u ratio
bull The longitudinal and transverse torsional reinforcement requiredby ACI was found to be larger than that required by BS and thedifference in value betweenthe reinforcementof the two codesisalmost constant It was found that these differences are due todifferences in material safety factors
Impact of Safety Factors on Ultimate Design Load
bull The difference in the factor of safety for the dead load betweenthe ACI and BS resulted in larger design bending moments
and shear forces by the BS equations than the ACI ones Thediverging difference increases linearly with the increase of thedead load
bull For the resulting different design loads it wasfound that both thelongitudinal and transverse reinforcements required by the ACIare lower than the BS in all beams
bull For different column aspect ratios the punching shear strength of 1047298at slabndashcolumn connections calculated using the ACI code wasfound to be larger than that calculated using the BS code for thesame geometry materials and loading conditions
bull In the ACI code punching shear strength remains constant for different percentages of 1047298exural reinforcement whereas in theBS code punching shear strength increases with increase of 1047298exural reinforcement
bull For different slab thicknesses ACI code estimates more punch-ing shear strength than BS code
Fig 7 Minimum area of 1047298exural reinforcement with different f cu
Fig 8 Minimum area of shear reinforcement with different f cu
222 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
Acp 5 area enclosed by outside perimeter of concrete
cross section
Al 5 area of longitudinal reinforcement to resist torsion
Al min 5 minimum area of longitudinal reinforcement to
resist torsion
Ao 5 gross area enclosed by shear 1047298ow path
Aoh 5 area enclosed by centerline of the outermost closed
transverse torsional reinforcement
As 5 area of longitudinal tension reinforcement to resist
bending moment
Asmin 5 minimum area of 1047298exural reinforcement to resist
bending moment
Asv 5 area of shear reinforcement to resist shear
Asvt 5 area of two legs of stirrups required for torsion At 5 area of one leg of a closed stirrup resisting torsion
At min 5 minimum area of shear reinforcement to resist
torsion
a 5 depth of equivalent rectangular stress block
b 5 width of section 1047298ange
bw 5 width of section web
d 5 effective depth of tension reinforcement (distance
from extreme compression 1047297ber to centroid of
longitudinal tension reinforcement)
f 9c 5 characteristic cylinder compressive strength of
concrete (150 mm 3 300 mm)
f cu 5 characteristic strength of concrete
(1503
1503
150 mm concrete cube strength) f y 5 characteristic yield strength of longitudinal
reinforcement for 1047298exure
f yl 5 characteristic yield strength of longitudinal
reinforcement for torsion
f yv 5 characteristic yield strength of transverse
reinforcement
h 5 overall depth of section
hmax 5 larger dimension of rectangular cross section
hmin 5 smaller dimension of rectangular cross section
L 5 effective beam span
M u 5 ultimate 1047298exural moment
ph 5 perimeter of centerline of outermost closed
transverse torsional reinforcement
S 5 center-to-center spacing of transverse reinforcement
S v 5 spacing of stirrups
T cr 5 torsional cracking moment
T n 5 nominal torsional moment strength
T u 5 ultimate design twisting moment
V c 5 nominal shear strength provided by concrete
V u 5 ultimate shear force
v 5 design shear stress
vc 5 concrete shear strength
vt 5 torsional shear stress
vt min 5 minimum torsional shear stress above which
reinforcement is required
vtu 5 maximum combinedshear stress (shear plustorsion)
x 1 5 smaller center to center dimension of rectangular
stirrups y1 5 larger center to center dimension of rectangular
stirrups
Z 5 lever arm
g m 5 partial safety factor for strength of material
u 5 angle between axis of strut compression diagonal
and tension chord of the member
r 5 reinforcement ratio ( As=bd ) and
f 5 strength reduction factor
References
Alnuaimi A S and Bhatt P (2006) ldquo
Design of solid reinforced concretebeamsrdquo Structures Buildings 159(4) 197ndash216Ameli M and Ronagh H R (2007) ldquoTreatment of torsion of reinforced
concrete beams in current structural standardsrdquo Asian J Civil Eng
for structural concrete and commentaryrdquo 318-05 Farmington Hills
MIAmerican Concrete Institute (ACI) (2008) ldquoBuilding code requirements
for structural concrete and commentaryrdquo 318-08 Farmington Hills
MIBari MS(2000)ldquoPunching shear strength of slab-column connectionsmdashA
comparative study of different codesrdquo J Inst Engineers (India) 80(4)163ndash168
Bernardo L F A and Lopes S M R (2009) ldquoTorsion in high strengthconcrete hollow beamsmdashStrength and ductility analysisrdquo ACI Struc-
tural J 106(1) 39ndash48British Standards Institution(BSI) (1985)ldquoStructuraluse of concrete Code
of practice for special circumstancesrdquo BS 811085 Part-2 London
British Standards Institution(BSI) (1997)ldquoStructuraluse of concrete Codeof practice for design and constructionrdquo BS 811097 London
Chiu H J Fang I K Young W T and Shiau J K (2007) ldquoBehavior
of reinforced concrete beams with minimum torsional reinforcementrdquo Eng Structures 29(9) 2193ndash2205
Jung S and Kim KS (2008) ldquoKnowledge-based prediction on shear strength of concrete beams without shear reinforcementrdquo Eng Struc-
tures 30(6) 1515ndash1525Ngo D T (2001) ldquoPunching shear resistance of high-strength concrete
slabsrdquo Electron J Structural Eng 1(1) 2ndash14
Sharma A K and Innis B C (2006) ldquoPunching shear strength of slab-column connectionmdashA comparative study of different codesrdquo ASCE
Conf Proc Structural Engineering and Public Safety 2006 StructuresCongress ASCE Reston VA 1ndash11
Subramanian N (2005) ldquoEvaluation and enhancing the punching shear resistance of 1047298at slabs using high strength concreterdquo Indian Concr J79(4) 31ndash37
224 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
spacing between stirrups fortorsional reinforcement in ACI 318 is thesmaller of ph=8 or 300 mm whereas BS 8110 speci1047297es the maximum spacing as the least of 08 x 1 y1eth095 f yvTHORN Asvt =T u x 1 y1=2 or 200 mm
As per Jung and Kim (2008) the response of structural concreteto the actions of bending moment is quite well understood andconsequently design procedures andprovisionsfor bendingmomentarereasonably effective and consistent between different codes Jung andKim also stated ldquoMany of shear design code provisions are principallyempirical vary greatly from code to code and do not provide uniform factors of safety against failurerdquo
Sharma and Inniss (2006) found that the slab punching shear capacity vc in ACI 318 is calculated from the concrete compressivestrength as 033
ffiffiffiffi f c9p
without any consideration to the effect of longitudinal reinforcement whereas in BS 8110
vc frac14 079g m
ffiffiffiffiffiffiffiffi400
d
4
r ffiffiffiffiffiffiffiffiffiffiffiffi100 As
bwd
3
r ffiffiffiffiffi f cu
25
3
r
which takes account of the longitudinal reinforcement in addition toconcrete strength
Subramanian (2005) pointed out that in BS 8110 the critical sectionfor checking the punching shear is 15d from edge of load pointwhereas in ACI 318 the critical section for checking punching shear is
05d from edge of load pointBari (2000) reviewed the shear strength of slabndashcolumn con-nections and concluded that the BS code predicts smaller shear strength than ACI for values of r less than 12 and larger strengthfor values of r greater than 12 However this limit may vary for differentcolumnshapes concretestrengths and effectivedepths Barialso concluded that with a ratio of column side length of 25 to 5 theBS code predictsgreater strength than theACI code whereas for ratioranges between 1 and 25 ACI predicts more shear strength than BS
Ngo (2001) stated ldquoDepending on method used the criticalsection forchecking punching shear in slabs is usually situated between05 to 2 times the effective depth from edge of load or the reactionrdquoHeconcluded that the punching shear strength values that are speci1047297ed indifferent codes vary with concrete compressive strength f c9 and are
usually expressed in terms of eth f c9THORN
n
In ACI 318 the punching shear strength is expressed as proportional to ffiffiffiffi
f c9p
whereas in BS 8110punching shear strength is assumed to be proportional to
ffiffiffiffiffi f cu
3p
Chiu et al (2007) carried out a parametric study based on ACI
31805(ACI 2005) and found that torsional strength decreases as theaspect ratio (longer dimensionshorter dimension) of specimenincreases
Bernardo and Lopes (2009) analyzed several codes of practice re-garding torsion andconcluded that the ACIcode hasclauses that imposemaximum and minimum amounts of torque reinforcement (for bothtransverse and longitudinal bars) The equations for minimum amount of reinforcement are however mainly empirical and sometimes lead toquestionable solutions namely negative minimum longitudinal rein-forcement or disproportional longitudinal reinforcement and stirrups
According to Ameli and Ronagh (2007) the area used in shear 1047298ow calculation is determined differently in different codes whichresults in different torsional shear strengths Taking the centers of longitudinal bars or center-to-center of stirrups for the calculation of this area will result in different sizes of area
Alnuaimi and Bhatt (2006) reported that ldquomost researchersbelieve that the shear stress owing to direct shear is resisted by thewhole width of cross section while the torsional shear stress isresisted by the outer skin of concrete section They differ howeveron the thickness of outer skinrdquo
Based on the literature it is clear that some research works havebeen carried out on the comparison between ACI and BS codes
However the comparisons were limited to few parameters and donot touch the effects of these differences on the amount of rein-forcement No study was found in the literature on the preference of design codes for structural design in Oman or the rest of the Gulf states In this research an intensive comparison work was carriedout to 1047297nd out the effects of design results on the amount of rein-forcement using ACI and BS codes Effects of different parameterswere studied including M u=V u ratio load safety factors requiredlength for transverse reinforcement minimum 1047298exural and shear re-inforcement etc A recommendation on a preferred code is presented
Design Equations
Bending
The design procedures in ACI 31808 and BS 811097 are based onthe simpli1047297ed rectangular stress block as given in ACI 31808ndash102and BS 811097ndash344 respectively The area of required 1047298exuralreinforcement in ACI 31808ndash1034 is given as
The design provision for torsional cracking strength of RC solidbeam in ACI 31808ndash1151 is speci1047297ed as
T cr frac14 ffiffiffiffi
f c9p
3
A2
cp
Pcp
(9)
If T u fT cr =4 no torsional reinforcement is neededThe torsional strength of a member is given by ACI 31808ndash
11535 as
T n frac14 2 At Ao f yv
s cot u (10)
where Ao 5 085 Aoh and u5 45 for RC memberIn BS 8110ndash285 (BSI 1985)ndash2441 the torsional shear stress
vt for rectangular beam is computed as
vt frac14 2T u
h2min
hmax2
hmin
3
(11)
The minimum torsion stress vt min below which torsion in thesection can be ignored based on BS 8110ndash285ndash246 is given for different grades of concrete as
vt min frac14 0067 ffiffiffiffiffi
f cu
p 04 N=mm 2 (12)
If v t vt min then torsional resistance is to be provided by closed
stirrups and longitudinal barsBased on ACI 31808ndash11537 the required longitudinal re-
inforcement is calculated as
Al frac14 At
sPh
f yv
f yl
cot 2u (13)
ACI 31808ndash11553 speci1047297es the minimum longitudinal torsionalreinforcement as
Al min frac14 042 ffiffiffiffi
f c9p
Acp
f yl
2
At
s
Ph
f yv
f yl
(14)
where At =s 0175bw= f yvIn addition ACI 31808ndash11562 restricts the maximum spacing
between bars of the longitudinal reinforcement required for torsion
to 300 mm The longitudinal bars shall be inside the closed stirrups
and at least one bar is required in each corner Longitudinal bar
diameter shall not be less than 10 mmThe required longitudinal reinforcement due to torsion is given
in BS 8110ndash
285ndash
248 as
Al frac14 Asvt f yveth x 1 thorn y1THORNsv f y
(15)
BS 8110ndash285ndash249 states that the longitudinal torsion reinforce-
ment shall be distributedevenly around theperimeter of stirrups The
clear distance between these bars should not exceed 300 mm Lon-
gitudinal bar diameter shall not be less than 12 mmThe required stirrups (by assuming u5 45) is given by ACI
31808ndash11535 as
At
sfrac14 T u
17f Aoh f yv
(16)
For pure torsion the minimum amount of closed stirrup is speci1047297edby ACI 31808ndash11552 as the greater result of the following
At min frac14 larger of
266664
2 At min
s frac14 0062
ffiffiffiffi f c9
q bw
f yv
2 At min
s$ 035
bw
f yv
377775 (17)
ACI 31808ndash11561 speci1047297es the maximum spacing of stirrups as
the smaller of ph=8 or 300 mmThe shear reinforcement made of closed stirrups is calculated
based on BS 8110ndash285ndash247 as
Asvt
S v frac14 T
u08 x 1 y1
095 f yv
(18)
S v should not exceed the least of x 1 y1=2 or 200 mmTo prevent crushing of surface concrete of solid section ACI
31808ndash11531 restricts the cross-sectional dimension as ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiV u
bwd
2
thorn
T uPh
17 A2oh
2v uut f
V c
bwd thorn 066
ffiffiffiffi f c9
q (19)
where V c 5 017 ffiffiffiffiffiffiffiffiffi
f c9bd p
PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013 215
For section dimensions check in BS 8110ndash285ndash245 thecomputed torsional shear stress vt should not exceed the followinglimit for sections with larger center-to-center dimensions of closedlink less than 550 mm
vt vtu y1
550 (20)
In no case should the sum of the shear stresses resulting from shear force and torsion (vtu 5 vs 1 vt ) exceed the maximum shear stress
speci1047297
ed by Eq (8) If a combination of applied shear stress vs andtorsional stress vt exceeds this limit the section should be resized
Design Results and Discussions
Here design results of rectangular beams with different load com-binations and spandepth ratios are presented The ACI 31808 andBS 811097 codes were used in the design and results were judgedbased on the amount of longitudinal and transverse reinforcement requirements The characteristic cube compressive strength of con-crete was 30N=mm 2 and the cylinder compressive strength was24 N=mm 2 with concrete density of 24 kN=m 3 and the charac-teristic yield strength of the longitudinal and transverse reinforce-ment was 460 N=mm 2
Design for Combined Bending Moment and Shear Force Using ACI 31808 and BS 811097
Tables 1ndash3 and Table 4 show the design results of three groups of simply supported beams and one group of two-span continuousbeams respectively In beam numbering the 1047297rst letter denotes thetype of member considered eg B means beam the second letter denotes the variable eg R means spandepth ratio the third letter denotes thetype of loading eg W means uniformly distributedloadThe 1047297rst numeral represents the value of R and the second numeralrepresents the value of W The beam cross-sectional dimension was
selected to be 3503 700 mm with effective depth of 625 mm Dif-ferent ultimate design uniformly distributed load values were used asshownin the caption of each table It wasassumedthat 50 of bottom longitudinal bars are curtailed at 01 L from support and transversestirrups were used for shear reinforcement ie no bent-up barsconsidered to resist shear The spandepth ratio was varied among eachgroup resulting in different M u=V u ratios The design was carried out using the ACI and BS codes for the same ultimate design load values
It is clear that the two codes gave almost the same results for bendingreinforcement with minimal effect of M u=V u ratio changesgiving a maximum difference of 26 in the case of single-spansimply supported beams and 084 in the case of the continuousbeams However theresults differ largelyon theshear reinforcement with the change of M u=V u ratio using ACI and BS codes as can be
Table 1 Simply Supported Beams with Ultimate Design UDL of 75 kN=m
seen for a typical beam in Fig 1 The differences become pronouncedwith the increase of M u=V u ratio leading to continually divergingcurves In most cases it wasfound that theBS requires less transversereinforcement than the ACI For the given geometry and loads thedifferences reached up to 181 in thecaseof simplysupported beamsand 314 in the case of continuous beams Further the length from the face of support to the point beyond which only minimum shear reinforcement is required was also investigated andis presented in thepenultimate columns of Tables 1ndash4 It was found that the length that needs shear reinforcement required by BS is less than that required
by ACI The differences become more pronounced with increaseof M u=V u ratio For the given geometry and loads the differencesreached up to 1108 in the case of simply supported beams and1533 in the case of continuous beams This indicates that with theincrease of loads the BS code becomes more economical on thetransverse reinforcement
Table 5 shows comparisonbetween theACI and BS resultson theshear strength capacity of concrete using
vc frac14
016
ffiffiffiffi f c9
q thorn 17r
V ud
M u
029
ffiffiffiffi f c9
q
as extracted from Eq (3) in the case of ACI code and Eq (4) in thecase of BS code for different values of r ranging from 02 to 20
In the ACI the values of V ud = M u were varied from 0 to 10 and inthe case ofBS the value of 400=d wastaken as constant equal to 1 It is obvious that the above equations lead to highly different resultsInitially when reinforcement ratio r is 02 vc of BS is less by
about60 than that of ACI for all values of V ud = M uAsthe V ud = M uandor r increases the concrete shear capacity increases Fig 2shows that the nonlinear curve resulting from the BS equation crossesthe linearly diverging curves made by the ACI equation for variablevalues of V ud = M u at different points The1047297rst crossing point occurredat r 5 08 with V ud = M u 5 0 The succeeding crosses occurredsequentially with the increased V ud = M u curves It isalsoclear that theBS rate of increasein shear capacity is more rapid than that of the ACIAppendix II shows formulation of both ACI and BS code equationsfor required shear reinforcement to produce two similar equations with
differences in the empirical values It can be seen that even in the casewhen vc in ACI is equal to vc in BS as shown in the crosses of Fig 2the values of spacing between stirrups S as shown by the resultingequations in Appendix II will be different and the ACI code requiresapproximately 26 more shear reinforcement than the BS code Thisdifference is attributed to differences in material safety factors
Design for Torsion Using ACI 31808 and BS 811097
Here 5003 700-mm beams with effective depth of 625 mm weresubjected to pure twisting moment Table 6 shows the design resultsof 1047297xed beams subjected to ultimate design torsion using ACI andBS codes In beam numbering the 1047297rst letter denotes the type of member eg B means beam the second letter denotes the variable
eg L means span and the numeral gives the value of L It is clear thatthe requiredlongitudinalreinforcement by ACI is 192 larger than that required by BS for most of the beams (ie BL6 BL8 andBL10) Because BL4 needs minimum steel in the ACI approach this
Table 4 Two Span Continuous Beam with Ultimate Design UDL of 60 kN=m
beam was not considered in the comparison The transverse re-inforcement required by ACI is approximately 19 larger than that required by BS This shows that BS is more economical than ACI inthe case of design for torsion in RC rectangular solid beams
Appendix I shows a comparison between the ACI and BS torsionequations that lead to required transverse and longitudinal reinforce-ment It is clear that the area of the shear 1047298ow Aoh is taken as 085 x 1 y1
in ACI whereas in BS it is taken as 08 x 1 y1 Further owing to dif-ferences in material safety factors ACI required about 19 moretransverse torsional reinforcement than BS Regarding longitudinal
reinforcementthederivedEqs(2)and(4)inAppendix I look identical inboth codes but since longitudinal reinforcement is dependent on theamount of transverse reinforcement the same difference of 19 that was found above for transverse reinforcement is carried to longitudinalreinforcement
DesignforCombinedBendingMomentShearForceand Twisting Moment Using ACI 31808 and BS 811097
Tables 7 and 8 show the design results of longitudinal reinforcement fortwo groupsof 1047297xed end beams withdifferent uniformly distributedload values and torsional moment of 125 kNm =m as shown in thecaption of each table The beam size considered was 400 3 700mm
with effective depth of 625 mm and design results were calculatednearthe supportIn beam numbering the1047297rstletter denotes thetypeof member considered eg B meansbeamthe second letter denotes thevariable eg R means spandepth ratio the third letter denotes thetype of loading eg W means uniformly distributed load The 1047297rst numeral represents the value of R and the second numeral representsthevalue of W It is clear that therequired topreinforcementfor ACIislarger than that for BS with a maximum difference of 84 for thegiven loads and beam geometry The bottom and face reinforcement required by ACIis largerby about 193than that required by BSNo
major changes were found in the longitudinal reinforcementdue to theincrease of L =d or M u=T u ratios However the results differ largely onthe transverse reinforcementwith the change of V u=T u ratio using ACIand BScodes ascanbe seenin Fig 3ItcanbeseenthattheACIcurveis linear whereas the BS curve is nonlinear The differences becomepronounced with increase of V u=T u ratio leading to continually di-verging curves In most cases it was found that BS requires lesstransverse reinforcement than ACI For the given geometry and loadsthe difference reached up to 193
Impactof Load SafetyFactors on DesignLoad Using ACI 31808 and BS 811097
In this section simply supported RC beams of 200-3 700-mm
cross section 625-mm effective depth and 6-m effective span withuniformly distributedlive anddead loads weredesignedusingthe ACIandBS codesThe live load waskeptconstant at 5 kN=m for all beamswhile the dead load values were varied from 20 to 40 kN=m The liveload was kept constant because the factor of safety for the live load isthe same inboth ACI and BScodes ie 16 It was assumed that50of bottom bars are curtailedat 01 L from thecenter of supportTable9shows theeffects of theACI andBS code factors of safety on requiredreinforcement In the beam numbering the1047297rst letterdenotes the typeof member eg B means a beam the second letter denotes thevariable eg R is the ratio of dead load to live load (DLLL) and thenumeral gives the value of R It is clear that because of the different values of dead load factors of safety 12 in ACI and 14 in BS thedifferences in design bending moments and shear forces between
the results from ACI and BS are linearly increasing with the increaseof the dead load For the given service loads the factored (ultimate)
design load usingBS waslarger than that forACI having a maximum
difference of 143 As a result to these load differences therequiredlongitudinal and transverse reinforcements are differing with maxi-mum of 165 for bending and 600 for shear reinforcementsrespectively The results for the1047298exural reinforcement indicates slight
diversion due to the effect of increasing dead load while the requiredshear reinforcement shows convergence on the required transversereinforcement with the increase of the DLLL ratio Beams BR4 andBR5 required minimum stirrups in ACIand hence are notconsidered in
the discussion It is interesting to notice that as seen in Tables 1ndash4 for
the ultimate design loading the difference in 1047298exural reinforcement using ACIandBS is negligible Forservice loadinghowever shown inTable 9 the required 1047298exural reinforcement for BS was larger than for ACI with differences varying from 99 to 165 This difference isattributed to thedifferentload safetyfactors that areused in ACIandBSfor dead and live load combinations Similarly as seen in Tables 1ndash4for the ultimate design loading the shear reinforcement required by BSis less compared with ACI whereas for service loading (Table 9) theresultis reversed This reversal of resultis also attributed to thedifferent load safety factors used in ACI and BS codes for the dead load
Punching Shear Strength (at SlabndashColumn Connection) Using ACI 31808 and BS 811097
Here a parametric study of punching shear capacity at slabndashcolumnconnection using ACI and BS codes was carried out with different column aspect ratios percentagesof 1047298exural reinforcement and slabthicknesses The characteristic cube and cylindrical compressivestrengths were taken as 35 and 28 N=mm 2 respectively and thecharacteristic yield strength of reinforcementwas taken as 460N=mm 2
Table 6 Fixed Beams with Ultimate Design Torsion
Beam
number
Span
(m)
T u
(kNm)
Al
(mm 2)Difference
in Al ()
At =s
(mm 2=mm)Difference
in At =s ()ACI BS ACI BS
BL4 4 50 min 583 mdash 068 057 193
BL6 6 75 1043 875 192 102 086 186
BL8 8 100 1391 1167 192 136 114 193
BL10 10 125 1738 1458 192 17 143 189
Table 7 Fixed End Beams with Ultimate Design UDL of 100 kN=m and Torsion of 125kNm =m
From Eqs (4) and (7) it can be seen that unlike BS 8110 ACI 318does not consider dowel action of 1047298exural reinforcement in thecalculation of shear capacity Fig 4 shows punching shear strengthof a 250-mm-thick slab with effective depth of 220 mm at interior column having r 5 10 with column sizes of 3003 3003003 600 3003 900 and 3003 1200 mm resulting in different aspectratios usingACI andBS codesThe concrete cube compressivestrength f cu was 35 Nmm 2 with concrete cylinder compressivestrength as 08 f cu and steel yield strength of 460 N=mm 2 It can beseen that punching shearstrength forACI is larger than for BS for all
aspect ratios This means that for the same ultimate design punchingshear force ACI requires less slab thickness than BS The largest difference is368 when column aspect ratio is 2 It canalsobe seenthat in BS code punching shear strength increases linearly ascolumn aspect ratio increases whereas in ACI code the curve isnonlinear having a larger rate of increase of punching shear strengthbetween column aspect ratio of 1 and 2 than between 2 and 4 Fig 5shows punching shear strength of 250-mm-thick slab at interior columnof size 3003 300 mm with different percentages of 1047298exural re-inforcement ranging between 015 and 3 using ACI and BS codesThe material strengths and effective depths of slab were the same as inthe previous slab It can be seen that in ACI code the punching shear strength is constant at 773 kN without any effect of the percentage of 1047298exural reinforcement whereas in BS code punching shear strength
increases with increase of reinforcement TheBS curve is nonlinear and
it crosses the ACI horizontal line at r 5 17 This shows that with thegiven data untilr 5 17 ACI leads to largerpunching shear strengththan BS with the largest difference of 1314 when r 5 015
Fig 6 shows punching shear strengthof slabat interiorcolumnof size3003 300 mm with area of 1047298exural reinforcement As 5 2 050 mm 2
with varying depth The material strengths were the same as in theprevious slab The effective depth of each slab is 35 mm less than theoverall thickness It can be seen that ACIestimates more punchingshear strength than BS The differences with the given data ranged between148 and 233 Both ACI and BS curves vary linearly with increase of
depth however the rate ofincreaseinthe ACIresults ismorethan inBSleading to diverging curves This shows that the difference in V c usingboth codes increases as depth increases
Comparison for Minimum Area of Flexural Reinforcement Using ACI 31808 and BS 811097
The equations of minimum required 1047298exural reinforcement basedon the ACI and BS codes are shown in Appendix I Fig 7 was de-veloped based on those equations for different values of f c9 which istakenas08 f cu Thebeamcross-sectional dimension is 3503 700 mm with effective depth of 625 mm The yield strength of reinforcement was taken as 460 N=mm 2 It can be seen that the minimum area of 1047298exural reinforcement required by ACI is much larger than that re-
quired by BS The BS curve is constant with all grades of concrete
Table 9 Parametric Study to Compare Steel Required for Bending and Shear with DL 1 LL Combination Using ACI and BS
while the ACI curve changes from being constant for concretegrades of 30ndash40 N=mm 2 to nonlinear for concrete grades larger than40 N=mm 2 The difference is constant at the value of 106 for theconcrete strengths of 30ndash40 N=mm 2 then it increases with the in-crease in the concrete strength The maximum difference for thegiven beam geometry and concrete strengths was 1335
Comparison for Minimum Area of Shear Reinforcement Using ACI 31808 and BS 811097
Fig 8 was developed based on Eqs (5) and (6) for different values of f c9 which is taken as 08 f cu The beam cross-sectional dimension is3503 700 mm with effective depth of 625 mm The yield strengthof reinforcement was taken as 460 N=mm 2 It can be seen that theminimum area of shear reinforcement required by BS is larger thanrequired by ACI The BS curve is constant for all grades of concretewhereas theACI curveis constant forconcretegrades of 30ndash40 N=mm 2
then reduces linearly for grades larger than 40 N=mm 2 The dif-ference is constant at the value of 185 for the concrete strengths
between 30 and 40 N=mm 2 then decreases with the increase in theconcretestrength Theminimum difference forthegiven beamgeometryand concrete strengths was 67 at concrete grade of 50 N=mm 2
Concluding Remarks and Recommendations
In this research design results of rectangular RC beams subjected to
bending shear and torsion and punching shear at the slabndashcolumnconnection using ACI 31808 and BS 811097 were comparedConclusions can be drawn as follows
Design for Combined Bending Moment Twisting Moment and Shear Force
bull Therequired 1047298exural reinforcementsfor thesame designbendingmoment using ACI and BS codes are almostthe same regardlessof M u=V u ratio
bull In most cases the required shear reinforcement by ACI code islargerthan that by BS code forthesame design load This difference
Fig 5 Punching shear strength versus percentage of r using ACI and BS codes
Fig 6 Punching shear strength versus slab thickness using ACI and BS codes
PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013 221
becomes morepronounced with the increase of M u=V u ratio It wasfound that empirical equations of shear capacity in BS and ACIcodes have led to highlydifferent results It wasalso established that owing to differences in material safety factors ACI equations leadto more required shear reinforcement than BS
bull The beam length that needs shear reinforcement (beyond whichonly minimum shear reinforcement is needed) required by BS
code is shorter than that for ACI code The difference becomesmore pronounced with the increase of M u=V u ratio
bull The longitudinal and transverse torsional reinforcement requiredby ACI was found to be larger than that required by BS and thedifference in value betweenthe reinforcementof the two codesisalmost constant It was found that these differences are due todifferences in material safety factors
Impact of Safety Factors on Ultimate Design Load
bull The difference in the factor of safety for the dead load betweenthe ACI and BS resulted in larger design bending moments
and shear forces by the BS equations than the ACI ones Thediverging difference increases linearly with the increase of thedead load
bull For the resulting different design loads it wasfound that both thelongitudinal and transverse reinforcements required by the ACIare lower than the BS in all beams
bull For different column aspect ratios the punching shear strength of 1047298at slabndashcolumn connections calculated using the ACI code wasfound to be larger than that calculated using the BS code for thesame geometry materials and loading conditions
bull In the ACI code punching shear strength remains constant for different percentages of 1047298exural reinforcement whereas in theBS code punching shear strength increases with increase of 1047298exural reinforcement
bull For different slab thicknesses ACI code estimates more punch-ing shear strength than BS code
Fig 7 Minimum area of 1047298exural reinforcement with different f cu
Fig 8 Minimum area of shear reinforcement with different f cu
222 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
Acp 5 area enclosed by outside perimeter of concrete
cross section
Al 5 area of longitudinal reinforcement to resist torsion
Al min 5 minimum area of longitudinal reinforcement to
resist torsion
Ao 5 gross area enclosed by shear 1047298ow path
Aoh 5 area enclosed by centerline of the outermost closed
transverse torsional reinforcement
As 5 area of longitudinal tension reinforcement to resist
bending moment
Asmin 5 minimum area of 1047298exural reinforcement to resist
bending moment
Asv 5 area of shear reinforcement to resist shear
Asvt 5 area of two legs of stirrups required for torsion At 5 area of one leg of a closed stirrup resisting torsion
At min 5 minimum area of shear reinforcement to resist
torsion
a 5 depth of equivalent rectangular stress block
b 5 width of section 1047298ange
bw 5 width of section web
d 5 effective depth of tension reinforcement (distance
from extreme compression 1047297ber to centroid of
longitudinal tension reinforcement)
f 9c 5 characteristic cylinder compressive strength of
concrete (150 mm 3 300 mm)
f cu 5 characteristic strength of concrete
(1503
1503
150 mm concrete cube strength) f y 5 characteristic yield strength of longitudinal
reinforcement for 1047298exure
f yl 5 characteristic yield strength of longitudinal
reinforcement for torsion
f yv 5 characteristic yield strength of transverse
reinforcement
h 5 overall depth of section
hmax 5 larger dimension of rectangular cross section
hmin 5 smaller dimension of rectangular cross section
L 5 effective beam span
M u 5 ultimate 1047298exural moment
ph 5 perimeter of centerline of outermost closed
transverse torsional reinforcement
S 5 center-to-center spacing of transverse reinforcement
S v 5 spacing of stirrups
T cr 5 torsional cracking moment
T n 5 nominal torsional moment strength
T u 5 ultimate design twisting moment
V c 5 nominal shear strength provided by concrete
V u 5 ultimate shear force
v 5 design shear stress
vc 5 concrete shear strength
vt 5 torsional shear stress
vt min 5 minimum torsional shear stress above which
reinforcement is required
vtu 5 maximum combinedshear stress (shear plustorsion)
x 1 5 smaller center to center dimension of rectangular
stirrups y1 5 larger center to center dimension of rectangular
stirrups
Z 5 lever arm
g m 5 partial safety factor for strength of material
u 5 angle between axis of strut compression diagonal
and tension chord of the member
r 5 reinforcement ratio ( As=bd ) and
f 5 strength reduction factor
References
Alnuaimi A S and Bhatt P (2006) ldquo
Design of solid reinforced concretebeamsrdquo Structures Buildings 159(4) 197ndash216Ameli M and Ronagh H R (2007) ldquoTreatment of torsion of reinforced
concrete beams in current structural standardsrdquo Asian J Civil Eng
for structural concrete and commentaryrdquo 318-05 Farmington Hills
MIAmerican Concrete Institute (ACI) (2008) ldquoBuilding code requirements
for structural concrete and commentaryrdquo 318-08 Farmington Hills
MIBari MS(2000)ldquoPunching shear strength of slab-column connectionsmdashA
comparative study of different codesrdquo J Inst Engineers (India) 80(4)163ndash168
Bernardo L F A and Lopes S M R (2009) ldquoTorsion in high strengthconcrete hollow beamsmdashStrength and ductility analysisrdquo ACI Struc-
tural J 106(1) 39ndash48British Standards Institution(BSI) (1985)ldquoStructuraluse of concrete Code
of practice for special circumstancesrdquo BS 811085 Part-2 London
British Standards Institution(BSI) (1997)ldquoStructuraluse of concrete Codeof practice for design and constructionrdquo BS 811097 London
Chiu H J Fang I K Young W T and Shiau J K (2007) ldquoBehavior
of reinforced concrete beams with minimum torsional reinforcementrdquo Eng Structures 29(9) 2193ndash2205
Jung S and Kim KS (2008) ldquoKnowledge-based prediction on shear strength of concrete beams without shear reinforcementrdquo Eng Struc-
tures 30(6) 1515ndash1525Ngo D T (2001) ldquoPunching shear resistance of high-strength concrete
slabsrdquo Electron J Structural Eng 1(1) 2ndash14
Sharma A K and Innis B C (2006) ldquoPunching shear strength of slab-column connectionmdashA comparative study of different codesrdquo ASCE
Conf Proc Structural Engineering and Public Safety 2006 StructuresCongress ASCE Reston VA 1ndash11
Subramanian N (2005) ldquoEvaluation and enhancing the punching shear resistance of 1047298at slabs using high strength concreterdquo Indian Concr J79(4) 31ndash37
224 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
The design provision for torsional cracking strength of RC solidbeam in ACI 31808ndash1151 is speci1047297ed as
T cr frac14 ffiffiffiffi
f c9p
3
A2
cp
Pcp
(9)
If T u fT cr =4 no torsional reinforcement is neededThe torsional strength of a member is given by ACI 31808ndash
11535 as
T n frac14 2 At Ao f yv
s cot u (10)
where Ao 5 085 Aoh and u5 45 for RC memberIn BS 8110ndash285 (BSI 1985)ndash2441 the torsional shear stress
vt for rectangular beam is computed as
vt frac14 2T u
h2min
hmax2
hmin
3
(11)
The minimum torsion stress vt min below which torsion in thesection can be ignored based on BS 8110ndash285ndash246 is given for different grades of concrete as
vt min frac14 0067 ffiffiffiffiffi
f cu
p 04 N=mm 2 (12)
If v t vt min then torsional resistance is to be provided by closed
stirrups and longitudinal barsBased on ACI 31808ndash11537 the required longitudinal re-
inforcement is calculated as
Al frac14 At
sPh
f yv
f yl
cot 2u (13)
ACI 31808ndash11553 speci1047297es the minimum longitudinal torsionalreinforcement as
Al min frac14 042 ffiffiffiffi
f c9p
Acp
f yl
2
At
s
Ph
f yv
f yl
(14)
where At =s 0175bw= f yvIn addition ACI 31808ndash11562 restricts the maximum spacing
between bars of the longitudinal reinforcement required for torsion
to 300 mm The longitudinal bars shall be inside the closed stirrups
and at least one bar is required in each corner Longitudinal bar
diameter shall not be less than 10 mmThe required longitudinal reinforcement due to torsion is given
in BS 8110ndash
285ndash
248 as
Al frac14 Asvt f yveth x 1 thorn y1THORNsv f y
(15)
BS 8110ndash285ndash249 states that the longitudinal torsion reinforce-
ment shall be distributedevenly around theperimeter of stirrups The
clear distance between these bars should not exceed 300 mm Lon-
gitudinal bar diameter shall not be less than 12 mmThe required stirrups (by assuming u5 45) is given by ACI
31808ndash11535 as
At
sfrac14 T u
17f Aoh f yv
(16)
For pure torsion the minimum amount of closed stirrup is speci1047297edby ACI 31808ndash11552 as the greater result of the following
At min frac14 larger of
266664
2 At min
s frac14 0062
ffiffiffiffi f c9
q bw
f yv
2 At min
s$ 035
bw
f yv
377775 (17)
ACI 31808ndash11561 speci1047297es the maximum spacing of stirrups as
the smaller of ph=8 or 300 mmThe shear reinforcement made of closed stirrups is calculated
based on BS 8110ndash285ndash247 as
Asvt
S v frac14 T
u08 x 1 y1
095 f yv
(18)
S v should not exceed the least of x 1 y1=2 or 200 mmTo prevent crushing of surface concrete of solid section ACI
31808ndash11531 restricts the cross-sectional dimension as ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiV u
bwd
2
thorn
T uPh
17 A2oh
2v uut f
V c
bwd thorn 066
ffiffiffiffi f c9
q (19)
where V c 5 017 ffiffiffiffiffiffiffiffiffi
f c9bd p
PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013 215
For section dimensions check in BS 8110ndash285ndash245 thecomputed torsional shear stress vt should not exceed the followinglimit for sections with larger center-to-center dimensions of closedlink less than 550 mm
vt vtu y1
550 (20)
In no case should the sum of the shear stresses resulting from shear force and torsion (vtu 5 vs 1 vt ) exceed the maximum shear stress
speci1047297
ed by Eq (8) If a combination of applied shear stress vs andtorsional stress vt exceeds this limit the section should be resized
Design Results and Discussions
Here design results of rectangular beams with different load com-binations and spandepth ratios are presented The ACI 31808 andBS 811097 codes were used in the design and results were judgedbased on the amount of longitudinal and transverse reinforcement requirements The characteristic cube compressive strength of con-crete was 30N=mm 2 and the cylinder compressive strength was24 N=mm 2 with concrete density of 24 kN=m 3 and the charac-teristic yield strength of the longitudinal and transverse reinforce-ment was 460 N=mm 2
Design for Combined Bending Moment and Shear Force Using ACI 31808 and BS 811097
Tables 1ndash3 and Table 4 show the design results of three groups of simply supported beams and one group of two-span continuousbeams respectively In beam numbering the 1047297rst letter denotes thetype of member considered eg B means beam the second letter denotes the variable eg R means spandepth ratio the third letter denotes thetype of loading eg W means uniformly distributedloadThe 1047297rst numeral represents the value of R and the second numeralrepresents the value of W The beam cross-sectional dimension was
selected to be 3503 700 mm with effective depth of 625 mm Dif-ferent ultimate design uniformly distributed load values were used asshownin the caption of each table It wasassumedthat 50 of bottom longitudinal bars are curtailed at 01 L from support and transversestirrups were used for shear reinforcement ie no bent-up barsconsidered to resist shear The spandepth ratio was varied among eachgroup resulting in different M u=V u ratios The design was carried out using the ACI and BS codes for the same ultimate design load values
It is clear that the two codes gave almost the same results for bendingreinforcement with minimal effect of M u=V u ratio changesgiving a maximum difference of 26 in the case of single-spansimply supported beams and 084 in the case of the continuousbeams However theresults differ largelyon theshear reinforcement with the change of M u=V u ratio using ACI and BS codes as can be
Table 1 Simply Supported Beams with Ultimate Design UDL of 75 kN=m
seen for a typical beam in Fig 1 The differences become pronouncedwith the increase of M u=V u ratio leading to continually divergingcurves In most cases it wasfound that theBS requires less transversereinforcement than the ACI For the given geometry and loads thedifferences reached up to 181 in thecaseof simplysupported beamsand 314 in the case of continuous beams Further the length from the face of support to the point beyond which only minimum shear reinforcement is required was also investigated andis presented in thepenultimate columns of Tables 1ndash4 It was found that the length that needs shear reinforcement required by BS is less than that required
by ACI The differences become more pronounced with increaseof M u=V u ratio For the given geometry and loads the differencesreached up to 1108 in the case of simply supported beams and1533 in the case of continuous beams This indicates that with theincrease of loads the BS code becomes more economical on thetransverse reinforcement
Table 5 shows comparisonbetween theACI and BS resultson theshear strength capacity of concrete using
vc frac14
016
ffiffiffiffi f c9
q thorn 17r
V ud
M u
029
ffiffiffiffi f c9
q
as extracted from Eq (3) in the case of ACI code and Eq (4) in thecase of BS code for different values of r ranging from 02 to 20
In the ACI the values of V ud = M u were varied from 0 to 10 and inthe case ofBS the value of 400=d wastaken as constant equal to 1 It is obvious that the above equations lead to highly different resultsInitially when reinforcement ratio r is 02 vc of BS is less by
about60 than that of ACI for all values of V ud = M uAsthe V ud = M uandor r increases the concrete shear capacity increases Fig 2shows that the nonlinear curve resulting from the BS equation crossesthe linearly diverging curves made by the ACI equation for variablevalues of V ud = M u at different points The1047297rst crossing point occurredat r 5 08 with V ud = M u 5 0 The succeeding crosses occurredsequentially with the increased V ud = M u curves It isalsoclear that theBS rate of increasein shear capacity is more rapid than that of the ACIAppendix II shows formulation of both ACI and BS code equationsfor required shear reinforcement to produce two similar equations with
differences in the empirical values It can be seen that even in the casewhen vc in ACI is equal to vc in BS as shown in the crosses of Fig 2the values of spacing between stirrups S as shown by the resultingequations in Appendix II will be different and the ACI code requiresapproximately 26 more shear reinforcement than the BS code Thisdifference is attributed to differences in material safety factors
Design for Torsion Using ACI 31808 and BS 811097
Here 5003 700-mm beams with effective depth of 625 mm weresubjected to pure twisting moment Table 6 shows the design resultsof 1047297xed beams subjected to ultimate design torsion using ACI andBS codes In beam numbering the 1047297rst letter denotes the type of member eg B means beam the second letter denotes the variable
eg L means span and the numeral gives the value of L It is clear thatthe requiredlongitudinalreinforcement by ACI is 192 larger than that required by BS for most of the beams (ie BL6 BL8 andBL10) Because BL4 needs minimum steel in the ACI approach this
Table 4 Two Span Continuous Beam with Ultimate Design UDL of 60 kN=m
beam was not considered in the comparison The transverse re-inforcement required by ACI is approximately 19 larger than that required by BS This shows that BS is more economical than ACI inthe case of design for torsion in RC rectangular solid beams
Appendix I shows a comparison between the ACI and BS torsionequations that lead to required transverse and longitudinal reinforce-ment It is clear that the area of the shear 1047298ow Aoh is taken as 085 x 1 y1
in ACI whereas in BS it is taken as 08 x 1 y1 Further owing to dif-ferences in material safety factors ACI required about 19 moretransverse torsional reinforcement than BS Regarding longitudinal
reinforcementthederivedEqs(2)and(4)inAppendix I look identical inboth codes but since longitudinal reinforcement is dependent on theamount of transverse reinforcement the same difference of 19 that was found above for transverse reinforcement is carried to longitudinalreinforcement
DesignforCombinedBendingMomentShearForceand Twisting Moment Using ACI 31808 and BS 811097
Tables 7 and 8 show the design results of longitudinal reinforcement fortwo groupsof 1047297xed end beams withdifferent uniformly distributedload values and torsional moment of 125 kNm =m as shown in thecaption of each table The beam size considered was 400 3 700mm
with effective depth of 625 mm and design results were calculatednearthe supportIn beam numbering the1047297rstletter denotes thetypeof member considered eg B meansbeamthe second letter denotes thevariable eg R means spandepth ratio the third letter denotes thetype of loading eg W means uniformly distributed load The 1047297rst numeral represents the value of R and the second numeral representsthevalue of W It is clear that therequired topreinforcementfor ACIislarger than that for BS with a maximum difference of 84 for thegiven loads and beam geometry The bottom and face reinforcement required by ACIis largerby about 193than that required by BSNo
major changes were found in the longitudinal reinforcementdue to theincrease of L =d or M u=T u ratios However the results differ largely onthe transverse reinforcementwith the change of V u=T u ratio using ACIand BScodes ascanbe seenin Fig 3ItcanbeseenthattheACIcurveis linear whereas the BS curve is nonlinear The differences becomepronounced with increase of V u=T u ratio leading to continually di-verging curves In most cases it was found that BS requires lesstransverse reinforcement than ACI For the given geometry and loadsthe difference reached up to 193
Impactof Load SafetyFactors on DesignLoad Using ACI 31808 and BS 811097
In this section simply supported RC beams of 200-3 700-mm
cross section 625-mm effective depth and 6-m effective span withuniformly distributedlive anddead loads weredesignedusingthe ACIandBS codesThe live load waskeptconstant at 5 kN=m for all beamswhile the dead load values were varied from 20 to 40 kN=m The liveload was kept constant because the factor of safety for the live load isthe same inboth ACI and BScodes ie 16 It was assumed that50of bottom bars are curtailedat 01 L from thecenter of supportTable9shows theeffects of theACI andBS code factors of safety on requiredreinforcement In the beam numbering the1047297rst letterdenotes the typeof member eg B means a beam the second letter denotes thevariable eg R is the ratio of dead load to live load (DLLL) and thenumeral gives the value of R It is clear that because of the different values of dead load factors of safety 12 in ACI and 14 in BS thedifferences in design bending moments and shear forces between
the results from ACI and BS are linearly increasing with the increaseof the dead load For the given service loads the factored (ultimate)
design load usingBS waslarger than that forACI having a maximum
difference of 143 As a result to these load differences therequiredlongitudinal and transverse reinforcements are differing with maxi-mum of 165 for bending and 600 for shear reinforcementsrespectively The results for the1047298exural reinforcement indicates slight
diversion due to the effect of increasing dead load while the requiredshear reinforcement shows convergence on the required transversereinforcement with the increase of the DLLL ratio Beams BR4 andBR5 required minimum stirrups in ACIand hence are notconsidered in
the discussion It is interesting to notice that as seen in Tables 1ndash4 for
the ultimate design loading the difference in 1047298exural reinforcement using ACIandBS is negligible Forservice loadinghowever shown inTable 9 the required 1047298exural reinforcement for BS was larger than for ACI with differences varying from 99 to 165 This difference isattributed to thedifferentload safetyfactors that areused in ACIandBSfor dead and live load combinations Similarly as seen in Tables 1ndash4for the ultimate design loading the shear reinforcement required by BSis less compared with ACI whereas for service loading (Table 9) theresultis reversed This reversal of resultis also attributed to thedifferent load safety factors used in ACI and BS codes for the dead load
Punching Shear Strength (at SlabndashColumn Connection) Using ACI 31808 and BS 811097
Here a parametric study of punching shear capacity at slabndashcolumnconnection using ACI and BS codes was carried out with different column aspect ratios percentagesof 1047298exural reinforcement and slabthicknesses The characteristic cube and cylindrical compressivestrengths were taken as 35 and 28 N=mm 2 respectively and thecharacteristic yield strength of reinforcementwas taken as 460N=mm 2
Table 6 Fixed Beams with Ultimate Design Torsion
Beam
number
Span
(m)
T u
(kNm)
Al
(mm 2)Difference
in Al ()
At =s
(mm 2=mm)Difference
in At =s ()ACI BS ACI BS
BL4 4 50 min 583 mdash 068 057 193
BL6 6 75 1043 875 192 102 086 186
BL8 8 100 1391 1167 192 136 114 193
BL10 10 125 1738 1458 192 17 143 189
Table 7 Fixed End Beams with Ultimate Design UDL of 100 kN=m and Torsion of 125kNm =m
From Eqs (4) and (7) it can be seen that unlike BS 8110 ACI 318does not consider dowel action of 1047298exural reinforcement in thecalculation of shear capacity Fig 4 shows punching shear strengthof a 250-mm-thick slab with effective depth of 220 mm at interior column having r 5 10 with column sizes of 3003 3003003 600 3003 900 and 3003 1200 mm resulting in different aspectratios usingACI andBS codesThe concrete cube compressivestrength f cu was 35 Nmm 2 with concrete cylinder compressivestrength as 08 f cu and steel yield strength of 460 N=mm 2 It can beseen that punching shearstrength forACI is larger than for BS for all
aspect ratios This means that for the same ultimate design punchingshear force ACI requires less slab thickness than BS The largest difference is368 when column aspect ratio is 2 It canalsobe seenthat in BS code punching shear strength increases linearly ascolumn aspect ratio increases whereas in ACI code the curve isnonlinear having a larger rate of increase of punching shear strengthbetween column aspect ratio of 1 and 2 than between 2 and 4 Fig 5shows punching shear strength of 250-mm-thick slab at interior columnof size 3003 300 mm with different percentages of 1047298exural re-inforcement ranging between 015 and 3 using ACI and BS codesThe material strengths and effective depths of slab were the same as inthe previous slab It can be seen that in ACI code the punching shear strength is constant at 773 kN without any effect of the percentage of 1047298exural reinforcement whereas in BS code punching shear strength
increases with increase of reinforcement TheBS curve is nonlinear and
it crosses the ACI horizontal line at r 5 17 This shows that with thegiven data untilr 5 17 ACI leads to largerpunching shear strengththan BS with the largest difference of 1314 when r 5 015
Fig 6 shows punching shear strengthof slabat interiorcolumnof size3003 300 mm with area of 1047298exural reinforcement As 5 2 050 mm 2
with varying depth The material strengths were the same as in theprevious slab The effective depth of each slab is 35 mm less than theoverall thickness It can be seen that ACIestimates more punchingshear strength than BS The differences with the given data ranged between148 and 233 Both ACI and BS curves vary linearly with increase of
depth however the rate ofincreaseinthe ACIresults ismorethan inBSleading to diverging curves This shows that the difference in V c usingboth codes increases as depth increases
Comparison for Minimum Area of Flexural Reinforcement Using ACI 31808 and BS 811097
The equations of minimum required 1047298exural reinforcement basedon the ACI and BS codes are shown in Appendix I Fig 7 was de-veloped based on those equations for different values of f c9 which istakenas08 f cu Thebeamcross-sectional dimension is 3503 700 mm with effective depth of 625 mm The yield strength of reinforcement was taken as 460 N=mm 2 It can be seen that the minimum area of 1047298exural reinforcement required by ACI is much larger than that re-
quired by BS The BS curve is constant with all grades of concrete
Table 9 Parametric Study to Compare Steel Required for Bending and Shear with DL 1 LL Combination Using ACI and BS
while the ACI curve changes from being constant for concretegrades of 30ndash40 N=mm 2 to nonlinear for concrete grades larger than40 N=mm 2 The difference is constant at the value of 106 for theconcrete strengths of 30ndash40 N=mm 2 then it increases with the in-crease in the concrete strength The maximum difference for thegiven beam geometry and concrete strengths was 1335
Comparison for Minimum Area of Shear Reinforcement Using ACI 31808 and BS 811097
Fig 8 was developed based on Eqs (5) and (6) for different values of f c9 which is taken as 08 f cu The beam cross-sectional dimension is3503 700 mm with effective depth of 625 mm The yield strengthof reinforcement was taken as 460 N=mm 2 It can be seen that theminimum area of shear reinforcement required by BS is larger thanrequired by ACI The BS curve is constant for all grades of concretewhereas theACI curveis constant forconcretegrades of 30ndash40 N=mm 2
then reduces linearly for grades larger than 40 N=mm 2 The dif-ference is constant at the value of 185 for the concrete strengths
between 30 and 40 N=mm 2 then decreases with the increase in theconcretestrength Theminimum difference forthegiven beamgeometryand concrete strengths was 67 at concrete grade of 50 N=mm 2
Concluding Remarks and Recommendations
In this research design results of rectangular RC beams subjected to
bending shear and torsion and punching shear at the slabndashcolumnconnection using ACI 31808 and BS 811097 were comparedConclusions can be drawn as follows
Design for Combined Bending Moment Twisting Moment and Shear Force
bull Therequired 1047298exural reinforcementsfor thesame designbendingmoment using ACI and BS codes are almostthe same regardlessof M u=V u ratio
bull In most cases the required shear reinforcement by ACI code islargerthan that by BS code forthesame design load This difference
Fig 5 Punching shear strength versus percentage of r using ACI and BS codes
Fig 6 Punching shear strength versus slab thickness using ACI and BS codes
PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013 221
becomes morepronounced with the increase of M u=V u ratio It wasfound that empirical equations of shear capacity in BS and ACIcodes have led to highlydifferent results It wasalso established that owing to differences in material safety factors ACI equations leadto more required shear reinforcement than BS
bull The beam length that needs shear reinforcement (beyond whichonly minimum shear reinforcement is needed) required by BS
code is shorter than that for ACI code The difference becomesmore pronounced with the increase of M u=V u ratio
bull The longitudinal and transverse torsional reinforcement requiredby ACI was found to be larger than that required by BS and thedifference in value betweenthe reinforcementof the two codesisalmost constant It was found that these differences are due todifferences in material safety factors
Impact of Safety Factors on Ultimate Design Load
bull The difference in the factor of safety for the dead load betweenthe ACI and BS resulted in larger design bending moments
and shear forces by the BS equations than the ACI ones Thediverging difference increases linearly with the increase of thedead load
bull For the resulting different design loads it wasfound that both thelongitudinal and transverse reinforcements required by the ACIare lower than the BS in all beams
bull For different column aspect ratios the punching shear strength of 1047298at slabndashcolumn connections calculated using the ACI code wasfound to be larger than that calculated using the BS code for thesame geometry materials and loading conditions
bull In the ACI code punching shear strength remains constant for different percentages of 1047298exural reinforcement whereas in theBS code punching shear strength increases with increase of 1047298exural reinforcement
bull For different slab thicknesses ACI code estimates more punch-ing shear strength than BS code
Fig 7 Minimum area of 1047298exural reinforcement with different f cu
Fig 8 Minimum area of shear reinforcement with different f cu
222 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
Acp 5 area enclosed by outside perimeter of concrete
cross section
Al 5 area of longitudinal reinforcement to resist torsion
Al min 5 minimum area of longitudinal reinforcement to
resist torsion
Ao 5 gross area enclosed by shear 1047298ow path
Aoh 5 area enclosed by centerline of the outermost closed
transverse torsional reinforcement
As 5 area of longitudinal tension reinforcement to resist
bending moment
Asmin 5 minimum area of 1047298exural reinforcement to resist
bending moment
Asv 5 area of shear reinforcement to resist shear
Asvt 5 area of two legs of stirrups required for torsion At 5 area of one leg of a closed stirrup resisting torsion
At min 5 minimum area of shear reinforcement to resist
torsion
a 5 depth of equivalent rectangular stress block
b 5 width of section 1047298ange
bw 5 width of section web
d 5 effective depth of tension reinforcement (distance
from extreme compression 1047297ber to centroid of
longitudinal tension reinforcement)
f 9c 5 characteristic cylinder compressive strength of
concrete (150 mm 3 300 mm)
f cu 5 characteristic strength of concrete
(1503
1503
150 mm concrete cube strength) f y 5 characteristic yield strength of longitudinal
reinforcement for 1047298exure
f yl 5 characteristic yield strength of longitudinal
reinforcement for torsion
f yv 5 characteristic yield strength of transverse
reinforcement
h 5 overall depth of section
hmax 5 larger dimension of rectangular cross section
hmin 5 smaller dimension of rectangular cross section
L 5 effective beam span
M u 5 ultimate 1047298exural moment
ph 5 perimeter of centerline of outermost closed
transverse torsional reinforcement
S 5 center-to-center spacing of transverse reinforcement
S v 5 spacing of stirrups
T cr 5 torsional cracking moment
T n 5 nominal torsional moment strength
T u 5 ultimate design twisting moment
V c 5 nominal shear strength provided by concrete
V u 5 ultimate shear force
v 5 design shear stress
vc 5 concrete shear strength
vt 5 torsional shear stress
vt min 5 minimum torsional shear stress above which
reinforcement is required
vtu 5 maximum combinedshear stress (shear plustorsion)
x 1 5 smaller center to center dimension of rectangular
stirrups y1 5 larger center to center dimension of rectangular
stirrups
Z 5 lever arm
g m 5 partial safety factor for strength of material
u 5 angle between axis of strut compression diagonal
and tension chord of the member
r 5 reinforcement ratio ( As=bd ) and
f 5 strength reduction factor
References
Alnuaimi A S and Bhatt P (2006) ldquo
Design of solid reinforced concretebeamsrdquo Structures Buildings 159(4) 197ndash216Ameli M and Ronagh H R (2007) ldquoTreatment of torsion of reinforced
concrete beams in current structural standardsrdquo Asian J Civil Eng
for structural concrete and commentaryrdquo 318-05 Farmington Hills
MIAmerican Concrete Institute (ACI) (2008) ldquoBuilding code requirements
for structural concrete and commentaryrdquo 318-08 Farmington Hills
MIBari MS(2000)ldquoPunching shear strength of slab-column connectionsmdashA
comparative study of different codesrdquo J Inst Engineers (India) 80(4)163ndash168
Bernardo L F A and Lopes S M R (2009) ldquoTorsion in high strengthconcrete hollow beamsmdashStrength and ductility analysisrdquo ACI Struc-
tural J 106(1) 39ndash48British Standards Institution(BSI) (1985)ldquoStructuraluse of concrete Code
of practice for special circumstancesrdquo BS 811085 Part-2 London
British Standards Institution(BSI) (1997)ldquoStructuraluse of concrete Codeof practice for design and constructionrdquo BS 811097 London
Chiu H J Fang I K Young W T and Shiau J K (2007) ldquoBehavior
of reinforced concrete beams with minimum torsional reinforcementrdquo Eng Structures 29(9) 2193ndash2205
Jung S and Kim KS (2008) ldquoKnowledge-based prediction on shear strength of concrete beams without shear reinforcementrdquo Eng Struc-
tures 30(6) 1515ndash1525Ngo D T (2001) ldquoPunching shear resistance of high-strength concrete
slabsrdquo Electron J Structural Eng 1(1) 2ndash14
Sharma A K and Innis B C (2006) ldquoPunching shear strength of slab-column connectionmdashA comparative study of different codesrdquo ASCE
Conf Proc Structural Engineering and Public Safety 2006 StructuresCongress ASCE Reston VA 1ndash11
Subramanian N (2005) ldquoEvaluation and enhancing the punching shear resistance of 1047298at slabs using high strength concreterdquo Indian Concr J79(4) 31ndash37
224 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
For section dimensions check in BS 8110ndash285ndash245 thecomputed torsional shear stress vt should not exceed the followinglimit for sections with larger center-to-center dimensions of closedlink less than 550 mm
vt vtu y1
550 (20)
In no case should the sum of the shear stresses resulting from shear force and torsion (vtu 5 vs 1 vt ) exceed the maximum shear stress
speci1047297
ed by Eq (8) If a combination of applied shear stress vs andtorsional stress vt exceeds this limit the section should be resized
Design Results and Discussions
Here design results of rectangular beams with different load com-binations and spandepth ratios are presented The ACI 31808 andBS 811097 codes were used in the design and results were judgedbased on the amount of longitudinal and transverse reinforcement requirements The characteristic cube compressive strength of con-crete was 30N=mm 2 and the cylinder compressive strength was24 N=mm 2 with concrete density of 24 kN=m 3 and the charac-teristic yield strength of the longitudinal and transverse reinforce-ment was 460 N=mm 2
Design for Combined Bending Moment and Shear Force Using ACI 31808 and BS 811097
Tables 1ndash3 and Table 4 show the design results of three groups of simply supported beams and one group of two-span continuousbeams respectively In beam numbering the 1047297rst letter denotes thetype of member considered eg B means beam the second letter denotes the variable eg R means spandepth ratio the third letter denotes thetype of loading eg W means uniformly distributedloadThe 1047297rst numeral represents the value of R and the second numeralrepresents the value of W The beam cross-sectional dimension was
selected to be 3503 700 mm with effective depth of 625 mm Dif-ferent ultimate design uniformly distributed load values were used asshownin the caption of each table It wasassumedthat 50 of bottom longitudinal bars are curtailed at 01 L from support and transversestirrups were used for shear reinforcement ie no bent-up barsconsidered to resist shear The spandepth ratio was varied among eachgroup resulting in different M u=V u ratios The design was carried out using the ACI and BS codes for the same ultimate design load values
It is clear that the two codes gave almost the same results for bendingreinforcement with minimal effect of M u=V u ratio changesgiving a maximum difference of 26 in the case of single-spansimply supported beams and 084 in the case of the continuousbeams However theresults differ largelyon theshear reinforcement with the change of M u=V u ratio using ACI and BS codes as can be
Table 1 Simply Supported Beams with Ultimate Design UDL of 75 kN=m
seen for a typical beam in Fig 1 The differences become pronouncedwith the increase of M u=V u ratio leading to continually divergingcurves In most cases it wasfound that theBS requires less transversereinforcement than the ACI For the given geometry and loads thedifferences reached up to 181 in thecaseof simplysupported beamsand 314 in the case of continuous beams Further the length from the face of support to the point beyond which only minimum shear reinforcement is required was also investigated andis presented in thepenultimate columns of Tables 1ndash4 It was found that the length that needs shear reinforcement required by BS is less than that required
by ACI The differences become more pronounced with increaseof M u=V u ratio For the given geometry and loads the differencesreached up to 1108 in the case of simply supported beams and1533 in the case of continuous beams This indicates that with theincrease of loads the BS code becomes more economical on thetransverse reinforcement
Table 5 shows comparisonbetween theACI and BS resultson theshear strength capacity of concrete using
vc frac14
016
ffiffiffiffi f c9
q thorn 17r
V ud
M u
029
ffiffiffiffi f c9
q
as extracted from Eq (3) in the case of ACI code and Eq (4) in thecase of BS code for different values of r ranging from 02 to 20
In the ACI the values of V ud = M u were varied from 0 to 10 and inthe case ofBS the value of 400=d wastaken as constant equal to 1 It is obvious that the above equations lead to highly different resultsInitially when reinforcement ratio r is 02 vc of BS is less by
about60 than that of ACI for all values of V ud = M uAsthe V ud = M uandor r increases the concrete shear capacity increases Fig 2shows that the nonlinear curve resulting from the BS equation crossesthe linearly diverging curves made by the ACI equation for variablevalues of V ud = M u at different points The1047297rst crossing point occurredat r 5 08 with V ud = M u 5 0 The succeeding crosses occurredsequentially with the increased V ud = M u curves It isalsoclear that theBS rate of increasein shear capacity is more rapid than that of the ACIAppendix II shows formulation of both ACI and BS code equationsfor required shear reinforcement to produce two similar equations with
differences in the empirical values It can be seen that even in the casewhen vc in ACI is equal to vc in BS as shown in the crosses of Fig 2the values of spacing between stirrups S as shown by the resultingequations in Appendix II will be different and the ACI code requiresapproximately 26 more shear reinforcement than the BS code Thisdifference is attributed to differences in material safety factors
Design for Torsion Using ACI 31808 and BS 811097
Here 5003 700-mm beams with effective depth of 625 mm weresubjected to pure twisting moment Table 6 shows the design resultsof 1047297xed beams subjected to ultimate design torsion using ACI andBS codes In beam numbering the 1047297rst letter denotes the type of member eg B means beam the second letter denotes the variable
eg L means span and the numeral gives the value of L It is clear thatthe requiredlongitudinalreinforcement by ACI is 192 larger than that required by BS for most of the beams (ie BL6 BL8 andBL10) Because BL4 needs minimum steel in the ACI approach this
Table 4 Two Span Continuous Beam with Ultimate Design UDL of 60 kN=m
beam was not considered in the comparison The transverse re-inforcement required by ACI is approximately 19 larger than that required by BS This shows that BS is more economical than ACI inthe case of design for torsion in RC rectangular solid beams
Appendix I shows a comparison between the ACI and BS torsionequations that lead to required transverse and longitudinal reinforce-ment It is clear that the area of the shear 1047298ow Aoh is taken as 085 x 1 y1
in ACI whereas in BS it is taken as 08 x 1 y1 Further owing to dif-ferences in material safety factors ACI required about 19 moretransverse torsional reinforcement than BS Regarding longitudinal
reinforcementthederivedEqs(2)and(4)inAppendix I look identical inboth codes but since longitudinal reinforcement is dependent on theamount of transverse reinforcement the same difference of 19 that was found above for transverse reinforcement is carried to longitudinalreinforcement
DesignforCombinedBendingMomentShearForceand Twisting Moment Using ACI 31808 and BS 811097
Tables 7 and 8 show the design results of longitudinal reinforcement fortwo groupsof 1047297xed end beams withdifferent uniformly distributedload values and torsional moment of 125 kNm =m as shown in thecaption of each table The beam size considered was 400 3 700mm
with effective depth of 625 mm and design results were calculatednearthe supportIn beam numbering the1047297rstletter denotes thetypeof member considered eg B meansbeamthe second letter denotes thevariable eg R means spandepth ratio the third letter denotes thetype of loading eg W means uniformly distributed load The 1047297rst numeral represents the value of R and the second numeral representsthevalue of W It is clear that therequired topreinforcementfor ACIislarger than that for BS with a maximum difference of 84 for thegiven loads and beam geometry The bottom and face reinforcement required by ACIis largerby about 193than that required by BSNo
major changes were found in the longitudinal reinforcementdue to theincrease of L =d or M u=T u ratios However the results differ largely onthe transverse reinforcementwith the change of V u=T u ratio using ACIand BScodes ascanbe seenin Fig 3ItcanbeseenthattheACIcurveis linear whereas the BS curve is nonlinear The differences becomepronounced with increase of V u=T u ratio leading to continually di-verging curves In most cases it was found that BS requires lesstransverse reinforcement than ACI For the given geometry and loadsthe difference reached up to 193
Impactof Load SafetyFactors on DesignLoad Using ACI 31808 and BS 811097
In this section simply supported RC beams of 200-3 700-mm
cross section 625-mm effective depth and 6-m effective span withuniformly distributedlive anddead loads weredesignedusingthe ACIandBS codesThe live load waskeptconstant at 5 kN=m for all beamswhile the dead load values were varied from 20 to 40 kN=m The liveload was kept constant because the factor of safety for the live load isthe same inboth ACI and BScodes ie 16 It was assumed that50of bottom bars are curtailedat 01 L from thecenter of supportTable9shows theeffects of theACI andBS code factors of safety on requiredreinforcement In the beam numbering the1047297rst letterdenotes the typeof member eg B means a beam the second letter denotes thevariable eg R is the ratio of dead load to live load (DLLL) and thenumeral gives the value of R It is clear that because of the different values of dead load factors of safety 12 in ACI and 14 in BS thedifferences in design bending moments and shear forces between
the results from ACI and BS are linearly increasing with the increaseof the dead load For the given service loads the factored (ultimate)
design load usingBS waslarger than that forACI having a maximum
difference of 143 As a result to these load differences therequiredlongitudinal and transverse reinforcements are differing with maxi-mum of 165 for bending and 600 for shear reinforcementsrespectively The results for the1047298exural reinforcement indicates slight
diversion due to the effect of increasing dead load while the requiredshear reinforcement shows convergence on the required transversereinforcement with the increase of the DLLL ratio Beams BR4 andBR5 required minimum stirrups in ACIand hence are notconsidered in
the discussion It is interesting to notice that as seen in Tables 1ndash4 for
the ultimate design loading the difference in 1047298exural reinforcement using ACIandBS is negligible Forservice loadinghowever shown inTable 9 the required 1047298exural reinforcement for BS was larger than for ACI with differences varying from 99 to 165 This difference isattributed to thedifferentload safetyfactors that areused in ACIandBSfor dead and live load combinations Similarly as seen in Tables 1ndash4for the ultimate design loading the shear reinforcement required by BSis less compared with ACI whereas for service loading (Table 9) theresultis reversed This reversal of resultis also attributed to thedifferent load safety factors used in ACI and BS codes for the dead load
Punching Shear Strength (at SlabndashColumn Connection) Using ACI 31808 and BS 811097
Here a parametric study of punching shear capacity at slabndashcolumnconnection using ACI and BS codes was carried out with different column aspect ratios percentagesof 1047298exural reinforcement and slabthicknesses The characteristic cube and cylindrical compressivestrengths were taken as 35 and 28 N=mm 2 respectively and thecharacteristic yield strength of reinforcementwas taken as 460N=mm 2
Table 6 Fixed Beams with Ultimate Design Torsion
Beam
number
Span
(m)
T u
(kNm)
Al
(mm 2)Difference
in Al ()
At =s
(mm 2=mm)Difference
in At =s ()ACI BS ACI BS
BL4 4 50 min 583 mdash 068 057 193
BL6 6 75 1043 875 192 102 086 186
BL8 8 100 1391 1167 192 136 114 193
BL10 10 125 1738 1458 192 17 143 189
Table 7 Fixed End Beams with Ultimate Design UDL of 100 kN=m and Torsion of 125kNm =m
From Eqs (4) and (7) it can be seen that unlike BS 8110 ACI 318does not consider dowel action of 1047298exural reinforcement in thecalculation of shear capacity Fig 4 shows punching shear strengthof a 250-mm-thick slab with effective depth of 220 mm at interior column having r 5 10 with column sizes of 3003 3003003 600 3003 900 and 3003 1200 mm resulting in different aspectratios usingACI andBS codesThe concrete cube compressivestrength f cu was 35 Nmm 2 with concrete cylinder compressivestrength as 08 f cu and steel yield strength of 460 N=mm 2 It can beseen that punching shearstrength forACI is larger than for BS for all
aspect ratios This means that for the same ultimate design punchingshear force ACI requires less slab thickness than BS The largest difference is368 when column aspect ratio is 2 It canalsobe seenthat in BS code punching shear strength increases linearly ascolumn aspect ratio increases whereas in ACI code the curve isnonlinear having a larger rate of increase of punching shear strengthbetween column aspect ratio of 1 and 2 than between 2 and 4 Fig 5shows punching shear strength of 250-mm-thick slab at interior columnof size 3003 300 mm with different percentages of 1047298exural re-inforcement ranging between 015 and 3 using ACI and BS codesThe material strengths and effective depths of slab were the same as inthe previous slab It can be seen that in ACI code the punching shear strength is constant at 773 kN without any effect of the percentage of 1047298exural reinforcement whereas in BS code punching shear strength
increases with increase of reinforcement TheBS curve is nonlinear and
it crosses the ACI horizontal line at r 5 17 This shows that with thegiven data untilr 5 17 ACI leads to largerpunching shear strengththan BS with the largest difference of 1314 when r 5 015
Fig 6 shows punching shear strengthof slabat interiorcolumnof size3003 300 mm with area of 1047298exural reinforcement As 5 2 050 mm 2
with varying depth The material strengths were the same as in theprevious slab The effective depth of each slab is 35 mm less than theoverall thickness It can be seen that ACIestimates more punchingshear strength than BS The differences with the given data ranged between148 and 233 Both ACI and BS curves vary linearly with increase of
depth however the rate ofincreaseinthe ACIresults ismorethan inBSleading to diverging curves This shows that the difference in V c usingboth codes increases as depth increases
Comparison for Minimum Area of Flexural Reinforcement Using ACI 31808 and BS 811097
The equations of minimum required 1047298exural reinforcement basedon the ACI and BS codes are shown in Appendix I Fig 7 was de-veloped based on those equations for different values of f c9 which istakenas08 f cu Thebeamcross-sectional dimension is 3503 700 mm with effective depth of 625 mm The yield strength of reinforcement was taken as 460 N=mm 2 It can be seen that the minimum area of 1047298exural reinforcement required by ACI is much larger than that re-
quired by BS The BS curve is constant with all grades of concrete
Table 9 Parametric Study to Compare Steel Required for Bending and Shear with DL 1 LL Combination Using ACI and BS
while the ACI curve changes from being constant for concretegrades of 30ndash40 N=mm 2 to nonlinear for concrete grades larger than40 N=mm 2 The difference is constant at the value of 106 for theconcrete strengths of 30ndash40 N=mm 2 then it increases with the in-crease in the concrete strength The maximum difference for thegiven beam geometry and concrete strengths was 1335
Comparison for Minimum Area of Shear Reinforcement Using ACI 31808 and BS 811097
Fig 8 was developed based on Eqs (5) and (6) for different values of f c9 which is taken as 08 f cu The beam cross-sectional dimension is3503 700 mm with effective depth of 625 mm The yield strengthof reinforcement was taken as 460 N=mm 2 It can be seen that theminimum area of shear reinforcement required by BS is larger thanrequired by ACI The BS curve is constant for all grades of concretewhereas theACI curveis constant forconcretegrades of 30ndash40 N=mm 2
then reduces linearly for grades larger than 40 N=mm 2 The dif-ference is constant at the value of 185 for the concrete strengths
between 30 and 40 N=mm 2 then decreases with the increase in theconcretestrength Theminimum difference forthegiven beamgeometryand concrete strengths was 67 at concrete grade of 50 N=mm 2
Concluding Remarks and Recommendations
In this research design results of rectangular RC beams subjected to
bending shear and torsion and punching shear at the slabndashcolumnconnection using ACI 31808 and BS 811097 were comparedConclusions can be drawn as follows
Design for Combined Bending Moment Twisting Moment and Shear Force
bull Therequired 1047298exural reinforcementsfor thesame designbendingmoment using ACI and BS codes are almostthe same regardlessof M u=V u ratio
bull In most cases the required shear reinforcement by ACI code islargerthan that by BS code forthesame design load This difference
Fig 5 Punching shear strength versus percentage of r using ACI and BS codes
Fig 6 Punching shear strength versus slab thickness using ACI and BS codes
PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013 221
becomes morepronounced with the increase of M u=V u ratio It wasfound that empirical equations of shear capacity in BS and ACIcodes have led to highlydifferent results It wasalso established that owing to differences in material safety factors ACI equations leadto more required shear reinforcement than BS
bull The beam length that needs shear reinforcement (beyond whichonly minimum shear reinforcement is needed) required by BS
code is shorter than that for ACI code The difference becomesmore pronounced with the increase of M u=V u ratio
bull The longitudinal and transverse torsional reinforcement requiredby ACI was found to be larger than that required by BS and thedifference in value betweenthe reinforcementof the two codesisalmost constant It was found that these differences are due todifferences in material safety factors
Impact of Safety Factors on Ultimate Design Load
bull The difference in the factor of safety for the dead load betweenthe ACI and BS resulted in larger design bending moments
and shear forces by the BS equations than the ACI ones Thediverging difference increases linearly with the increase of thedead load
bull For the resulting different design loads it wasfound that both thelongitudinal and transverse reinforcements required by the ACIare lower than the BS in all beams
bull For different column aspect ratios the punching shear strength of 1047298at slabndashcolumn connections calculated using the ACI code wasfound to be larger than that calculated using the BS code for thesame geometry materials and loading conditions
bull In the ACI code punching shear strength remains constant for different percentages of 1047298exural reinforcement whereas in theBS code punching shear strength increases with increase of 1047298exural reinforcement
bull For different slab thicknesses ACI code estimates more punch-ing shear strength than BS code
Fig 7 Minimum area of 1047298exural reinforcement with different f cu
Fig 8 Minimum area of shear reinforcement with different f cu
222 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
Acp 5 area enclosed by outside perimeter of concrete
cross section
Al 5 area of longitudinal reinforcement to resist torsion
Al min 5 minimum area of longitudinal reinforcement to
resist torsion
Ao 5 gross area enclosed by shear 1047298ow path
Aoh 5 area enclosed by centerline of the outermost closed
transverse torsional reinforcement
As 5 area of longitudinal tension reinforcement to resist
bending moment
Asmin 5 minimum area of 1047298exural reinforcement to resist
bending moment
Asv 5 area of shear reinforcement to resist shear
Asvt 5 area of two legs of stirrups required for torsion At 5 area of one leg of a closed stirrup resisting torsion
At min 5 minimum area of shear reinforcement to resist
torsion
a 5 depth of equivalent rectangular stress block
b 5 width of section 1047298ange
bw 5 width of section web
d 5 effective depth of tension reinforcement (distance
from extreme compression 1047297ber to centroid of
longitudinal tension reinforcement)
f 9c 5 characteristic cylinder compressive strength of
concrete (150 mm 3 300 mm)
f cu 5 characteristic strength of concrete
(1503
1503
150 mm concrete cube strength) f y 5 characteristic yield strength of longitudinal
reinforcement for 1047298exure
f yl 5 characteristic yield strength of longitudinal
reinforcement for torsion
f yv 5 characteristic yield strength of transverse
reinforcement
h 5 overall depth of section
hmax 5 larger dimension of rectangular cross section
hmin 5 smaller dimension of rectangular cross section
L 5 effective beam span
M u 5 ultimate 1047298exural moment
ph 5 perimeter of centerline of outermost closed
transverse torsional reinforcement
S 5 center-to-center spacing of transverse reinforcement
S v 5 spacing of stirrups
T cr 5 torsional cracking moment
T n 5 nominal torsional moment strength
T u 5 ultimate design twisting moment
V c 5 nominal shear strength provided by concrete
V u 5 ultimate shear force
v 5 design shear stress
vc 5 concrete shear strength
vt 5 torsional shear stress
vt min 5 minimum torsional shear stress above which
reinforcement is required
vtu 5 maximum combinedshear stress (shear plustorsion)
x 1 5 smaller center to center dimension of rectangular
stirrups y1 5 larger center to center dimension of rectangular
stirrups
Z 5 lever arm
g m 5 partial safety factor for strength of material
u 5 angle between axis of strut compression diagonal
and tension chord of the member
r 5 reinforcement ratio ( As=bd ) and
f 5 strength reduction factor
References
Alnuaimi A S and Bhatt P (2006) ldquo
Design of solid reinforced concretebeamsrdquo Structures Buildings 159(4) 197ndash216Ameli M and Ronagh H R (2007) ldquoTreatment of torsion of reinforced
concrete beams in current structural standardsrdquo Asian J Civil Eng
for structural concrete and commentaryrdquo 318-05 Farmington Hills
MIAmerican Concrete Institute (ACI) (2008) ldquoBuilding code requirements
for structural concrete and commentaryrdquo 318-08 Farmington Hills
MIBari MS(2000)ldquoPunching shear strength of slab-column connectionsmdashA
comparative study of different codesrdquo J Inst Engineers (India) 80(4)163ndash168
Bernardo L F A and Lopes S M R (2009) ldquoTorsion in high strengthconcrete hollow beamsmdashStrength and ductility analysisrdquo ACI Struc-
tural J 106(1) 39ndash48British Standards Institution(BSI) (1985)ldquoStructuraluse of concrete Code
of practice for special circumstancesrdquo BS 811085 Part-2 London
British Standards Institution(BSI) (1997)ldquoStructuraluse of concrete Codeof practice for design and constructionrdquo BS 811097 London
Chiu H J Fang I K Young W T and Shiau J K (2007) ldquoBehavior
of reinforced concrete beams with minimum torsional reinforcementrdquo Eng Structures 29(9) 2193ndash2205
Jung S and Kim KS (2008) ldquoKnowledge-based prediction on shear strength of concrete beams without shear reinforcementrdquo Eng Struc-
tures 30(6) 1515ndash1525Ngo D T (2001) ldquoPunching shear resistance of high-strength concrete
slabsrdquo Electron J Structural Eng 1(1) 2ndash14
Sharma A K and Innis B C (2006) ldquoPunching shear strength of slab-column connectionmdashA comparative study of different codesrdquo ASCE
Conf Proc Structural Engineering and Public Safety 2006 StructuresCongress ASCE Reston VA 1ndash11
Subramanian N (2005) ldquoEvaluation and enhancing the punching shear resistance of 1047298at slabs using high strength concreterdquo Indian Concr J79(4) 31ndash37
224 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
seen for a typical beam in Fig 1 The differences become pronouncedwith the increase of M u=V u ratio leading to continually divergingcurves In most cases it wasfound that theBS requires less transversereinforcement than the ACI For the given geometry and loads thedifferences reached up to 181 in thecaseof simplysupported beamsand 314 in the case of continuous beams Further the length from the face of support to the point beyond which only minimum shear reinforcement is required was also investigated andis presented in thepenultimate columns of Tables 1ndash4 It was found that the length that needs shear reinforcement required by BS is less than that required
by ACI The differences become more pronounced with increaseof M u=V u ratio For the given geometry and loads the differencesreached up to 1108 in the case of simply supported beams and1533 in the case of continuous beams This indicates that with theincrease of loads the BS code becomes more economical on thetransverse reinforcement
Table 5 shows comparisonbetween theACI and BS resultson theshear strength capacity of concrete using
vc frac14
016
ffiffiffiffi f c9
q thorn 17r
V ud
M u
029
ffiffiffiffi f c9
q
as extracted from Eq (3) in the case of ACI code and Eq (4) in thecase of BS code for different values of r ranging from 02 to 20
In the ACI the values of V ud = M u were varied from 0 to 10 and inthe case ofBS the value of 400=d wastaken as constant equal to 1 It is obvious that the above equations lead to highly different resultsInitially when reinforcement ratio r is 02 vc of BS is less by
about60 than that of ACI for all values of V ud = M uAsthe V ud = M uandor r increases the concrete shear capacity increases Fig 2shows that the nonlinear curve resulting from the BS equation crossesthe linearly diverging curves made by the ACI equation for variablevalues of V ud = M u at different points The1047297rst crossing point occurredat r 5 08 with V ud = M u 5 0 The succeeding crosses occurredsequentially with the increased V ud = M u curves It isalsoclear that theBS rate of increasein shear capacity is more rapid than that of the ACIAppendix II shows formulation of both ACI and BS code equationsfor required shear reinforcement to produce two similar equations with
differences in the empirical values It can be seen that even in the casewhen vc in ACI is equal to vc in BS as shown in the crosses of Fig 2the values of spacing between stirrups S as shown by the resultingequations in Appendix II will be different and the ACI code requiresapproximately 26 more shear reinforcement than the BS code Thisdifference is attributed to differences in material safety factors
Design for Torsion Using ACI 31808 and BS 811097
Here 5003 700-mm beams with effective depth of 625 mm weresubjected to pure twisting moment Table 6 shows the design resultsof 1047297xed beams subjected to ultimate design torsion using ACI andBS codes In beam numbering the 1047297rst letter denotes the type of member eg B means beam the second letter denotes the variable
eg L means span and the numeral gives the value of L It is clear thatthe requiredlongitudinalreinforcement by ACI is 192 larger than that required by BS for most of the beams (ie BL6 BL8 andBL10) Because BL4 needs minimum steel in the ACI approach this
Table 4 Two Span Continuous Beam with Ultimate Design UDL of 60 kN=m
beam was not considered in the comparison The transverse re-inforcement required by ACI is approximately 19 larger than that required by BS This shows that BS is more economical than ACI inthe case of design for torsion in RC rectangular solid beams
Appendix I shows a comparison between the ACI and BS torsionequations that lead to required transverse and longitudinal reinforce-ment It is clear that the area of the shear 1047298ow Aoh is taken as 085 x 1 y1
in ACI whereas in BS it is taken as 08 x 1 y1 Further owing to dif-ferences in material safety factors ACI required about 19 moretransverse torsional reinforcement than BS Regarding longitudinal
reinforcementthederivedEqs(2)and(4)inAppendix I look identical inboth codes but since longitudinal reinforcement is dependent on theamount of transverse reinforcement the same difference of 19 that was found above for transverse reinforcement is carried to longitudinalreinforcement
DesignforCombinedBendingMomentShearForceand Twisting Moment Using ACI 31808 and BS 811097
Tables 7 and 8 show the design results of longitudinal reinforcement fortwo groupsof 1047297xed end beams withdifferent uniformly distributedload values and torsional moment of 125 kNm =m as shown in thecaption of each table The beam size considered was 400 3 700mm
with effective depth of 625 mm and design results were calculatednearthe supportIn beam numbering the1047297rstletter denotes thetypeof member considered eg B meansbeamthe second letter denotes thevariable eg R means spandepth ratio the third letter denotes thetype of loading eg W means uniformly distributed load The 1047297rst numeral represents the value of R and the second numeral representsthevalue of W It is clear that therequired topreinforcementfor ACIislarger than that for BS with a maximum difference of 84 for thegiven loads and beam geometry The bottom and face reinforcement required by ACIis largerby about 193than that required by BSNo
major changes were found in the longitudinal reinforcementdue to theincrease of L =d or M u=T u ratios However the results differ largely onthe transverse reinforcementwith the change of V u=T u ratio using ACIand BScodes ascanbe seenin Fig 3ItcanbeseenthattheACIcurveis linear whereas the BS curve is nonlinear The differences becomepronounced with increase of V u=T u ratio leading to continually di-verging curves In most cases it was found that BS requires lesstransverse reinforcement than ACI For the given geometry and loadsthe difference reached up to 193
Impactof Load SafetyFactors on DesignLoad Using ACI 31808 and BS 811097
In this section simply supported RC beams of 200-3 700-mm
cross section 625-mm effective depth and 6-m effective span withuniformly distributedlive anddead loads weredesignedusingthe ACIandBS codesThe live load waskeptconstant at 5 kN=m for all beamswhile the dead load values were varied from 20 to 40 kN=m The liveload was kept constant because the factor of safety for the live load isthe same inboth ACI and BScodes ie 16 It was assumed that50of bottom bars are curtailedat 01 L from thecenter of supportTable9shows theeffects of theACI andBS code factors of safety on requiredreinforcement In the beam numbering the1047297rst letterdenotes the typeof member eg B means a beam the second letter denotes thevariable eg R is the ratio of dead load to live load (DLLL) and thenumeral gives the value of R It is clear that because of the different values of dead load factors of safety 12 in ACI and 14 in BS thedifferences in design bending moments and shear forces between
the results from ACI and BS are linearly increasing with the increaseof the dead load For the given service loads the factored (ultimate)
design load usingBS waslarger than that forACI having a maximum
difference of 143 As a result to these load differences therequiredlongitudinal and transverse reinforcements are differing with maxi-mum of 165 for bending and 600 for shear reinforcementsrespectively The results for the1047298exural reinforcement indicates slight
diversion due to the effect of increasing dead load while the requiredshear reinforcement shows convergence on the required transversereinforcement with the increase of the DLLL ratio Beams BR4 andBR5 required minimum stirrups in ACIand hence are notconsidered in
the discussion It is interesting to notice that as seen in Tables 1ndash4 for
the ultimate design loading the difference in 1047298exural reinforcement using ACIandBS is negligible Forservice loadinghowever shown inTable 9 the required 1047298exural reinforcement for BS was larger than for ACI with differences varying from 99 to 165 This difference isattributed to thedifferentload safetyfactors that areused in ACIandBSfor dead and live load combinations Similarly as seen in Tables 1ndash4for the ultimate design loading the shear reinforcement required by BSis less compared with ACI whereas for service loading (Table 9) theresultis reversed This reversal of resultis also attributed to thedifferent load safety factors used in ACI and BS codes for the dead load
Punching Shear Strength (at SlabndashColumn Connection) Using ACI 31808 and BS 811097
Here a parametric study of punching shear capacity at slabndashcolumnconnection using ACI and BS codes was carried out with different column aspect ratios percentagesof 1047298exural reinforcement and slabthicknesses The characteristic cube and cylindrical compressivestrengths were taken as 35 and 28 N=mm 2 respectively and thecharacteristic yield strength of reinforcementwas taken as 460N=mm 2
Table 6 Fixed Beams with Ultimate Design Torsion
Beam
number
Span
(m)
T u
(kNm)
Al
(mm 2)Difference
in Al ()
At =s
(mm 2=mm)Difference
in At =s ()ACI BS ACI BS
BL4 4 50 min 583 mdash 068 057 193
BL6 6 75 1043 875 192 102 086 186
BL8 8 100 1391 1167 192 136 114 193
BL10 10 125 1738 1458 192 17 143 189
Table 7 Fixed End Beams with Ultimate Design UDL of 100 kN=m and Torsion of 125kNm =m
From Eqs (4) and (7) it can be seen that unlike BS 8110 ACI 318does not consider dowel action of 1047298exural reinforcement in thecalculation of shear capacity Fig 4 shows punching shear strengthof a 250-mm-thick slab with effective depth of 220 mm at interior column having r 5 10 with column sizes of 3003 3003003 600 3003 900 and 3003 1200 mm resulting in different aspectratios usingACI andBS codesThe concrete cube compressivestrength f cu was 35 Nmm 2 with concrete cylinder compressivestrength as 08 f cu and steel yield strength of 460 N=mm 2 It can beseen that punching shearstrength forACI is larger than for BS for all
aspect ratios This means that for the same ultimate design punchingshear force ACI requires less slab thickness than BS The largest difference is368 when column aspect ratio is 2 It canalsobe seenthat in BS code punching shear strength increases linearly ascolumn aspect ratio increases whereas in ACI code the curve isnonlinear having a larger rate of increase of punching shear strengthbetween column aspect ratio of 1 and 2 than between 2 and 4 Fig 5shows punching shear strength of 250-mm-thick slab at interior columnof size 3003 300 mm with different percentages of 1047298exural re-inforcement ranging between 015 and 3 using ACI and BS codesThe material strengths and effective depths of slab were the same as inthe previous slab It can be seen that in ACI code the punching shear strength is constant at 773 kN without any effect of the percentage of 1047298exural reinforcement whereas in BS code punching shear strength
increases with increase of reinforcement TheBS curve is nonlinear and
it crosses the ACI horizontal line at r 5 17 This shows that with thegiven data untilr 5 17 ACI leads to largerpunching shear strengththan BS with the largest difference of 1314 when r 5 015
Fig 6 shows punching shear strengthof slabat interiorcolumnof size3003 300 mm with area of 1047298exural reinforcement As 5 2 050 mm 2
with varying depth The material strengths were the same as in theprevious slab The effective depth of each slab is 35 mm less than theoverall thickness It can be seen that ACIestimates more punchingshear strength than BS The differences with the given data ranged between148 and 233 Both ACI and BS curves vary linearly with increase of
depth however the rate ofincreaseinthe ACIresults ismorethan inBSleading to diverging curves This shows that the difference in V c usingboth codes increases as depth increases
Comparison for Minimum Area of Flexural Reinforcement Using ACI 31808 and BS 811097
The equations of minimum required 1047298exural reinforcement basedon the ACI and BS codes are shown in Appendix I Fig 7 was de-veloped based on those equations for different values of f c9 which istakenas08 f cu Thebeamcross-sectional dimension is 3503 700 mm with effective depth of 625 mm The yield strength of reinforcement was taken as 460 N=mm 2 It can be seen that the minimum area of 1047298exural reinforcement required by ACI is much larger than that re-
quired by BS The BS curve is constant with all grades of concrete
Table 9 Parametric Study to Compare Steel Required for Bending and Shear with DL 1 LL Combination Using ACI and BS
while the ACI curve changes from being constant for concretegrades of 30ndash40 N=mm 2 to nonlinear for concrete grades larger than40 N=mm 2 The difference is constant at the value of 106 for theconcrete strengths of 30ndash40 N=mm 2 then it increases with the in-crease in the concrete strength The maximum difference for thegiven beam geometry and concrete strengths was 1335
Comparison for Minimum Area of Shear Reinforcement Using ACI 31808 and BS 811097
Fig 8 was developed based on Eqs (5) and (6) for different values of f c9 which is taken as 08 f cu The beam cross-sectional dimension is3503 700 mm with effective depth of 625 mm The yield strengthof reinforcement was taken as 460 N=mm 2 It can be seen that theminimum area of shear reinforcement required by BS is larger thanrequired by ACI The BS curve is constant for all grades of concretewhereas theACI curveis constant forconcretegrades of 30ndash40 N=mm 2
then reduces linearly for grades larger than 40 N=mm 2 The dif-ference is constant at the value of 185 for the concrete strengths
between 30 and 40 N=mm 2 then decreases with the increase in theconcretestrength Theminimum difference forthegiven beamgeometryand concrete strengths was 67 at concrete grade of 50 N=mm 2
Concluding Remarks and Recommendations
In this research design results of rectangular RC beams subjected to
bending shear and torsion and punching shear at the slabndashcolumnconnection using ACI 31808 and BS 811097 were comparedConclusions can be drawn as follows
Design for Combined Bending Moment Twisting Moment and Shear Force
bull Therequired 1047298exural reinforcementsfor thesame designbendingmoment using ACI and BS codes are almostthe same regardlessof M u=V u ratio
bull In most cases the required shear reinforcement by ACI code islargerthan that by BS code forthesame design load This difference
Fig 5 Punching shear strength versus percentage of r using ACI and BS codes
Fig 6 Punching shear strength versus slab thickness using ACI and BS codes
PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013 221
becomes morepronounced with the increase of M u=V u ratio It wasfound that empirical equations of shear capacity in BS and ACIcodes have led to highlydifferent results It wasalso established that owing to differences in material safety factors ACI equations leadto more required shear reinforcement than BS
bull The beam length that needs shear reinforcement (beyond whichonly minimum shear reinforcement is needed) required by BS
code is shorter than that for ACI code The difference becomesmore pronounced with the increase of M u=V u ratio
bull The longitudinal and transverse torsional reinforcement requiredby ACI was found to be larger than that required by BS and thedifference in value betweenthe reinforcementof the two codesisalmost constant It was found that these differences are due todifferences in material safety factors
Impact of Safety Factors on Ultimate Design Load
bull The difference in the factor of safety for the dead load betweenthe ACI and BS resulted in larger design bending moments
and shear forces by the BS equations than the ACI ones Thediverging difference increases linearly with the increase of thedead load
bull For the resulting different design loads it wasfound that both thelongitudinal and transverse reinforcements required by the ACIare lower than the BS in all beams
bull For different column aspect ratios the punching shear strength of 1047298at slabndashcolumn connections calculated using the ACI code wasfound to be larger than that calculated using the BS code for thesame geometry materials and loading conditions
bull In the ACI code punching shear strength remains constant for different percentages of 1047298exural reinforcement whereas in theBS code punching shear strength increases with increase of 1047298exural reinforcement
bull For different slab thicknesses ACI code estimates more punch-ing shear strength than BS code
Fig 7 Minimum area of 1047298exural reinforcement with different f cu
Fig 8 Minimum area of shear reinforcement with different f cu
222 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
Acp 5 area enclosed by outside perimeter of concrete
cross section
Al 5 area of longitudinal reinforcement to resist torsion
Al min 5 minimum area of longitudinal reinforcement to
resist torsion
Ao 5 gross area enclosed by shear 1047298ow path
Aoh 5 area enclosed by centerline of the outermost closed
transverse torsional reinforcement
As 5 area of longitudinal tension reinforcement to resist
bending moment
Asmin 5 minimum area of 1047298exural reinforcement to resist
bending moment
Asv 5 area of shear reinforcement to resist shear
Asvt 5 area of two legs of stirrups required for torsion At 5 area of one leg of a closed stirrup resisting torsion
At min 5 minimum area of shear reinforcement to resist
torsion
a 5 depth of equivalent rectangular stress block
b 5 width of section 1047298ange
bw 5 width of section web
d 5 effective depth of tension reinforcement (distance
from extreme compression 1047297ber to centroid of
longitudinal tension reinforcement)
f 9c 5 characteristic cylinder compressive strength of
concrete (150 mm 3 300 mm)
f cu 5 characteristic strength of concrete
(1503
1503
150 mm concrete cube strength) f y 5 characteristic yield strength of longitudinal
reinforcement for 1047298exure
f yl 5 characteristic yield strength of longitudinal
reinforcement for torsion
f yv 5 characteristic yield strength of transverse
reinforcement
h 5 overall depth of section
hmax 5 larger dimension of rectangular cross section
hmin 5 smaller dimension of rectangular cross section
L 5 effective beam span
M u 5 ultimate 1047298exural moment
ph 5 perimeter of centerline of outermost closed
transverse torsional reinforcement
S 5 center-to-center spacing of transverse reinforcement
S v 5 spacing of stirrups
T cr 5 torsional cracking moment
T n 5 nominal torsional moment strength
T u 5 ultimate design twisting moment
V c 5 nominal shear strength provided by concrete
V u 5 ultimate shear force
v 5 design shear stress
vc 5 concrete shear strength
vt 5 torsional shear stress
vt min 5 minimum torsional shear stress above which
reinforcement is required
vtu 5 maximum combinedshear stress (shear plustorsion)
x 1 5 smaller center to center dimension of rectangular
stirrups y1 5 larger center to center dimension of rectangular
stirrups
Z 5 lever arm
g m 5 partial safety factor for strength of material
u 5 angle between axis of strut compression diagonal
and tension chord of the member
r 5 reinforcement ratio ( As=bd ) and
f 5 strength reduction factor
References
Alnuaimi A S and Bhatt P (2006) ldquo
Design of solid reinforced concretebeamsrdquo Structures Buildings 159(4) 197ndash216Ameli M and Ronagh H R (2007) ldquoTreatment of torsion of reinforced
concrete beams in current structural standardsrdquo Asian J Civil Eng
for structural concrete and commentaryrdquo 318-05 Farmington Hills
MIAmerican Concrete Institute (ACI) (2008) ldquoBuilding code requirements
for structural concrete and commentaryrdquo 318-08 Farmington Hills
MIBari MS(2000)ldquoPunching shear strength of slab-column connectionsmdashA
comparative study of different codesrdquo J Inst Engineers (India) 80(4)163ndash168
Bernardo L F A and Lopes S M R (2009) ldquoTorsion in high strengthconcrete hollow beamsmdashStrength and ductility analysisrdquo ACI Struc-
tural J 106(1) 39ndash48British Standards Institution(BSI) (1985)ldquoStructuraluse of concrete Code
of practice for special circumstancesrdquo BS 811085 Part-2 London
British Standards Institution(BSI) (1997)ldquoStructuraluse of concrete Codeof practice for design and constructionrdquo BS 811097 London
Chiu H J Fang I K Young W T and Shiau J K (2007) ldquoBehavior
of reinforced concrete beams with minimum torsional reinforcementrdquo Eng Structures 29(9) 2193ndash2205
Jung S and Kim KS (2008) ldquoKnowledge-based prediction on shear strength of concrete beams without shear reinforcementrdquo Eng Struc-
tures 30(6) 1515ndash1525Ngo D T (2001) ldquoPunching shear resistance of high-strength concrete
slabsrdquo Electron J Structural Eng 1(1) 2ndash14
Sharma A K and Innis B C (2006) ldquoPunching shear strength of slab-column connectionmdashA comparative study of different codesrdquo ASCE
Conf Proc Structural Engineering and Public Safety 2006 StructuresCongress ASCE Reston VA 1ndash11
Subramanian N (2005) ldquoEvaluation and enhancing the punching shear resistance of 1047298at slabs using high strength concreterdquo Indian Concr J79(4) 31ndash37
224 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
beam was not considered in the comparison The transverse re-inforcement required by ACI is approximately 19 larger than that required by BS This shows that BS is more economical than ACI inthe case of design for torsion in RC rectangular solid beams
Appendix I shows a comparison between the ACI and BS torsionequations that lead to required transverse and longitudinal reinforce-ment It is clear that the area of the shear 1047298ow Aoh is taken as 085 x 1 y1
in ACI whereas in BS it is taken as 08 x 1 y1 Further owing to dif-ferences in material safety factors ACI required about 19 moretransverse torsional reinforcement than BS Regarding longitudinal
reinforcementthederivedEqs(2)and(4)inAppendix I look identical inboth codes but since longitudinal reinforcement is dependent on theamount of transverse reinforcement the same difference of 19 that was found above for transverse reinforcement is carried to longitudinalreinforcement
DesignforCombinedBendingMomentShearForceand Twisting Moment Using ACI 31808 and BS 811097
Tables 7 and 8 show the design results of longitudinal reinforcement fortwo groupsof 1047297xed end beams withdifferent uniformly distributedload values and torsional moment of 125 kNm =m as shown in thecaption of each table The beam size considered was 400 3 700mm
with effective depth of 625 mm and design results were calculatednearthe supportIn beam numbering the1047297rstletter denotes thetypeof member considered eg B meansbeamthe second letter denotes thevariable eg R means spandepth ratio the third letter denotes thetype of loading eg W means uniformly distributed load The 1047297rst numeral represents the value of R and the second numeral representsthevalue of W It is clear that therequired topreinforcementfor ACIislarger than that for BS with a maximum difference of 84 for thegiven loads and beam geometry The bottom and face reinforcement required by ACIis largerby about 193than that required by BSNo
major changes were found in the longitudinal reinforcementdue to theincrease of L =d or M u=T u ratios However the results differ largely onthe transverse reinforcementwith the change of V u=T u ratio using ACIand BScodes ascanbe seenin Fig 3ItcanbeseenthattheACIcurveis linear whereas the BS curve is nonlinear The differences becomepronounced with increase of V u=T u ratio leading to continually di-verging curves In most cases it was found that BS requires lesstransverse reinforcement than ACI For the given geometry and loadsthe difference reached up to 193
Impactof Load SafetyFactors on DesignLoad Using ACI 31808 and BS 811097
In this section simply supported RC beams of 200-3 700-mm
cross section 625-mm effective depth and 6-m effective span withuniformly distributedlive anddead loads weredesignedusingthe ACIandBS codesThe live load waskeptconstant at 5 kN=m for all beamswhile the dead load values were varied from 20 to 40 kN=m The liveload was kept constant because the factor of safety for the live load isthe same inboth ACI and BScodes ie 16 It was assumed that50of bottom bars are curtailedat 01 L from thecenter of supportTable9shows theeffects of theACI andBS code factors of safety on requiredreinforcement In the beam numbering the1047297rst letterdenotes the typeof member eg B means a beam the second letter denotes thevariable eg R is the ratio of dead load to live load (DLLL) and thenumeral gives the value of R It is clear that because of the different values of dead load factors of safety 12 in ACI and 14 in BS thedifferences in design bending moments and shear forces between
the results from ACI and BS are linearly increasing with the increaseof the dead load For the given service loads the factored (ultimate)
design load usingBS waslarger than that forACI having a maximum
difference of 143 As a result to these load differences therequiredlongitudinal and transverse reinforcements are differing with maxi-mum of 165 for bending and 600 for shear reinforcementsrespectively The results for the1047298exural reinforcement indicates slight
diversion due to the effect of increasing dead load while the requiredshear reinforcement shows convergence on the required transversereinforcement with the increase of the DLLL ratio Beams BR4 andBR5 required minimum stirrups in ACIand hence are notconsidered in
the discussion It is interesting to notice that as seen in Tables 1ndash4 for
the ultimate design loading the difference in 1047298exural reinforcement using ACIandBS is negligible Forservice loadinghowever shown inTable 9 the required 1047298exural reinforcement for BS was larger than for ACI with differences varying from 99 to 165 This difference isattributed to thedifferentload safetyfactors that areused in ACIandBSfor dead and live load combinations Similarly as seen in Tables 1ndash4for the ultimate design loading the shear reinforcement required by BSis less compared with ACI whereas for service loading (Table 9) theresultis reversed This reversal of resultis also attributed to thedifferent load safety factors used in ACI and BS codes for the dead load
Punching Shear Strength (at SlabndashColumn Connection) Using ACI 31808 and BS 811097
Here a parametric study of punching shear capacity at slabndashcolumnconnection using ACI and BS codes was carried out with different column aspect ratios percentagesof 1047298exural reinforcement and slabthicknesses The characteristic cube and cylindrical compressivestrengths were taken as 35 and 28 N=mm 2 respectively and thecharacteristic yield strength of reinforcementwas taken as 460N=mm 2
Table 6 Fixed Beams with Ultimate Design Torsion
Beam
number
Span
(m)
T u
(kNm)
Al
(mm 2)Difference
in Al ()
At =s
(mm 2=mm)Difference
in At =s ()ACI BS ACI BS
BL4 4 50 min 583 mdash 068 057 193
BL6 6 75 1043 875 192 102 086 186
BL8 8 100 1391 1167 192 136 114 193
BL10 10 125 1738 1458 192 17 143 189
Table 7 Fixed End Beams with Ultimate Design UDL of 100 kN=m and Torsion of 125kNm =m
From Eqs (4) and (7) it can be seen that unlike BS 8110 ACI 318does not consider dowel action of 1047298exural reinforcement in thecalculation of shear capacity Fig 4 shows punching shear strengthof a 250-mm-thick slab with effective depth of 220 mm at interior column having r 5 10 with column sizes of 3003 3003003 600 3003 900 and 3003 1200 mm resulting in different aspectratios usingACI andBS codesThe concrete cube compressivestrength f cu was 35 Nmm 2 with concrete cylinder compressivestrength as 08 f cu and steel yield strength of 460 N=mm 2 It can beseen that punching shearstrength forACI is larger than for BS for all
aspect ratios This means that for the same ultimate design punchingshear force ACI requires less slab thickness than BS The largest difference is368 when column aspect ratio is 2 It canalsobe seenthat in BS code punching shear strength increases linearly ascolumn aspect ratio increases whereas in ACI code the curve isnonlinear having a larger rate of increase of punching shear strengthbetween column aspect ratio of 1 and 2 than between 2 and 4 Fig 5shows punching shear strength of 250-mm-thick slab at interior columnof size 3003 300 mm with different percentages of 1047298exural re-inforcement ranging between 015 and 3 using ACI and BS codesThe material strengths and effective depths of slab were the same as inthe previous slab It can be seen that in ACI code the punching shear strength is constant at 773 kN without any effect of the percentage of 1047298exural reinforcement whereas in BS code punching shear strength
increases with increase of reinforcement TheBS curve is nonlinear and
it crosses the ACI horizontal line at r 5 17 This shows that with thegiven data untilr 5 17 ACI leads to largerpunching shear strengththan BS with the largest difference of 1314 when r 5 015
Fig 6 shows punching shear strengthof slabat interiorcolumnof size3003 300 mm with area of 1047298exural reinforcement As 5 2 050 mm 2
with varying depth The material strengths were the same as in theprevious slab The effective depth of each slab is 35 mm less than theoverall thickness It can be seen that ACIestimates more punchingshear strength than BS The differences with the given data ranged between148 and 233 Both ACI and BS curves vary linearly with increase of
depth however the rate ofincreaseinthe ACIresults ismorethan inBSleading to diverging curves This shows that the difference in V c usingboth codes increases as depth increases
Comparison for Minimum Area of Flexural Reinforcement Using ACI 31808 and BS 811097
The equations of minimum required 1047298exural reinforcement basedon the ACI and BS codes are shown in Appendix I Fig 7 was de-veloped based on those equations for different values of f c9 which istakenas08 f cu Thebeamcross-sectional dimension is 3503 700 mm with effective depth of 625 mm The yield strength of reinforcement was taken as 460 N=mm 2 It can be seen that the minimum area of 1047298exural reinforcement required by ACI is much larger than that re-
quired by BS The BS curve is constant with all grades of concrete
Table 9 Parametric Study to Compare Steel Required for Bending and Shear with DL 1 LL Combination Using ACI and BS
while the ACI curve changes from being constant for concretegrades of 30ndash40 N=mm 2 to nonlinear for concrete grades larger than40 N=mm 2 The difference is constant at the value of 106 for theconcrete strengths of 30ndash40 N=mm 2 then it increases with the in-crease in the concrete strength The maximum difference for thegiven beam geometry and concrete strengths was 1335
Comparison for Minimum Area of Shear Reinforcement Using ACI 31808 and BS 811097
Fig 8 was developed based on Eqs (5) and (6) for different values of f c9 which is taken as 08 f cu The beam cross-sectional dimension is3503 700 mm with effective depth of 625 mm The yield strengthof reinforcement was taken as 460 N=mm 2 It can be seen that theminimum area of shear reinforcement required by BS is larger thanrequired by ACI The BS curve is constant for all grades of concretewhereas theACI curveis constant forconcretegrades of 30ndash40 N=mm 2
then reduces linearly for grades larger than 40 N=mm 2 The dif-ference is constant at the value of 185 for the concrete strengths
between 30 and 40 N=mm 2 then decreases with the increase in theconcretestrength Theminimum difference forthegiven beamgeometryand concrete strengths was 67 at concrete grade of 50 N=mm 2
Concluding Remarks and Recommendations
In this research design results of rectangular RC beams subjected to
bending shear and torsion and punching shear at the slabndashcolumnconnection using ACI 31808 and BS 811097 were comparedConclusions can be drawn as follows
Design for Combined Bending Moment Twisting Moment and Shear Force
bull Therequired 1047298exural reinforcementsfor thesame designbendingmoment using ACI and BS codes are almostthe same regardlessof M u=V u ratio
bull In most cases the required shear reinforcement by ACI code islargerthan that by BS code forthesame design load This difference
Fig 5 Punching shear strength versus percentage of r using ACI and BS codes
Fig 6 Punching shear strength versus slab thickness using ACI and BS codes
PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013 221
becomes morepronounced with the increase of M u=V u ratio It wasfound that empirical equations of shear capacity in BS and ACIcodes have led to highlydifferent results It wasalso established that owing to differences in material safety factors ACI equations leadto more required shear reinforcement than BS
bull The beam length that needs shear reinforcement (beyond whichonly minimum shear reinforcement is needed) required by BS
code is shorter than that for ACI code The difference becomesmore pronounced with the increase of M u=V u ratio
bull The longitudinal and transverse torsional reinforcement requiredby ACI was found to be larger than that required by BS and thedifference in value betweenthe reinforcementof the two codesisalmost constant It was found that these differences are due todifferences in material safety factors
Impact of Safety Factors on Ultimate Design Load
bull The difference in the factor of safety for the dead load betweenthe ACI and BS resulted in larger design bending moments
and shear forces by the BS equations than the ACI ones Thediverging difference increases linearly with the increase of thedead load
bull For the resulting different design loads it wasfound that both thelongitudinal and transverse reinforcements required by the ACIare lower than the BS in all beams
bull For different column aspect ratios the punching shear strength of 1047298at slabndashcolumn connections calculated using the ACI code wasfound to be larger than that calculated using the BS code for thesame geometry materials and loading conditions
bull In the ACI code punching shear strength remains constant for different percentages of 1047298exural reinforcement whereas in theBS code punching shear strength increases with increase of 1047298exural reinforcement
bull For different slab thicknesses ACI code estimates more punch-ing shear strength than BS code
Fig 7 Minimum area of 1047298exural reinforcement with different f cu
Fig 8 Minimum area of shear reinforcement with different f cu
222 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
Acp 5 area enclosed by outside perimeter of concrete
cross section
Al 5 area of longitudinal reinforcement to resist torsion
Al min 5 minimum area of longitudinal reinforcement to
resist torsion
Ao 5 gross area enclosed by shear 1047298ow path
Aoh 5 area enclosed by centerline of the outermost closed
transverse torsional reinforcement
As 5 area of longitudinal tension reinforcement to resist
bending moment
Asmin 5 minimum area of 1047298exural reinforcement to resist
bending moment
Asv 5 area of shear reinforcement to resist shear
Asvt 5 area of two legs of stirrups required for torsion At 5 area of one leg of a closed stirrup resisting torsion
At min 5 minimum area of shear reinforcement to resist
torsion
a 5 depth of equivalent rectangular stress block
b 5 width of section 1047298ange
bw 5 width of section web
d 5 effective depth of tension reinforcement (distance
from extreme compression 1047297ber to centroid of
longitudinal tension reinforcement)
f 9c 5 characteristic cylinder compressive strength of
concrete (150 mm 3 300 mm)
f cu 5 characteristic strength of concrete
(1503
1503
150 mm concrete cube strength) f y 5 characteristic yield strength of longitudinal
reinforcement for 1047298exure
f yl 5 characteristic yield strength of longitudinal
reinforcement for torsion
f yv 5 characteristic yield strength of transverse
reinforcement
h 5 overall depth of section
hmax 5 larger dimension of rectangular cross section
hmin 5 smaller dimension of rectangular cross section
L 5 effective beam span
M u 5 ultimate 1047298exural moment
ph 5 perimeter of centerline of outermost closed
transverse torsional reinforcement
S 5 center-to-center spacing of transverse reinforcement
S v 5 spacing of stirrups
T cr 5 torsional cracking moment
T n 5 nominal torsional moment strength
T u 5 ultimate design twisting moment
V c 5 nominal shear strength provided by concrete
V u 5 ultimate shear force
v 5 design shear stress
vc 5 concrete shear strength
vt 5 torsional shear stress
vt min 5 minimum torsional shear stress above which
reinforcement is required
vtu 5 maximum combinedshear stress (shear plustorsion)
x 1 5 smaller center to center dimension of rectangular
stirrups y1 5 larger center to center dimension of rectangular
stirrups
Z 5 lever arm
g m 5 partial safety factor for strength of material
u 5 angle between axis of strut compression diagonal
and tension chord of the member
r 5 reinforcement ratio ( As=bd ) and
f 5 strength reduction factor
References
Alnuaimi A S and Bhatt P (2006) ldquo
Design of solid reinforced concretebeamsrdquo Structures Buildings 159(4) 197ndash216Ameli M and Ronagh H R (2007) ldquoTreatment of torsion of reinforced
concrete beams in current structural standardsrdquo Asian J Civil Eng
for structural concrete and commentaryrdquo 318-05 Farmington Hills
MIAmerican Concrete Institute (ACI) (2008) ldquoBuilding code requirements
for structural concrete and commentaryrdquo 318-08 Farmington Hills
MIBari MS(2000)ldquoPunching shear strength of slab-column connectionsmdashA
comparative study of different codesrdquo J Inst Engineers (India) 80(4)163ndash168
Bernardo L F A and Lopes S M R (2009) ldquoTorsion in high strengthconcrete hollow beamsmdashStrength and ductility analysisrdquo ACI Struc-
tural J 106(1) 39ndash48British Standards Institution(BSI) (1985)ldquoStructuraluse of concrete Code
of practice for special circumstancesrdquo BS 811085 Part-2 London
British Standards Institution(BSI) (1997)ldquoStructuraluse of concrete Codeof practice for design and constructionrdquo BS 811097 London
Chiu H J Fang I K Young W T and Shiau J K (2007) ldquoBehavior
of reinforced concrete beams with minimum torsional reinforcementrdquo Eng Structures 29(9) 2193ndash2205
Jung S and Kim KS (2008) ldquoKnowledge-based prediction on shear strength of concrete beams without shear reinforcementrdquo Eng Struc-
tures 30(6) 1515ndash1525Ngo D T (2001) ldquoPunching shear resistance of high-strength concrete
slabsrdquo Electron J Structural Eng 1(1) 2ndash14
Sharma A K and Innis B C (2006) ldquoPunching shear strength of slab-column connectionmdashA comparative study of different codesrdquo ASCE
Conf Proc Structural Engineering and Public Safety 2006 StructuresCongress ASCE Reston VA 1ndash11
Subramanian N (2005) ldquoEvaluation and enhancing the punching shear resistance of 1047298at slabs using high strength concreterdquo Indian Concr J79(4) 31ndash37
224 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
design load usingBS waslarger than that forACI having a maximum
difference of 143 As a result to these load differences therequiredlongitudinal and transverse reinforcements are differing with maxi-mum of 165 for bending and 600 for shear reinforcementsrespectively The results for the1047298exural reinforcement indicates slight
diversion due to the effect of increasing dead load while the requiredshear reinforcement shows convergence on the required transversereinforcement with the increase of the DLLL ratio Beams BR4 andBR5 required minimum stirrups in ACIand hence are notconsidered in
the discussion It is interesting to notice that as seen in Tables 1ndash4 for
the ultimate design loading the difference in 1047298exural reinforcement using ACIandBS is negligible Forservice loadinghowever shown inTable 9 the required 1047298exural reinforcement for BS was larger than for ACI with differences varying from 99 to 165 This difference isattributed to thedifferentload safetyfactors that areused in ACIandBSfor dead and live load combinations Similarly as seen in Tables 1ndash4for the ultimate design loading the shear reinforcement required by BSis less compared with ACI whereas for service loading (Table 9) theresultis reversed This reversal of resultis also attributed to thedifferent load safety factors used in ACI and BS codes for the dead load
Punching Shear Strength (at SlabndashColumn Connection) Using ACI 31808 and BS 811097
Here a parametric study of punching shear capacity at slabndashcolumnconnection using ACI and BS codes was carried out with different column aspect ratios percentagesof 1047298exural reinforcement and slabthicknesses The characteristic cube and cylindrical compressivestrengths were taken as 35 and 28 N=mm 2 respectively and thecharacteristic yield strength of reinforcementwas taken as 460N=mm 2
Table 6 Fixed Beams with Ultimate Design Torsion
Beam
number
Span
(m)
T u
(kNm)
Al
(mm 2)Difference
in Al ()
At =s
(mm 2=mm)Difference
in At =s ()ACI BS ACI BS
BL4 4 50 min 583 mdash 068 057 193
BL6 6 75 1043 875 192 102 086 186
BL8 8 100 1391 1167 192 136 114 193
BL10 10 125 1738 1458 192 17 143 189
Table 7 Fixed End Beams with Ultimate Design UDL of 100 kN=m and Torsion of 125kNm =m
From Eqs (4) and (7) it can be seen that unlike BS 8110 ACI 318does not consider dowel action of 1047298exural reinforcement in thecalculation of shear capacity Fig 4 shows punching shear strengthof a 250-mm-thick slab with effective depth of 220 mm at interior column having r 5 10 with column sizes of 3003 3003003 600 3003 900 and 3003 1200 mm resulting in different aspectratios usingACI andBS codesThe concrete cube compressivestrength f cu was 35 Nmm 2 with concrete cylinder compressivestrength as 08 f cu and steel yield strength of 460 N=mm 2 It can beseen that punching shearstrength forACI is larger than for BS for all
aspect ratios This means that for the same ultimate design punchingshear force ACI requires less slab thickness than BS The largest difference is368 when column aspect ratio is 2 It canalsobe seenthat in BS code punching shear strength increases linearly ascolumn aspect ratio increases whereas in ACI code the curve isnonlinear having a larger rate of increase of punching shear strengthbetween column aspect ratio of 1 and 2 than between 2 and 4 Fig 5shows punching shear strength of 250-mm-thick slab at interior columnof size 3003 300 mm with different percentages of 1047298exural re-inforcement ranging between 015 and 3 using ACI and BS codesThe material strengths and effective depths of slab were the same as inthe previous slab It can be seen that in ACI code the punching shear strength is constant at 773 kN without any effect of the percentage of 1047298exural reinforcement whereas in BS code punching shear strength
increases with increase of reinforcement TheBS curve is nonlinear and
it crosses the ACI horizontal line at r 5 17 This shows that with thegiven data untilr 5 17 ACI leads to largerpunching shear strengththan BS with the largest difference of 1314 when r 5 015
Fig 6 shows punching shear strengthof slabat interiorcolumnof size3003 300 mm with area of 1047298exural reinforcement As 5 2 050 mm 2
with varying depth The material strengths were the same as in theprevious slab The effective depth of each slab is 35 mm less than theoverall thickness It can be seen that ACIestimates more punchingshear strength than BS The differences with the given data ranged between148 and 233 Both ACI and BS curves vary linearly with increase of
depth however the rate ofincreaseinthe ACIresults ismorethan inBSleading to diverging curves This shows that the difference in V c usingboth codes increases as depth increases
Comparison for Minimum Area of Flexural Reinforcement Using ACI 31808 and BS 811097
The equations of minimum required 1047298exural reinforcement basedon the ACI and BS codes are shown in Appendix I Fig 7 was de-veloped based on those equations for different values of f c9 which istakenas08 f cu Thebeamcross-sectional dimension is 3503 700 mm with effective depth of 625 mm The yield strength of reinforcement was taken as 460 N=mm 2 It can be seen that the minimum area of 1047298exural reinforcement required by ACI is much larger than that re-
quired by BS The BS curve is constant with all grades of concrete
Table 9 Parametric Study to Compare Steel Required for Bending and Shear with DL 1 LL Combination Using ACI and BS
while the ACI curve changes from being constant for concretegrades of 30ndash40 N=mm 2 to nonlinear for concrete grades larger than40 N=mm 2 The difference is constant at the value of 106 for theconcrete strengths of 30ndash40 N=mm 2 then it increases with the in-crease in the concrete strength The maximum difference for thegiven beam geometry and concrete strengths was 1335
Comparison for Minimum Area of Shear Reinforcement Using ACI 31808 and BS 811097
Fig 8 was developed based on Eqs (5) and (6) for different values of f c9 which is taken as 08 f cu The beam cross-sectional dimension is3503 700 mm with effective depth of 625 mm The yield strengthof reinforcement was taken as 460 N=mm 2 It can be seen that theminimum area of shear reinforcement required by BS is larger thanrequired by ACI The BS curve is constant for all grades of concretewhereas theACI curveis constant forconcretegrades of 30ndash40 N=mm 2
then reduces linearly for grades larger than 40 N=mm 2 The dif-ference is constant at the value of 185 for the concrete strengths
between 30 and 40 N=mm 2 then decreases with the increase in theconcretestrength Theminimum difference forthegiven beamgeometryand concrete strengths was 67 at concrete grade of 50 N=mm 2
Concluding Remarks and Recommendations
In this research design results of rectangular RC beams subjected to
bending shear and torsion and punching shear at the slabndashcolumnconnection using ACI 31808 and BS 811097 were comparedConclusions can be drawn as follows
Design for Combined Bending Moment Twisting Moment and Shear Force
bull Therequired 1047298exural reinforcementsfor thesame designbendingmoment using ACI and BS codes are almostthe same regardlessof M u=V u ratio
bull In most cases the required shear reinforcement by ACI code islargerthan that by BS code forthesame design load This difference
Fig 5 Punching shear strength versus percentage of r using ACI and BS codes
Fig 6 Punching shear strength versus slab thickness using ACI and BS codes
PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013 221
becomes morepronounced with the increase of M u=V u ratio It wasfound that empirical equations of shear capacity in BS and ACIcodes have led to highlydifferent results It wasalso established that owing to differences in material safety factors ACI equations leadto more required shear reinforcement than BS
bull The beam length that needs shear reinforcement (beyond whichonly minimum shear reinforcement is needed) required by BS
code is shorter than that for ACI code The difference becomesmore pronounced with the increase of M u=V u ratio
bull The longitudinal and transverse torsional reinforcement requiredby ACI was found to be larger than that required by BS and thedifference in value betweenthe reinforcementof the two codesisalmost constant It was found that these differences are due todifferences in material safety factors
Impact of Safety Factors on Ultimate Design Load
bull The difference in the factor of safety for the dead load betweenthe ACI and BS resulted in larger design bending moments
and shear forces by the BS equations than the ACI ones Thediverging difference increases linearly with the increase of thedead load
bull For the resulting different design loads it wasfound that both thelongitudinal and transverse reinforcements required by the ACIare lower than the BS in all beams
bull For different column aspect ratios the punching shear strength of 1047298at slabndashcolumn connections calculated using the ACI code wasfound to be larger than that calculated using the BS code for thesame geometry materials and loading conditions
bull In the ACI code punching shear strength remains constant for different percentages of 1047298exural reinforcement whereas in theBS code punching shear strength increases with increase of 1047298exural reinforcement
bull For different slab thicknesses ACI code estimates more punch-ing shear strength than BS code
Fig 7 Minimum area of 1047298exural reinforcement with different f cu
Fig 8 Minimum area of shear reinforcement with different f cu
222 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
Acp 5 area enclosed by outside perimeter of concrete
cross section
Al 5 area of longitudinal reinforcement to resist torsion
Al min 5 minimum area of longitudinal reinforcement to
resist torsion
Ao 5 gross area enclosed by shear 1047298ow path
Aoh 5 area enclosed by centerline of the outermost closed
transverse torsional reinforcement
As 5 area of longitudinal tension reinforcement to resist
bending moment
Asmin 5 minimum area of 1047298exural reinforcement to resist
bending moment
Asv 5 area of shear reinforcement to resist shear
Asvt 5 area of two legs of stirrups required for torsion At 5 area of one leg of a closed stirrup resisting torsion
At min 5 minimum area of shear reinforcement to resist
torsion
a 5 depth of equivalent rectangular stress block
b 5 width of section 1047298ange
bw 5 width of section web
d 5 effective depth of tension reinforcement (distance
from extreme compression 1047297ber to centroid of
longitudinal tension reinforcement)
f 9c 5 characteristic cylinder compressive strength of
concrete (150 mm 3 300 mm)
f cu 5 characteristic strength of concrete
(1503
1503
150 mm concrete cube strength) f y 5 characteristic yield strength of longitudinal
reinforcement for 1047298exure
f yl 5 characteristic yield strength of longitudinal
reinforcement for torsion
f yv 5 characteristic yield strength of transverse
reinforcement
h 5 overall depth of section
hmax 5 larger dimension of rectangular cross section
hmin 5 smaller dimension of rectangular cross section
L 5 effective beam span
M u 5 ultimate 1047298exural moment
ph 5 perimeter of centerline of outermost closed
transverse torsional reinforcement
S 5 center-to-center spacing of transverse reinforcement
S v 5 spacing of stirrups
T cr 5 torsional cracking moment
T n 5 nominal torsional moment strength
T u 5 ultimate design twisting moment
V c 5 nominal shear strength provided by concrete
V u 5 ultimate shear force
v 5 design shear stress
vc 5 concrete shear strength
vt 5 torsional shear stress
vt min 5 minimum torsional shear stress above which
reinforcement is required
vtu 5 maximum combinedshear stress (shear plustorsion)
x 1 5 smaller center to center dimension of rectangular
stirrups y1 5 larger center to center dimension of rectangular
stirrups
Z 5 lever arm
g m 5 partial safety factor for strength of material
u 5 angle between axis of strut compression diagonal
and tension chord of the member
r 5 reinforcement ratio ( As=bd ) and
f 5 strength reduction factor
References
Alnuaimi A S and Bhatt P (2006) ldquo
Design of solid reinforced concretebeamsrdquo Structures Buildings 159(4) 197ndash216Ameli M and Ronagh H R (2007) ldquoTreatment of torsion of reinforced
concrete beams in current structural standardsrdquo Asian J Civil Eng
for structural concrete and commentaryrdquo 318-05 Farmington Hills
MIAmerican Concrete Institute (ACI) (2008) ldquoBuilding code requirements
for structural concrete and commentaryrdquo 318-08 Farmington Hills
MIBari MS(2000)ldquoPunching shear strength of slab-column connectionsmdashA
comparative study of different codesrdquo J Inst Engineers (India) 80(4)163ndash168
Bernardo L F A and Lopes S M R (2009) ldquoTorsion in high strengthconcrete hollow beamsmdashStrength and ductility analysisrdquo ACI Struc-
tural J 106(1) 39ndash48British Standards Institution(BSI) (1985)ldquoStructuraluse of concrete Code
of practice for special circumstancesrdquo BS 811085 Part-2 London
British Standards Institution(BSI) (1997)ldquoStructuraluse of concrete Codeof practice for design and constructionrdquo BS 811097 London
Chiu H J Fang I K Young W T and Shiau J K (2007) ldquoBehavior
of reinforced concrete beams with minimum torsional reinforcementrdquo Eng Structures 29(9) 2193ndash2205
Jung S and Kim KS (2008) ldquoKnowledge-based prediction on shear strength of concrete beams without shear reinforcementrdquo Eng Struc-
tures 30(6) 1515ndash1525Ngo D T (2001) ldquoPunching shear resistance of high-strength concrete
slabsrdquo Electron J Structural Eng 1(1) 2ndash14
Sharma A K and Innis B C (2006) ldquoPunching shear strength of slab-column connectionmdashA comparative study of different codesrdquo ASCE
Conf Proc Structural Engineering and Public Safety 2006 StructuresCongress ASCE Reston VA 1ndash11
Subramanian N (2005) ldquoEvaluation and enhancing the punching shear resistance of 1047298at slabs using high strength concreterdquo Indian Concr J79(4) 31ndash37
224 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
From Eqs (4) and (7) it can be seen that unlike BS 8110 ACI 318does not consider dowel action of 1047298exural reinforcement in thecalculation of shear capacity Fig 4 shows punching shear strengthof a 250-mm-thick slab with effective depth of 220 mm at interior column having r 5 10 with column sizes of 3003 3003003 600 3003 900 and 3003 1200 mm resulting in different aspectratios usingACI andBS codesThe concrete cube compressivestrength f cu was 35 Nmm 2 with concrete cylinder compressivestrength as 08 f cu and steel yield strength of 460 N=mm 2 It can beseen that punching shearstrength forACI is larger than for BS for all
aspect ratios This means that for the same ultimate design punchingshear force ACI requires less slab thickness than BS The largest difference is368 when column aspect ratio is 2 It canalsobe seenthat in BS code punching shear strength increases linearly ascolumn aspect ratio increases whereas in ACI code the curve isnonlinear having a larger rate of increase of punching shear strengthbetween column aspect ratio of 1 and 2 than between 2 and 4 Fig 5shows punching shear strength of 250-mm-thick slab at interior columnof size 3003 300 mm with different percentages of 1047298exural re-inforcement ranging between 015 and 3 using ACI and BS codesThe material strengths and effective depths of slab were the same as inthe previous slab It can be seen that in ACI code the punching shear strength is constant at 773 kN without any effect of the percentage of 1047298exural reinforcement whereas in BS code punching shear strength
increases with increase of reinforcement TheBS curve is nonlinear and
it crosses the ACI horizontal line at r 5 17 This shows that with thegiven data untilr 5 17 ACI leads to largerpunching shear strengththan BS with the largest difference of 1314 when r 5 015
Fig 6 shows punching shear strengthof slabat interiorcolumnof size3003 300 mm with area of 1047298exural reinforcement As 5 2 050 mm 2
with varying depth The material strengths were the same as in theprevious slab The effective depth of each slab is 35 mm less than theoverall thickness It can be seen that ACIestimates more punchingshear strength than BS The differences with the given data ranged between148 and 233 Both ACI and BS curves vary linearly with increase of
depth however the rate ofincreaseinthe ACIresults ismorethan inBSleading to diverging curves This shows that the difference in V c usingboth codes increases as depth increases
Comparison for Minimum Area of Flexural Reinforcement Using ACI 31808 and BS 811097
The equations of minimum required 1047298exural reinforcement basedon the ACI and BS codes are shown in Appendix I Fig 7 was de-veloped based on those equations for different values of f c9 which istakenas08 f cu Thebeamcross-sectional dimension is 3503 700 mm with effective depth of 625 mm The yield strength of reinforcement was taken as 460 N=mm 2 It can be seen that the minimum area of 1047298exural reinforcement required by ACI is much larger than that re-
quired by BS The BS curve is constant with all grades of concrete
Table 9 Parametric Study to Compare Steel Required for Bending and Shear with DL 1 LL Combination Using ACI and BS
while the ACI curve changes from being constant for concretegrades of 30ndash40 N=mm 2 to nonlinear for concrete grades larger than40 N=mm 2 The difference is constant at the value of 106 for theconcrete strengths of 30ndash40 N=mm 2 then it increases with the in-crease in the concrete strength The maximum difference for thegiven beam geometry and concrete strengths was 1335
Comparison for Minimum Area of Shear Reinforcement Using ACI 31808 and BS 811097
Fig 8 was developed based on Eqs (5) and (6) for different values of f c9 which is taken as 08 f cu The beam cross-sectional dimension is3503 700 mm with effective depth of 625 mm The yield strengthof reinforcement was taken as 460 N=mm 2 It can be seen that theminimum area of shear reinforcement required by BS is larger thanrequired by ACI The BS curve is constant for all grades of concretewhereas theACI curveis constant forconcretegrades of 30ndash40 N=mm 2
then reduces linearly for grades larger than 40 N=mm 2 The dif-ference is constant at the value of 185 for the concrete strengths
between 30 and 40 N=mm 2 then decreases with the increase in theconcretestrength Theminimum difference forthegiven beamgeometryand concrete strengths was 67 at concrete grade of 50 N=mm 2
Concluding Remarks and Recommendations
In this research design results of rectangular RC beams subjected to
bending shear and torsion and punching shear at the slabndashcolumnconnection using ACI 31808 and BS 811097 were comparedConclusions can be drawn as follows
Design for Combined Bending Moment Twisting Moment and Shear Force
bull Therequired 1047298exural reinforcementsfor thesame designbendingmoment using ACI and BS codes are almostthe same regardlessof M u=V u ratio
bull In most cases the required shear reinforcement by ACI code islargerthan that by BS code forthesame design load This difference
Fig 5 Punching shear strength versus percentage of r using ACI and BS codes
Fig 6 Punching shear strength versus slab thickness using ACI and BS codes
PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013 221
becomes morepronounced with the increase of M u=V u ratio It wasfound that empirical equations of shear capacity in BS and ACIcodes have led to highlydifferent results It wasalso established that owing to differences in material safety factors ACI equations leadto more required shear reinforcement than BS
bull The beam length that needs shear reinforcement (beyond whichonly minimum shear reinforcement is needed) required by BS
code is shorter than that for ACI code The difference becomesmore pronounced with the increase of M u=V u ratio
bull The longitudinal and transverse torsional reinforcement requiredby ACI was found to be larger than that required by BS and thedifference in value betweenthe reinforcementof the two codesisalmost constant It was found that these differences are due todifferences in material safety factors
Impact of Safety Factors on Ultimate Design Load
bull The difference in the factor of safety for the dead load betweenthe ACI and BS resulted in larger design bending moments
and shear forces by the BS equations than the ACI ones Thediverging difference increases linearly with the increase of thedead load
bull For the resulting different design loads it wasfound that both thelongitudinal and transverse reinforcements required by the ACIare lower than the BS in all beams
bull For different column aspect ratios the punching shear strength of 1047298at slabndashcolumn connections calculated using the ACI code wasfound to be larger than that calculated using the BS code for thesame geometry materials and loading conditions
bull In the ACI code punching shear strength remains constant for different percentages of 1047298exural reinforcement whereas in theBS code punching shear strength increases with increase of 1047298exural reinforcement
bull For different slab thicknesses ACI code estimates more punch-ing shear strength than BS code
Fig 7 Minimum area of 1047298exural reinforcement with different f cu
Fig 8 Minimum area of shear reinforcement with different f cu
222 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
Acp 5 area enclosed by outside perimeter of concrete
cross section
Al 5 area of longitudinal reinforcement to resist torsion
Al min 5 minimum area of longitudinal reinforcement to
resist torsion
Ao 5 gross area enclosed by shear 1047298ow path
Aoh 5 area enclosed by centerline of the outermost closed
transverse torsional reinforcement
As 5 area of longitudinal tension reinforcement to resist
bending moment
Asmin 5 minimum area of 1047298exural reinforcement to resist
bending moment
Asv 5 area of shear reinforcement to resist shear
Asvt 5 area of two legs of stirrups required for torsion At 5 area of one leg of a closed stirrup resisting torsion
At min 5 minimum area of shear reinforcement to resist
torsion
a 5 depth of equivalent rectangular stress block
b 5 width of section 1047298ange
bw 5 width of section web
d 5 effective depth of tension reinforcement (distance
from extreme compression 1047297ber to centroid of
longitudinal tension reinforcement)
f 9c 5 characteristic cylinder compressive strength of
concrete (150 mm 3 300 mm)
f cu 5 characteristic strength of concrete
(1503
1503
150 mm concrete cube strength) f y 5 characteristic yield strength of longitudinal
reinforcement for 1047298exure
f yl 5 characteristic yield strength of longitudinal
reinforcement for torsion
f yv 5 characteristic yield strength of transverse
reinforcement
h 5 overall depth of section
hmax 5 larger dimension of rectangular cross section
hmin 5 smaller dimension of rectangular cross section
L 5 effective beam span
M u 5 ultimate 1047298exural moment
ph 5 perimeter of centerline of outermost closed
transverse torsional reinforcement
S 5 center-to-center spacing of transverse reinforcement
S v 5 spacing of stirrups
T cr 5 torsional cracking moment
T n 5 nominal torsional moment strength
T u 5 ultimate design twisting moment
V c 5 nominal shear strength provided by concrete
V u 5 ultimate shear force
v 5 design shear stress
vc 5 concrete shear strength
vt 5 torsional shear stress
vt min 5 minimum torsional shear stress above which
reinforcement is required
vtu 5 maximum combinedshear stress (shear plustorsion)
x 1 5 smaller center to center dimension of rectangular
stirrups y1 5 larger center to center dimension of rectangular
stirrups
Z 5 lever arm
g m 5 partial safety factor for strength of material
u 5 angle between axis of strut compression diagonal
and tension chord of the member
r 5 reinforcement ratio ( As=bd ) and
f 5 strength reduction factor
References
Alnuaimi A S and Bhatt P (2006) ldquo
Design of solid reinforced concretebeamsrdquo Structures Buildings 159(4) 197ndash216Ameli M and Ronagh H R (2007) ldquoTreatment of torsion of reinforced
concrete beams in current structural standardsrdquo Asian J Civil Eng
for structural concrete and commentaryrdquo 318-05 Farmington Hills
MIAmerican Concrete Institute (ACI) (2008) ldquoBuilding code requirements
for structural concrete and commentaryrdquo 318-08 Farmington Hills
MIBari MS(2000)ldquoPunching shear strength of slab-column connectionsmdashA
comparative study of different codesrdquo J Inst Engineers (India) 80(4)163ndash168
Bernardo L F A and Lopes S M R (2009) ldquoTorsion in high strengthconcrete hollow beamsmdashStrength and ductility analysisrdquo ACI Struc-
tural J 106(1) 39ndash48British Standards Institution(BSI) (1985)ldquoStructuraluse of concrete Code
of practice for special circumstancesrdquo BS 811085 Part-2 London
British Standards Institution(BSI) (1997)ldquoStructuraluse of concrete Codeof practice for design and constructionrdquo BS 811097 London
Chiu H J Fang I K Young W T and Shiau J K (2007) ldquoBehavior
of reinforced concrete beams with minimum torsional reinforcementrdquo Eng Structures 29(9) 2193ndash2205
Jung S and Kim KS (2008) ldquoKnowledge-based prediction on shear strength of concrete beams without shear reinforcementrdquo Eng Struc-
tures 30(6) 1515ndash1525Ngo D T (2001) ldquoPunching shear resistance of high-strength concrete
slabsrdquo Electron J Structural Eng 1(1) 2ndash14
Sharma A K and Innis B C (2006) ldquoPunching shear strength of slab-column connectionmdashA comparative study of different codesrdquo ASCE
Conf Proc Structural Engineering and Public Safety 2006 StructuresCongress ASCE Reston VA 1ndash11
Subramanian N (2005) ldquoEvaluation and enhancing the punching shear resistance of 1047298at slabs using high strength concreterdquo Indian Concr J79(4) 31ndash37
224 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
while the ACI curve changes from being constant for concretegrades of 30ndash40 N=mm 2 to nonlinear for concrete grades larger than40 N=mm 2 The difference is constant at the value of 106 for theconcrete strengths of 30ndash40 N=mm 2 then it increases with the in-crease in the concrete strength The maximum difference for thegiven beam geometry and concrete strengths was 1335
Comparison for Minimum Area of Shear Reinforcement Using ACI 31808 and BS 811097
Fig 8 was developed based on Eqs (5) and (6) for different values of f c9 which is taken as 08 f cu The beam cross-sectional dimension is3503 700 mm with effective depth of 625 mm The yield strengthof reinforcement was taken as 460 N=mm 2 It can be seen that theminimum area of shear reinforcement required by BS is larger thanrequired by ACI The BS curve is constant for all grades of concretewhereas theACI curveis constant forconcretegrades of 30ndash40 N=mm 2
then reduces linearly for grades larger than 40 N=mm 2 The dif-ference is constant at the value of 185 for the concrete strengths
between 30 and 40 N=mm 2 then decreases with the increase in theconcretestrength Theminimum difference forthegiven beamgeometryand concrete strengths was 67 at concrete grade of 50 N=mm 2
Concluding Remarks and Recommendations
In this research design results of rectangular RC beams subjected to
bending shear and torsion and punching shear at the slabndashcolumnconnection using ACI 31808 and BS 811097 were comparedConclusions can be drawn as follows
Design for Combined Bending Moment Twisting Moment and Shear Force
bull Therequired 1047298exural reinforcementsfor thesame designbendingmoment using ACI and BS codes are almostthe same regardlessof M u=V u ratio
bull In most cases the required shear reinforcement by ACI code islargerthan that by BS code forthesame design load This difference
Fig 5 Punching shear strength versus percentage of r using ACI and BS codes
Fig 6 Punching shear strength versus slab thickness using ACI and BS codes
PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013 221
becomes morepronounced with the increase of M u=V u ratio It wasfound that empirical equations of shear capacity in BS and ACIcodes have led to highlydifferent results It wasalso established that owing to differences in material safety factors ACI equations leadto more required shear reinforcement than BS
bull The beam length that needs shear reinforcement (beyond whichonly minimum shear reinforcement is needed) required by BS
code is shorter than that for ACI code The difference becomesmore pronounced with the increase of M u=V u ratio
bull The longitudinal and transverse torsional reinforcement requiredby ACI was found to be larger than that required by BS and thedifference in value betweenthe reinforcementof the two codesisalmost constant It was found that these differences are due todifferences in material safety factors
Impact of Safety Factors on Ultimate Design Load
bull The difference in the factor of safety for the dead load betweenthe ACI and BS resulted in larger design bending moments
and shear forces by the BS equations than the ACI ones Thediverging difference increases linearly with the increase of thedead load
bull For the resulting different design loads it wasfound that both thelongitudinal and transverse reinforcements required by the ACIare lower than the BS in all beams
bull For different column aspect ratios the punching shear strength of 1047298at slabndashcolumn connections calculated using the ACI code wasfound to be larger than that calculated using the BS code for thesame geometry materials and loading conditions
bull In the ACI code punching shear strength remains constant for different percentages of 1047298exural reinforcement whereas in theBS code punching shear strength increases with increase of 1047298exural reinforcement
bull For different slab thicknesses ACI code estimates more punch-ing shear strength than BS code
Fig 7 Minimum area of 1047298exural reinforcement with different f cu
Fig 8 Minimum area of shear reinforcement with different f cu
222 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
Acp 5 area enclosed by outside perimeter of concrete
cross section
Al 5 area of longitudinal reinforcement to resist torsion
Al min 5 minimum area of longitudinal reinforcement to
resist torsion
Ao 5 gross area enclosed by shear 1047298ow path
Aoh 5 area enclosed by centerline of the outermost closed
transverse torsional reinforcement
As 5 area of longitudinal tension reinforcement to resist
bending moment
Asmin 5 minimum area of 1047298exural reinforcement to resist
bending moment
Asv 5 area of shear reinforcement to resist shear
Asvt 5 area of two legs of stirrups required for torsion At 5 area of one leg of a closed stirrup resisting torsion
At min 5 minimum area of shear reinforcement to resist
torsion
a 5 depth of equivalent rectangular stress block
b 5 width of section 1047298ange
bw 5 width of section web
d 5 effective depth of tension reinforcement (distance
from extreme compression 1047297ber to centroid of
longitudinal tension reinforcement)
f 9c 5 characteristic cylinder compressive strength of
concrete (150 mm 3 300 mm)
f cu 5 characteristic strength of concrete
(1503
1503
150 mm concrete cube strength) f y 5 characteristic yield strength of longitudinal
reinforcement for 1047298exure
f yl 5 characteristic yield strength of longitudinal
reinforcement for torsion
f yv 5 characteristic yield strength of transverse
reinforcement
h 5 overall depth of section
hmax 5 larger dimension of rectangular cross section
hmin 5 smaller dimension of rectangular cross section
L 5 effective beam span
M u 5 ultimate 1047298exural moment
ph 5 perimeter of centerline of outermost closed
transverse torsional reinforcement
S 5 center-to-center spacing of transverse reinforcement
S v 5 spacing of stirrups
T cr 5 torsional cracking moment
T n 5 nominal torsional moment strength
T u 5 ultimate design twisting moment
V c 5 nominal shear strength provided by concrete
V u 5 ultimate shear force
v 5 design shear stress
vc 5 concrete shear strength
vt 5 torsional shear stress
vt min 5 minimum torsional shear stress above which
reinforcement is required
vtu 5 maximum combinedshear stress (shear plustorsion)
x 1 5 smaller center to center dimension of rectangular
stirrups y1 5 larger center to center dimension of rectangular
stirrups
Z 5 lever arm
g m 5 partial safety factor for strength of material
u 5 angle between axis of strut compression diagonal
and tension chord of the member
r 5 reinforcement ratio ( As=bd ) and
f 5 strength reduction factor
References
Alnuaimi A S and Bhatt P (2006) ldquo
Design of solid reinforced concretebeamsrdquo Structures Buildings 159(4) 197ndash216Ameli M and Ronagh H R (2007) ldquoTreatment of torsion of reinforced
concrete beams in current structural standardsrdquo Asian J Civil Eng
for structural concrete and commentaryrdquo 318-05 Farmington Hills
MIAmerican Concrete Institute (ACI) (2008) ldquoBuilding code requirements
for structural concrete and commentaryrdquo 318-08 Farmington Hills
MIBari MS(2000)ldquoPunching shear strength of slab-column connectionsmdashA
comparative study of different codesrdquo J Inst Engineers (India) 80(4)163ndash168
Bernardo L F A and Lopes S M R (2009) ldquoTorsion in high strengthconcrete hollow beamsmdashStrength and ductility analysisrdquo ACI Struc-
tural J 106(1) 39ndash48British Standards Institution(BSI) (1985)ldquoStructuraluse of concrete Code
of practice for special circumstancesrdquo BS 811085 Part-2 London
British Standards Institution(BSI) (1997)ldquoStructuraluse of concrete Codeof practice for design and constructionrdquo BS 811097 London
Chiu H J Fang I K Young W T and Shiau J K (2007) ldquoBehavior
of reinforced concrete beams with minimum torsional reinforcementrdquo Eng Structures 29(9) 2193ndash2205
Jung S and Kim KS (2008) ldquoKnowledge-based prediction on shear strength of concrete beams without shear reinforcementrdquo Eng Struc-
tures 30(6) 1515ndash1525Ngo D T (2001) ldquoPunching shear resistance of high-strength concrete
slabsrdquo Electron J Structural Eng 1(1) 2ndash14
Sharma A K and Innis B C (2006) ldquoPunching shear strength of slab-column connectionmdashA comparative study of different codesrdquo ASCE
Conf Proc Structural Engineering and Public Safety 2006 StructuresCongress ASCE Reston VA 1ndash11
Subramanian N (2005) ldquoEvaluation and enhancing the punching shear resistance of 1047298at slabs using high strength concreterdquo Indian Concr J79(4) 31ndash37
224 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
becomes morepronounced with the increase of M u=V u ratio It wasfound that empirical equations of shear capacity in BS and ACIcodes have led to highlydifferent results It wasalso established that owing to differences in material safety factors ACI equations leadto more required shear reinforcement than BS
bull The beam length that needs shear reinforcement (beyond whichonly minimum shear reinforcement is needed) required by BS
code is shorter than that for ACI code The difference becomesmore pronounced with the increase of M u=V u ratio
bull The longitudinal and transverse torsional reinforcement requiredby ACI was found to be larger than that required by BS and thedifference in value betweenthe reinforcementof the two codesisalmost constant It was found that these differences are due todifferences in material safety factors
Impact of Safety Factors on Ultimate Design Load
bull The difference in the factor of safety for the dead load betweenthe ACI and BS resulted in larger design bending moments
and shear forces by the BS equations than the ACI ones Thediverging difference increases linearly with the increase of thedead load
bull For the resulting different design loads it wasfound that both thelongitudinal and transverse reinforcements required by the ACIare lower than the BS in all beams
bull For different column aspect ratios the punching shear strength of 1047298at slabndashcolumn connections calculated using the ACI code wasfound to be larger than that calculated using the BS code for thesame geometry materials and loading conditions
bull In the ACI code punching shear strength remains constant for different percentages of 1047298exural reinforcement whereas in theBS code punching shear strength increases with increase of 1047298exural reinforcement
bull For different slab thicknesses ACI code estimates more punch-ing shear strength than BS code
Fig 7 Minimum area of 1047298exural reinforcement with different f cu
Fig 8 Minimum area of shear reinforcement with different f cu
222 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
Acp 5 area enclosed by outside perimeter of concrete
cross section
Al 5 area of longitudinal reinforcement to resist torsion
Al min 5 minimum area of longitudinal reinforcement to
resist torsion
Ao 5 gross area enclosed by shear 1047298ow path
Aoh 5 area enclosed by centerline of the outermost closed
transverse torsional reinforcement
As 5 area of longitudinal tension reinforcement to resist
bending moment
Asmin 5 minimum area of 1047298exural reinforcement to resist
bending moment
Asv 5 area of shear reinforcement to resist shear
Asvt 5 area of two legs of stirrups required for torsion At 5 area of one leg of a closed stirrup resisting torsion
At min 5 minimum area of shear reinforcement to resist
torsion
a 5 depth of equivalent rectangular stress block
b 5 width of section 1047298ange
bw 5 width of section web
d 5 effective depth of tension reinforcement (distance
from extreme compression 1047297ber to centroid of
longitudinal tension reinforcement)
f 9c 5 characteristic cylinder compressive strength of
concrete (150 mm 3 300 mm)
f cu 5 characteristic strength of concrete
(1503
1503
150 mm concrete cube strength) f y 5 characteristic yield strength of longitudinal
reinforcement for 1047298exure
f yl 5 characteristic yield strength of longitudinal
reinforcement for torsion
f yv 5 characteristic yield strength of transverse
reinforcement
h 5 overall depth of section
hmax 5 larger dimension of rectangular cross section
hmin 5 smaller dimension of rectangular cross section
L 5 effective beam span
M u 5 ultimate 1047298exural moment
ph 5 perimeter of centerline of outermost closed
transverse torsional reinforcement
S 5 center-to-center spacing of transverse reinforcement
S v 5 spacing of stirrups
T cr 5 torsional cracking moment
T n 5 nominal torsional moment strength
T u 5 ultimate design twisting moment
V c 5 nominal shear strength provided by concrete
V u 5 ultimate shear force
v 5 design shear stress
vc 5 concrete shear strength
vt 5 torsional shear stress
vt min 5 minimum torsional shear stress above which
reinforcement is required
vtu 5 maximum combinedshear stress (shear plustorsion)
x 1 5 smaller center to center dimension of rectangular
stirrups y1 5 larger center to center dimension of rectangular
stirrups
Z 5 lever arm
g m 5 partial safety factor for strength of material
u 5 angle between axis of strut compression diagonal
and tension chord of the member
r 5 reinforcement ratio ( As=bd ) and
f 5 strength reduction factor
References
Alnuaimi A S and Bhatt P (2006) ldquo
Design of solid reinforced concretebeamsrdquo Structures Buildings 159(4) 197ndash216Ameli M and Ronagh H R (2007) ldquoTreatment of torsion of reinforced
concrete beams in current structural standardsrdquo Asian J Civil Eng
for structural concrete and commentaryrdquo 318-05 Farmington Hills
MIAmerican Concrete Institute (ACI) (2008) ldquoBuilding code requirements
for structural concrete and commentaryrdquo 318-08 Farmington Hills
MIBari MS(2000)ldquoPunching shear strength of slab-column connectionsmdashA
comparative study of different codesrdquo J Inst Engineers (India) 80(4)163ndash168
Bernardo L F A and Lopes S M R (2009) ldquoTorsion in high strengthconcrete hollow beamsmdashStrength and ductility analysisrdquo ACI Struc-
tural J 106(1) 39ndash48British Standards Institution(BSI) (1985)ldquoStructuraluse of concrete Code
of practice for special circumstancesrdquo BS 811085 Part-2 London
British Standards Institution(BSI) (1997)ldquoStructuraluse of concrete Codeof practice for design and constructionrdquo BS 811097 London
Chiu H J Fang I K Young W T and Shiau J K (2007) ldquoBehavior
of reinforced concrete beams with minimum torsional reinforcementrdquo Eng Structures 29(9) 2193ndash2205
Jung S and Kim KS (2008) ldquoKnowledge-based prediction on shear strength of concrete beams without shear reinforcementrdquo Eng Struc-
tures 30(6) 1515ndash1525Ngo D T (2001) ldquoPunching shear resistance of high-strength concrete
slabsrdquo Electron J Structural Eng 1(1) 2ndash14
Sharma A K and Innis B C (2006) ldquoPunching shear strength of slab-column connectionmdashA comparative study of different codesrdquo ASCE
Conf Proc Structural Engineering and Public Safety 2006 StructuresCongress ASCE Reston VA 1ndash11
Subramanian N (2005) ldquoEvaluation and enhancing the punching shear resistance of 1047298at slabs using high strength concreterdquo Indian Concr J79(4) 31ndash37
224 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
Acp 5 area enclosed by outside perimeter of concrete
cross section
Al 5 area of longitudinal reinforcement to resist torsion
Al min 5 minimum area of longitudinal reinforcement to
resist torsion
Ao 5 gross area enclosed by shear 1047298ow path
Aoh 5 area enclosed by centerline of the outermost closed
transverse torsional reinforcement
As 5 area of longitudinal tension reinforcement to resist
bending moment
Asmin 5 minimum area of 1047298exural reinforcement to resist
bending moment
Asv 5 area of shear reinforcement to resist shear
Asvt 5 area of two legs of stirrups required for torsion At 5 area of one leg of a closed stirrup resisting torsion
At min 5 minimum area of shear reinforcement to resist
torsion
a 5 depth of equivalent rectangular stress block
b 5 width of section 1047298ange
bw 5 width of section web
d 5 effective depth of tension reinforcement (distance
from extreme compression 1047297ber to centroid of
longitudinal tension reinforcement)
f 9c 5 characteristic cylinder compressive strength of
concrete (150 mm 3 300 mm)
f cu 5 characteristic strength of concrete
(1503
1503
150 mm concrete cube strength) f y 5 characteristic yield strength of longitudinal
reinforcement for 1047298exure
f yl 5 characteristic yield strength of longitudinal
reinforcement for torsion
f yv 5 characteristic yield strength of transverse
reinforcement
h 5 overall depth of section
hmax 5 larger dimension of rectangular cross section
hmin 5 smaller dimension of rectangular cross section
L 5 effective beam span
M u 5 ultimate 1047298exural moment
ph 5 perimeter of centerline of outermost closed
transverse torsional reinforcement
S 5 center-to-center spacing of transverse reinforcement
S v 5 spacing of stirrups
T cr 5 torsional cracking moment
T n 5 nominal torsional moment strength
T u 5 ultimate design twisting moment
V c 5 nominal shear strength provided by concrete
V u 5 ultimate shear force
v 5 design shear stress
vc 5 concrete shear strength
vt 5 torsional shear stress
vt min 5 minimum torsional shear stress above which
reinforcement is required
vtu 5 maximum combinedshear stress (shear plustorsion)
x 1 5 smaller center to center dimension of rectangular
stirrups y1 5 larger center to center dimension of rectangular
stirrups
Z 5 lever arm
g m 5 partial safety factor for strength of material
u 5 angle between axis of strut compression diagonal
and tension chord of the member
r 5 reinforcement ratio ( As=bd ) and
f 5 strength reduction factor
References
Alnuaimi A S and Bhatt P (2006) ldquo
Design of solid reinforced concretebeamsrdquo Structures Buildings 159(4) 197ndash216Ameli M and Ronagh H R (2007) ldquoTreatment of torsion of reinforced
concrete beams in current structural standardsrdquo Asian J Civil Eng
for structural concrete and commentaryrdquo 318-05 Farmington Hills
MIAmerican Concrete Institute (ACI) (2008) ldquoBuilding code requirements
for structural concrete and commentaryrdquo 318-08 Farmington Hills
MIBari MS(2000)ldquoPunching shear strength of slab-column connectionsmdashA
comparative study of different codesrdquo J Inst Engineers (India) 80(4)163ndash168
Bernardo L F A and Lopes S M R (2009) ldquoTorsion in high strengthconcrete hollow beamsmdashStrength and ductility analysisrdquo ACI Struc-
tural J 106(1) 39ndash48British Standards Institution(BSI) (1985)ldquoStructuraluse of concrete Code
of practice for special circumstancesrdquo BS 811085 Part-2 London
British Standards Institution(BSI) (1997)ldquoStructuraluse of concrete Codeof practice for design and constructionrdquo BS 811097 London
Chiu H J Fang I K Young W T and Shiau J K (2007) ldquoBehavior
of reinforced concrete beams with minimum torsional reinforcementrdquo Eng Structures 29(9) 2193ndash2205
Jung S and Kim KS (2008) ldquoKnowledge-based prediction on shear strength of concrete beams without shear reinforcementrdquo Eng Struc-
tures 30(6) 1515ndash1525Ngo D T (2001) ldquoPunching shear resistance of high-strength concrete
slabsrdquo Electron J Structural Eng 1(1) 2ndash14
Sharma A K and Innis B C (2006) ldquoPunching shear strength of slab-column connectionmdashA comparative study of different codesrdquo ASCE
Conf Proc Structural Engineering and Public Safety 2006 StructuresCongress ASCE Reston VA 1ndash11
Subramanian N (2005) ldquoEvaluation and enhancing the punching shear resistance of 1047298at slabs using high strength concreterdquo Indian Concr J79(4) 31ndash37
224 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013
Acp 5 area enclosed by outside perimeter of concrete
cross section
Al 5 area of longitudinal reinforcement to resist torsion
Al min 5 minimum area of longitudinal reinforcement to
resist torsion
Ao 5 gross area enclosed by shear 1047298ow path
Aoh 5 area enclosed by centerline of the outermost closed
transverse torsional reinforcement
As 5 area of longitudinal tension reinforcement to resist
bending moment
Asmin 5 minimum area of 1047298exural reinforcement to resist
bending moment
Asv 5 area of shear reinforcement to resist shear
Asvt 5 area of two legs of stirrups required for torsion At 5 area of one leg of a closed stirrup resisting torsion
At min 5 minimum area of shear reinforcement to resist
torsion
a 5 depth of equivalent rectangular stress block
b 5 width of section 1047298ange
bw 5 width of section web
d 5 effective depth of tension reinforcement (distance
from extreme compression 1047297ber to centroid of
longitudinal tension reinforcement)
f 9c 5 characteristic cylinder compressive strength of
concrete (150 mm 3 300 mm)
f cu 5 characteristic strength of concrete
(1503
1503
150 mm concrete cube strength) f y 5 characteristic yield strength of longitudinal
reinforcement for 1047298exure
f yl 5 characteristic yield strength of longitudinal
reinforcement for torsion
f yv 5 characteristic yield strength of transverse
reinforcement
h 5 overall depth of section
hmax 5 larger dimension of rectangular cross section
hmin 5 smaller dimension of rectangular cross section
L 5 effective beam span
M u 5 ultimate 1047298exural moment
ph 5 perimeter of centerline of outermost closed
transverse torsional reinforcement
S 5 center-to-center spacing of transverse reinforcement
S v 5 spacing of stirrups
T cr 5 torsional cracking moment
T n 5 nominal torsional moment strength
T u 5 ultimate design twisting moment
V c 5 nominal shear strength provided by concrete
V u 5 ultimate shear force
v 5 design shear stress
vc 5 concrete shear strength
vt 5 torsional shear stress
vt min 5 minimum torsional shear stress above which
reinforcement is required
vtu 5 maximum combinedshear stress (shear plustorsion)
x 1 5 smaller center to center dimension of rectangular
stirrups y1 5 larger center to center dimension of rectangular
stirrups
Z 5 lever arm
g m 5 partial safety factor for strength of material
u 5 angle between axis of strut compression diagonal
and tension chord of the member
r 5 reinforcement ratio ( As=bd ) and
f 5 strength reduction factor
References
Alnuaimi A S and Bhatt P (2006) ldquo
Design of solid reinforced concretebeamsrdquo Structures Buildings 159(4) 197ndash216Ameli M and Ronagh H R (2007) ldquoTreatment of torsion of reinforced
concrete beams in current structural standardsrdquo Asian J Civil Eng
for structural concrete and commentaryrdquo 318-05 Farmington Hills
MIAmerican Concrete Institute (ACI) (2008) ldquoBuilding code requirements
for structural concrete and commentaryrdquo 318-08 Farmington Hills
MIBari MS(2000)ldquoPunching shear strength of slab-column connectionsmdashA
comparative study of different codesrdquo J Inst Engineers (India) 80(4)163ndash168
Bernardo L F A and Lopes S M R (2009) ldquoTorsion in high strengthconcrete hollow beamsmdashStrength and ductility analysisrdquo ACI Struc-
tural J 106(1) 39ndash48British Standards Institution(BSI) (1985)ldquoStructuraluse of concrete Code
of practice for special circumstancesrdquo BS 811085 Part-2 London
British Standards Institution(BSI) (1997)ldquoStructuraluse of concrete Codeof practice for design and constructionrdquo BS 811097 London
Chiu H J Fang I K Young W T and Shiau J K (2007) ldquoBehavior
of reinforced concrete beams with minimum torsional reinforcementrdquo Eng Structures 29(9) 2193ndash2205
Jung S and Kim KS (2008) ldquoKnowledge-based prediction on shear strength of concrete beams without shear reinforcementrdquo Eng Struc-
tures 30(6) 1515ndash1525Ngo D T (2001) ldquoPunching shear resistance of high-strength concrete
slabsrdquo Electron J Structural Eng 1(1) 2ndash14
Sharma A K and Innis B C (2006) ldquoPunching shear strength of slab-column connectionmdashA comparative study of different codesrdquo ASCE
Conf Proc Structural Engineering and Public Safety 2006 StructuresCongress ASCE Reston VA 1ndash11
Subramanian N (2005) ldquoEvaluation and enhancing the punching shear resistance of 1047298at slabs using high strength concreterdquo Indian Concr J79(4) 31ndash37
224 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013