ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8
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Seismic design of steel building accordance to
Eurocode 3 and 8
Valentinos Neophytou BEng, MSc
JULY 2013
-‐Worked examples – Hand calculations
ETABS manual
Page 2
ABOUT THIS DOCUMENT
This publication provides a concise compilation of selected rules in the Eurocode 8, together
with relevant Cyprus National Annex, that relate to the design of common forms of concrete
building structure in the South Europe. It id offers a detail view of the design of steel framed
buildings to the structural Eurocodes and includes a set of worked examples showing the
design of structural elements with using software (CSI ETABS). It is intended to be of
particular to the people who want to become acquainted with design to the Eurocodes. Rules
from EN 1998-1-1 for global analysis, type of analysis and verification checks are presented.
Detail design rules for steel composite beam, steel column, steel bracing and composite slab
with steel sheeting from EN 1998-1-1, EN1993-1-1 and EN1994-1-1 are presented. This
guide covers the design of orthodox members in steel frames. It does not cover design rules
for regularities. Certain practical limitations are given to the scope.
Due to time constraints and knowledge, I may not be able to address the whole issues.
Please send me your suggestions for improvement. Anyone interested to share his/her
knowledge or willing to contribute either totally a new section about Eurocode 8 or within
this section is encouraged.
For further details:
My LinkedIn Profile:
http://www.linkedin.com/profile/view?id=125833097&trk=hb_tab_pro_top
Email: valentinos_n@hotmail.com
Slideshare Account: http://www.slideshare.net/ValentinosNeophytou
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List of contents
1.1 DESIGN AND ANALYSIS EXAMPLE OF STEEL FRAME WITH CONCENTRIC BRACING ................................................................................................................................. 7
1.1 LAYOUT OF STRUCTURE ............................................................................................... 7
1.2 PRELIMINARY DESIGN................................................................................................... 9
1.2.1 PRELIMINARY DESIGN OF COLUMNS AND BEAMS ............................................ 9
1.3 MATERIAL PROPERTIES .............................................................................................. 11
1.3.1 MATERIAL PROPERTIES OF CONCRETE ............................................................... 11
1.3.2 MATERIAL PROPERTIES OF STEEL ........................................................................ 12
1.3.3 MATERIAL PROPERTIES OF STEEL AND CONCRETE AS DEFINE IN ETABS 13
1.3.4.1 MODELING REQUIREMENTS OF EC8 FOR CONCRETE MEMBERS ............... 15
1.3.4.2 MODELING REQUIREMENTS OF EC8 FOR FLOOR DIAPHRAGMS ................ 15
1.3.4.3 MESHING OF SLABS ................................................................................................ 16
1.4 JOINT MODELING (EN1993-1-1,CL.5.1.2) ................................................................... 17
2.0 MODAL RESPONSE SPECTRUM ANALYSIS ............................................................. 20
2.1 STRUCTURAL TYPES AND BEHAVIOR FACTOR ACCORDING TO EN1998-1-1,CL.6.3 ................................................................................................................................... 20
2.2 DEFINE DESIGN HORIZONTAL RESPONSE SPECTRUM ........................................ 24
2.2.1 VERTICAL RESPONSE SPECTRUM (EN1998-1-1,CL.3.2.2.3) ................................ 24
2.2.2 HORIZONTAL RESPONSE SPECTRUM (EN1998-1-1,CL.3.2.2.5) .......................... 24
2.2.3 PARAMETERS OF ELASTIC RESPONSE SPECTRUM (EN1998-1-1,CL.3.2.2.5) .. 25
2.2.3.1 GROUND INVESTIGATION CONDITIONS ........................................................... 29
2.2.3.2 IMPORTANCE FACTOR ........................................................................................... 29
2.2.3.3 DUCTILITY CLASS ................................................................................................... 30
2.3 ANALYSIS TYPES .......................................................................................................... 31
2.3.1 MODAL RESPONSE SPECTRUM ANALYSIS .......................................................... 31
2.3.1.1 ACCIDENTAL ECCENTRICITY .............................................................................. 32
2.3.2 LATERAL FORCE ANALYSIS REQUIREMENTS .................................................... 34
2.3.4 ESTIMATION OF FUNDAMENTAL PERIOD T1 ...................................................... 35
2.3.5 AUTOMATIC LATERAL FORCE ANALYSIS USING ETABS ................................ 36
2.3.6 USER LOADS - LATERAL FORCE ANALYSIS USING ETABS ............................. 38
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2.3.7 TORSIONAL EFFECTS ................................................................................................ 45
2.3.8 SUMMARY OF ANALYSIS PROCESS IN SEISMIC DESIGN SITUATION ........... 46
3.0 DEFINE STATIC LOADS ................................................................................................ 47
4.0 SEISMIC MASS REQUIREMENTS ACCORDING TO EC8 ......................................... 48
4.1 MASS SOURCE OPTION ................................................................................................ 49
5.0 WIND LOADING ON STRUCTURE (EN1991-1-4:2004) .............................................. 51
5.1 CALCULATION OF WIND LOAD ACCORDING TO EN1991-1-4:2004 .................... 51
5.2 APPLICATION OF WIND LOADING USING ETABS ................................................. 54
6.0 LOAD COMBINATION ................................................................................................... 59
7.0 DESIGN PREFERENCES ................................................................................................ 61
8.0 ANALYSIS AND DESIGN REQUIREMENTS FOR CONCENTRICALLY BRACED FRAMES ACCORDING TO EN1998-1-1,CL.6.7.2 .............................................................. 64
8.1 STEPS OF THE DESIGN DETAIL OF CONCENTRIC STEEL FRAMES ................... 65
8.2 CLASSIFICATION OF STEEL SECTIONS .................................................................... 66
8.3 DESIGN OF COMPOSITE SLAB UNDER GRAVITY LOADS .................................... 68
8.4 DESIGN OF COMPOSITE BEAM (WITH STEEL SHEETING) UNDER GRAVITY LOADS .................................................................................................................................... 72
8.5 DETAIL DESIGN OF STEEL COLUMNS UNDER GRAVITY LOADS ...................... 79
8.6 DETAIL DESIGN RULES OF STEEL CONCENTRIC BRACED FRAMES (CBF) ACCORDING TO EUROCODE 8 .......................................................................................... 87
8.6.1 DETAIL DESIGN RULES OF STEEL BRACING ACCORDING TO EUROCODE 8.................................................................................................................................................. 87
8.7 DETAIL DESIGN RULES OF STEEL COLUMNS AND BEAMS ACCORDING TO EUROCODE 8 ......................................................................................................................... 88
8.8 DETAIL DESIGN RULES OF STEEL COMPOSITE MEMBERS ACCORDING TO EUROCODE 8 ......................................................................................................................... 89
8.9 DETAIL DESIGN RULES OF STEEL MOMENT RESISTANCE FRAMES (MRF) ACCORDING TO EUROCODE 8 .......................................................................................... 90
8.9.1 DETAIL DESIGN RULES FOR MRF - DESIGN CRITERIA .................................... 90
8.9.2 DETAIL DESIGN RULES OF STEEL BEAM FOR MRF ........................................... 90
8.9.3 DETAIL DESIGN RULES OF STEEL COLUMN FOR MRF ..................................... 91
9.0 DESIGN OF STEEL FRAMES ......................................................................................... 92
9.1 DESIGN OF STEEL MEMBER OVERWRITES DATA ................................................. 92
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9.2 DESIGN OF COLUMNS / BEAMS USING ETABS – GRAVITY LOAD ANALYSIS ONLY ...................................................................................................................................... 97
9.3 DESIGN OF STEEL COLUMN (GRAVITY DESIGN SITUATION) – HAND CALCULATIONS ................................................................................................................. 105
9.4 DESIGN OF STEEL COLUMN (SEISMIC DESIGN SITUATIONN) ......................... 118
9.4.1 DESIGN OF STEEL COLUMN (SEISMIC DESIGN SITUATION – HAND CALCULATION) .................................................................................................................. 124
9.5 DESIGN OF COMPOSITE BEAMS - HAND CALCULATIONS ................................ 128
9.5 DESIGN OF STEEL BRACING ..................................................................................... 145
9.5.1 MAIN CONFIGURATION OF DESIGN OF STEEL BRACING .............................. 145
9.5.2 SIMPLIFIED DESIGN OF FRAMES WITH X BRACING (EXTRACT FROM DESIGN GUIDANCE TO EC8) ........................................................................................... 147
9.5.3 MODEL IN ETABS ..................................................................................................... 148
9.5.4 DESIGN OF STEEL BRACING (GRAVITY/SEISMIC DESIGN SITUATION) – HAND CALCULATION ....................................................................................................... 156
10.0 MODAL RESPONSE SPECTRUM ANALYSIS ......................................................... 170
10.1 SET THE ANALYSIS OPTIONS ................................................................................. 170
10.2 EVALUATE THE ANALYSIS RESULTS OF THE STRUCTURE ACCORDING TO THE MODAL ANALYSIS REQUIREMENTS ................................................................... 171
10.2.1 ASSESS THE MODAL ANALYSIS RESULTS BASED ON THE EN1998 ........... 172
11.0 SECOND ORDER EFFECTS (P – Δ EFFECTS) ACCORDING TO EN1998-1-1,CL.4.4.2.2 ........................................................................................................................... 173
11.1 DISPLACEMENT CALCULATION ACCORDING TO EN1998-1-1,CL.4.4.2.2 ..... 174
11.2 INTERSTOREY DRIFT ................................................................................................ 174
11.3 CALCULATION OF SECOND ORDER EFFECT USING ETABS ........................... 175
11.3.1 INTERSTOREY DRIFT DISPLACEMENT ............................................................. 176
11.3.2 TOTAL GRAVITY LOAD PTOT ................................................................................ 178
11.3.2 TOTAL SEISMIC STOREY SHEAR VTOT ............................................................... 180
12.0 DAMAGE LIMITATION ACCORDING TO EN1998-1-1,CL.4.4.3 .......................... 184
12.1 CALCULATION OF DAMAGE LIMITATION .......................................................... 185
ANNEX - A .......................................................................................................................... 186
ANNEX A.1 - ASSUMPTIONS MADE IN THE DESIGN ALGORITHM (MANUAL OF ETABS – EC3 & EC8) .......................................................................................................... 186
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A1.1:LIMITATION MADE IN THE DESIGN ALGORITHM (MANUAL OF ETABS – EC3&EC8) ............................................................................................................................. 187
ANNEX –B: STEEL DESIGN FLOWCHARTS .................................................................. 188
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1.1 Design and analysis example of steel frame with concentric bracing
1.1 Layout of structure
Figure 1.1: Plan view
Figure 1.2: Side Elevation (4) & (1)
Page 8
Figure 1.3: Side Elevation (A) & (D)
Table 1.1: Dimensions of the building
Dimensions Symbol Value Units
Storey height h 3.0 m
Total height of the building H 9.0 m
Beam length in X-direction lx 5.0 m
Beam length in Y-direction ly 5.0 m
Building width in X-direction Lx 15.0 m
Building width in Y-direction Ly 15.0 m
Page 9
1.2 Preliminary design
Table 1.2: Seismic design data
Data Symbol Value Units
Seismic zone - 3 -
Reference peak ground acceleration on type A ground, agR.
agR 0.25 m/s2
Importance class γI 1.0 -
Design ground acceleration on type A ground ag 0.25 m/s2
Design spectrum - Type 1 -
Ground type - B -
Structural system Steel frame with concentric bracing
Behavior factor q 4.0 -
1.2.1 Preliminary design of columns and beams
Preliminary design of steel beam
Design data:
Span of beam
Bay width
Overall depth of slab
Loading data:
Density of concrete
Loads of floor per meter
Live load
Live load per meter
Partial factor for actions:
Safety factor are obtain from Table A.1(2)B EN1990 Permanent actions, γ G
Variable actions, γ Q
Total load
Lx 5000mm:=
wbay 5000mm:=
h 130mm:=
γ c 25kNm 3−⋅:=
gfloor γ c h⋅ Lx⋅ 16.25 kNm 1−⋅⋅=:=
qoffice 2kNm 2−⋅:=
qservice qoffice Lx⋅ 10 kNm 1−⋅⋅=:=
γG 1.35:=
γQ 1.5:=
Ed γG gfloor⋅ γQ qservice⋅+ 36.94 kNm 1−⋅⋅=:=
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Material properties:
Young Modulus of Elasticity
Structural steel (clause 6.1(1) EN 1993 1-1)
Structural steel properties:
Yield strength, fy
Ultimate strength, fu
Yield strength of reinforcement, fyk
Deflection limitation:
Deflection limit - General purpose
Second moment area required
Second moment area provided (IPE240)
Moment resistance check:
Design moment (Fixed end)
Plastic modulus required
Plastic modulus provided (IPE240)
Weak Beam - Strong column -Capacity design:
Plastic modulus of column required
Plastic modulus of column provided (HE220A)
Es 210kNmm 2−⋅:=
γM0 1.0:=
fy 355N mm 2−⋅:=
fu 450N mm 2−⋅:=
fyk 500N mm 2−⋅:=
FLx300
:=
Ireq300 Ed⋅ Lx
3⋅
384 Es⋅1.718 103× cm4⋅=:=
Iprov 3892cm4:=
Check_1 if Iprov Ireq> "OK", "NOT OK", ( ):=
Check_1 "OK"=
MEdEd Lx
2⋅
1276.953kNm⋅⋅=:=
Wpl.y.reqMEdfy
216.769cm3⋅=:=
Wpl.y 324.4cm3:=
Check_2 if Wpl.y Wpl.y.req> "OK", "NOT OK", ( ):=
Check_2 "OK"=
Wpl.y.c.req 1.3Wpl.y⋅ 421.72cm3=:=
Wpl.y.c 515cm3:=
Check_3 if Wpl.y.c Wpl.y.c.req> "OK", "NOT OK", ( ):=
Check_3 "OK"=
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1.3 Material properties
ETABS: Define > Material properties
1.3.1 Material properties of concrete
Design requirement Poisson ratio is equal to v = 0 (cracked concrete) and v = 0.2 (un-cracked concrete) as
(EN1992-1-1,cl.3.1.3).
Table 1.3: Concrete properties (EN 1992, Table 3.1)
Property Data for concrete
C16/20
(N/mm2)
C20/25
(N/mm2)
C25/30
(N/mm2)
C30/37
(N/mm2)
Mass per unit Volume 2,5E-09 2,5E-09 2,5E-09 2,5E-09
Weight per unit volume 2,5E-05 2,5E-05 2,5E-05 2,5E-05
Modulus of Elasticity 29000 30000 31000 33000
Poisson’s Ratio (cracked concrete) 0 0 0 0
Coeff. of thermal expansion 10E-06 10E-06 10E-06 10E-06
Charact. ConcCyl. Strength, fck 16 20 25 30
Bending Reinf. Yield stress, fyk 500 500 500 500
Shear Reinf. Yield stress, fyk 500 500 500 500
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1.3.2 Material properties of steel
Table 1.4: Material properties of steel
Material Properties Symbol Value Units References
Mass per unit Volume γs 7.85E-09 kg/mm3 EN1991-1-1,table A.4
Weight per unit Volume
γs 7.70E-05 N/mm3 EN1991-1-1,table A.4
Modulus of Elasticity Es 210,000 N/mm2 EN1993-1-1,cl.3.2.6(1)
Poisson’s ratio ν 0.3 - EN1993-1-1,cl.3.2.6(1)
Coeff of Thermal Expansion (Steel structures)
α 1.2x10-5 per K (for T ≤ 100oC) K EN1993-1-1,cl.3.2.6(1)
Coeff of Thermal Expansion (Composite Concrete-Steel structures)
α 1.2x10-5 per K (for T ≤ 100oC) K EN1993-1-1,cl.3.2.6(1)
Shear Modulus G ≈81,000 N/mm2 EN1993-1-1,cl.3.2.6(1)
Characteristic yield strength of steel profile
fy 275 N/mm2 EN1993-1-1,table 3.1
Ultimate strength fu 430 N/mm2 EN1993-1-1,table 3.1
Table 1.5: Strength vales of steel sections (EN1993-1-1,table 3.1)
Steel grade
Nominal thickness of the element t (mm)
t ≤ 40mm 40mm < t ≤ 80mm Grade
reference fy (N/mm2) fu (N/mm2) fy (N/mm2) fu (N/mm2)
S235 235 360 215 360 EN 10025-2
S275 275 430 255 410 EN 10025-2
S355 355 510 335 470 EN 10025-2
S450 440 550 410 550 EN 10025-2
Note: You may use the product standard instead of those given in EN1993-1-1
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1.3.3 Material properties of steel and concrete as define in ETABS
Figure 1.4: Material properties of concrete (C25/30)
Figure 1.5: Material properties of steel (S275)
1.3.4 Slab modeling
Page 14
Table 1.6: Slab properties
Data Symbol Value Units
Slab depth hs 170 mm
Diameter of stud d 19 mm
Height of stud haw 152 mm
Tensile strength of stud fu 430 N/mm2
ETABS: Define > Wall/Slab/Deck Sections/Add new deck
Figure 1.6: Deck section properties
Press “Set Modifier” in order to modify the slab properties
Page 15
1.3.4.1 Modeling requirements of EC8 for concrete members
1. Unless a more accurate analysis of the cracked elements is performed, the elastic
flexural and shear stiffness properties of concrete and masonry elements may be taken
to be equal to one-half of the corresponding stiffness of the un-cracked elements
(EN1998-1-1,cl.4.3.1(7)).
Figure 1.7: Modified “Stiffness Modifiers”
1.3.4.2 Modeling requirements of EC8 for floor diaphragms
ETABS: Select > Wall/Slab/Deck section > Select Deck
ETABS: Define > Diaphragms
ETABS: Select “D1” (Rigid diaphragms)
2. When the floor diaphragms of the building may be taken as being rigid in their planes,
the masses and the moments of inertia of each floor may be lumped at the centre of
gravity (EN1998-1-1,cl.4.3.1(4)).
Page 16
1.3.4.3 Meshing of slabs
ETABS: Select > Wall/Slab/Deck section > Select Deck
ETABS: Assign > Shell area > Auto Object Auto mesh option
When you have a composite beam floor system, ETABS, by default, automatically meshes
(divides) the deck at every beam and girder. This allows ETABS to automatically distribute
the loading on the deck to each beam or girder in an appropriate manner.
Figure 1.8: Meshing of composite slab
Figure 1.9: Meshing of normal slab
Page 17
1.4 Joint modeling (EN1993-1-1,cl.5.1.2)
(1) The effects of the behavior of the joints on the distribution of internal forces and
moments within a structure, and on the overall deformations of the structure, may
generally be neglected, but where such effects are significant (such as in the case of
semi-continuous joints) they should be taken into account, see EN 1993-1-8.
(2) (2) To identify whether the effects of joint behavior on the analysis need be taken into
account, a distinction may be made between three joint models as follows, see EN
1993-1-8, 5.1.1:
– simple, in which the joint may be assumed not to transmit bending
moments.
– continuous, in which the behavior of the joint may be assumed to have no
effect on the analysis.
– semi-continuous, in which the behavior of the joint needs to be taken into
account in the analysis.
Page 18
Table 1.7: Example of joint types
Simple joint Continuous Fixed joint Semi- continuous joint
ETABS: Pin joint in ETABS The pin-joint in ETABS can be achieved by selecting the members that you assumed to be
pinned in the analysis process. This can be done as follow:
Select member > Assign > Frame/Line > Frame Releases Partial Fixity
Figure 1.10: Pinned joint (both ends)
Page 19
ETABS: Fixed joint in ETABS The fixed-joint in ETABS can be achieved by selecting the members that you assumed to be
fixed in the analysis process. This can be done as follow:
Select member > Assign > Frame/Line > Frame Releases Partial Fixity
Figure 1.11: Fixed joint
Page 20
2.0 Modal Response Spectrum Analysis
2.1 Structural types and behavior factor according to EN1998-1-1,cl.6.3
Table 2.1: Structural types and behavior factor
Structural Type q-factor DCM DCH
Moment resisting frames (MRF)
αu/ α1 =1.1 αu/ α1 =1.2 (1 bay) αu/ α1 =1.3 (multi-bay)
dissipative zones in beams and column bases
4 5αu/ α1
Concentrically braced frames (CBF)
Dissipative zones in tension diagonals
4 4
V-braced frames (CBF)
2 2.5
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Dissipative zones in tension and compression diagonals
Frames with K-bracing (CBF)
Not allowed in dissipative design
Eccentrically braced frame (EBF)
αu/ α1 =1.2 dissipative zones in bending or shear links
4 5αu/ α1
Inverted pendulum system
αu/ α1 =1.0 αu/ α1 =1.1
dissipative zones in column base, or column ends (NEd/Npl,Rd < 0.3)
2 2αu/ α1
Moment-resisting frames with concentric bracing (MRF) + (CBF)
4 4αu/ α1
Page 22
αu/ α1 =1.2
dissipative zones in moment frame and tension diagonals Moment frames with infills
Unconnected concrete or masonry infills,
in contact with the frame
2 2
Connected reinforced concrete
Infills
See EN1998-1-1,table 5.1
Infills isolated from moment frame
4 5αu/ α1
Structures with concrete cores or walls
See EN1998-1-1,table
5.1
Note: If the building is non-regular in elevation (see EN1998-1-1,cl.4.2.3.3) the upper limit values of q listed above should be reduced by 20 %
Page 23
Table 2.2: Values of behavior factor for regular and irregular structure
Structural type Regular in plan
and elevation
Irregular in
plan / Regular
in elevation
Regular in plan
/ Irregular in
elevation
Irregular in
plan &
elevation
Irregular in
plan / Regular
in elevation
Regular in plan
/ Irregular in
elevation
Irregular in
plan &
elevation
DCM DCH DCM DCM DCM DCH DCH DCH
Moment resisting frame
Single storey portal 4.0 5.5 3.2 3.2 3.2 5.25 4.4 4.2
One bay multi-storey 4.0 6.0 3.2 3.2 3.2 5.5 4.8 4.4
Multi-bay, multi-storey 4.0 6.5 3.2 3.2 3.2 5.75 5.2 4.6
Concentrically braced frame
Diagonal bracing 4.0 4.0 3.2 4.0 4.0 4.0 3.2 3.2
V-bracing 2.0 2.5 1.6 2.5 2.5 2.5 2.0 2.0
Frame with masonry infill
panels 2.0 2.0 1.6 2.0 2.0 2.0 1.6 1.6
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2.2 Define design horizontal response spectrum
2.2.1 Vertical response spectrum (EN1998-1-1,cl.3.2.2.3)
The vertical component of the seismic action should be taken into account if the avg>0.25g
(2.5m/s2) in the cases listed below:
• for horizontal structural member spanning 20m or more,
• for horizontal cantilever components longer than 5m,
• for horizontal pre-stressed components,
• for beams supporting columns,
• in based-isolated structures.
2.2.2 Horizontal response spectrum (EN1998-1-1,cl.3.2.2.5)
For the horizontal components of the seismic action the design spectrum, Sd(T), shall be
defined by the following expressions:
0 ≤ 𝑇 ≤ 𝑇!: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙!!+ !
!!∙ !.!
!− !
!(ΕΝ1998-1-1,Eq. 3.13)
𝑇! ≤ 𝑇 ≤ 𝑇!: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙!.!!
(ΕΝ1998-1-1,Eq. 3.14)
𝑇! ≤ 𝑇 ≤ 𝑇!: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙2.5𝑞
𝑇!𝑇
≥ 𝛽 ∙ 𝑎! (ΕΝ1998-1-1,Eq. 3.15)
𝑇! ≤ 𝑇 ≤ 4𝑠: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙!.!!
!!!!!!
≥ 𝛽 ∙ 𝑎! (ΕΝ1998-1-1,Eq. 3.5)
Design ground acceleration on type A ground: ag=γIagR
Lower bound factor for the horizontal spectrum: β=0.2
Note: the value of q are already incorporate with an appropriation value of damping viscous,
however the symbol η is not present in the above expressions.
Page 25
2.2.3 Parameters of elastic response spectrum (EN1998-1-1,cl.3.2.2.5)
Table 2.3: Parameters of Type 1 elastic response spectrum (CYS NA EN1998-1-1,table
3.2)
Ground
Type
S TB (s) TC (s) TD (s)
A 1.0 0.15 0.4 2.0
B 1.2 0.15 0.5 2.0
C 1.15 0.20 0.6 2.0
D 1.35 0.20 0.8 2.0
E 1.4 0.15 0.5 2.0
Note: For important structures (γI>1.0), topographic amplification effects should be taken
into account (see Annex A EN1998-5:2004 provides information for topographic
amplification effects).
ETABS: Define > Response spectrum function
1. Peak ground acceleration agR=0,25g,
2. Type C or D for building within category of importance I and II,
3. Define two response spectrum cases if the factor q is different in each direction,
Select EUROCODE8 Spectrum
Add New Function
Page 26
4. Modify the existing values of elastic response spectrum case in order to change it into
the design response spectrum.
Figure 2.1: Response Spectrum to EC8
PERIOD ACCELERATION g = 9.81 m/sec2
T Sd(T) β = 0.2 -‐
0.0000 0.2000 SoilType = B -‐
0.1000 0.1917 q = 4.00 -‐
0.1500 0.1875 αgR = 0.25 -‐
0.2000 0.1875 S = 1.20 -‐
0.4000 0.1875 TB = 0.15 sec
0.6000 0.1563 TC = 0.50 sec
0.8000 0.1172 TD = 2.00 sec
1.0000 0.0938 T = 0.50 sec
1.5000 0.0625 2.0000 0.0469 Data for soil type -‐ Type Spectrum 1 2.5000 0.0300 index Soil Type S TB TC TD 3.0000 0.0500 1 A 1 0.15 0.4 2 4.0000 0.0500 2 B 1.2 0.15 0.5 2 5.0000 0.0500 3 C 1.15 0.2 0.6 2 6.0000 0.0500 4 D 1.35 0.2 0.8 2 8.0000 0.0500 5 E 1.4 0.15 0.5 2 10.0000 0.0500
Convert the existing elastic response spectrum case to design response
spectrum case
Page 27
Page 28
Figure 2.2: Amendment Response spectrum (q = 4)
Page 29
2.2.3.1 Ground investigation conditions
Table 2.4: Geological studies depend on the importance class (CYS NA EN1998-1-1, NA
2.3 / cl.3.1.1 (4))
Importance class of buildings
Ground
Type
I II III IV
A NRGS NRGS RGS RGS
B NRGS NRGS RGS RGS
C NRGS NRGS RGS RGS
D NRGS NRGS RGS RGS
E NRGS NRGS RGS RGS
NRGS: Not required geological studies
RGS: required geological studies if there is not adequate information
2.2.3.2 Importance factor
Table 2.5: Importance classes for buildings (ΕΝ1998-1-1,table.4.3 and CYS NA EN1998-
1-1,cl NA2.12)
Importance
class
Buildings Important
factor γI
Consequences
Class
I Buildings of minor importance for public
safety, e.g. argricultural buildings, etc. 0.8 CC1
II Ordinary buildings, not belonging in the other
categories. 1.0 CC2
III
Buildings whose seismic resistance is of
importance in view of the consequences
associated with a collapse, e.g. schools,
assembly halls, cultural institutions etc.
1.2 CC3
IV
Buildings whose integrity during earthquakes
is of vital importance for civil protection, e.g.
hospitals, fire stations, power plants, etc.
1.4 CC3
Page 30
CC1: Low consequence for loss of human life, and economic, social or environmental
consequences small or negligible.
CC2: Medium consequence for loss of human life, economic, social or environmental
consequences considerable.
CC3: High consequence for loss of human life, or economic, social or environmental
consequences very great
2.2.3.3 Ductility class
Table 2.6: Requirement for importance class relate to ductility class (CYS NA EN1998-
1-1,cl NA2.16 & cl.5.2.1(5))
Importance
class Zone 1 Zone 2 Zone 3
I DCL DCL DCL
II DCM/DCH DCM/DCH DCM/DCH
III DCM/DCH DCM/DCH DCM/DCH
IV DCH DCH DCH
DCL: Ductility class low.
DCM: Ductility class medium.
DCH: Ductility class high.
Page 31
2.3 Analysis types
2.3.1 Modal Response spectrum analysis
Table 2.7: Requirements of modal response spectrum analysis according to Eurocode 8
Requirements Values References
Regular in plan YES / NO ΕΝ1998-1-1,table 4.1
Regular in elevation NO ΕΝ1998-1-1,table 4.1
Sum of the effective
modal masses
≥ 90% EN1998-1-1,cl.4.3.3.1(3)
≥ 5% of total mass
Minimum number of
modes
k ≥3.√n
k: is the number of modes
n: is the number of storey
EN1998-1-1,cl.4.3.3.1(5)
Behaviour factor q
Tk ≤ 0.20sec
Tk: is the period of vibration of
mode k.
EN1998-1-1,cl.4.3.3.1(5)
Fundamental period Tj ≤ 0.9 Ti SRSS
EN1998-1-1,cl.4.3.3.2.1(2) Tj ≥ 0.9 Ti CQC
Accidental eccentricity See section 2.1.1.1 EN1998-1-1,cl.4.3.2
1. Independently in X and Y direction,
2. Define design spectrum,
3. Use CQC rule for the combination of different modes (EN1998-1-1,cl.4.3.3.3.2(3))
4. Use SRS rule for combined the results of modal analysis for both horizontal directions
(EN1998-1-1,cl.4.3.3.5.1(21)).
5. Modal Combination: “Complete Quadratic Combination” (CQC) can be used if the Tj
≤ 0,9 Ti (EN1998-1-1,cl.4.3.3.3.2(3)P).
Page 32
2.3.1.1 Accidental eccentricity
Accidental eccentricity of each storey cause of uncertainties location of masses have been
taken into account 5% (EN1998-1-1,cl.4.3.2). Moreover, if there are masonry infills with a
moderately irregular and asymmetric distribution in plan, is doubled further in Eurocode 8
(i.e., to 10% of the storey orthogonal dimension in the baseline case, or 20% if accidental
torsional effects are evaluated in a simplified way when using two separate 2D models).
Table 2.8: Summary of accidental eccentricity
Percentage of
accidental
eccentricity
Geometry
of model
(3D/2D)
Asymmetric
distribution of mass
(Regular/Irregular)
Masonry infills
(Regular/Irregular)
5% 3D Regular Regular
10% 3D Irregular Irregular
20% 2D - -
Note: Accidental eccentricity is automatically included during response-spectrum analysis in
ETABS, though equivalent static-load procedures are also available for manual evaluation.
Note that floor diaphragms must be rigid, otherwise torsional effects are not substantial.
ETABS implements an efficient and practical approach while formulating dynamic response
from accidental eccentricity. After the response-spectrum load case is run, the X and Y
acceleration at each joint location is determined, then multiplied by the tributary mass and the
diaphragm eccentricity along either Y or X. The larger absolute value of these resultant
moments (m*Xacc*dY or m*Yacc*dX) is then applied as torsion about the joint location.
Static response is then added to response-spectrum output to account for the additional design
forces caused by accidental eccentricity.
Page 33
Define > Response spectrum cases
Note: Add two response spectrum cases: EQX and EQY as showing below (figure 9).
Figure 2.3: Response Spectrum case Data for EQY& EQX
Page 34
2.3.2 Lateral force analysis requirements
Table 2.9: Requirements of lateral force analysis according to Eurocode 8
Requirements Values References
Regular in plan YES / NO ΕΝ1998-1-1,table 4.1
Regular in elevation YES ΕΝ1998-1-1,table 4.1
Ground acceleration 0.10-0.25g CYS NA EN1998-1-
1:Seismic zonation map
Spectrum type 1 EN1998-1-1,cl.3.2.2.2(2)P
Ground type
A,B,C,D,E
Normally type B or C can be used
normal condition
EN1998-1-1,cl.3.1.2(1)
Lower bound factor for
the horizontal design
spectrum
λ = 0.85 if T1 ≤ 2TC and more than
2 storey
λ=1.0 in all other case
EN1998-1-1,cl.4.3.3.2.2(1Ρ)
Behaviour factor q
Concrete DCM q= 1.5 – 3.90 EN1998-1-1,cl.5.2.2.2(2)
Concrete DCH q= 1.6 – 5.85 EN1998-1-1,cl.5.2.2.2(2)
Steel DCM q= 2.0 – 4.00 EN1998-1-1,cl.6.3.2(1)
Steel DCH q= 2.0 – 5.85 EN1998-1-1,cl.6.3.2(1)
Fundamental period T1≤4Tc
T1≤2,0s EN1998-1-1,cl.4.3.3.2.1(2)
Accidental eccentricity See section 2.1.1.1 EN1998-1-1,cl.4.3.2
Table 2.10: Equivalent Static Force Case
Load case name Direction and Eccentricity % Eccentricity
EQXA X Dir + Eccen. Y 0.05
EQYA X Dir – Eccen. Y 0.05
EQXB Y Dir + Eccen. X 0.05
EQYB Y Dir – Eccen. X 0.05
Page 35
2.3.4 Estimation of fundamental period T1
Table 2.11: Estimation of fundamental period T1
Reference structure Period T1
Exact formula for Single Degree of Freedom
Oscillator. Mass M lumped at top of a vertical
cantilever of height H. Cantilever mass MB = 0. 𝑇! = 2𝜋
𝑀𝐻!
3𝐸𝐼
Exact formula for Single Degree of Freedom
Oscillator. Vertical cantilever of height H and of
total mass MB. 𝑇! = 2𝜋
0.24𝑀!𝐻!
3𝐸𝐼
Exact formula for Single Degree of Freedom
Oscillator. Mass M lumped at top of a vertical
cantilever of height H and of total mass MB. 𝑇! = 2𝜋
𝑀 + 0.24𝑀! 𝐻!
3𝐸𝐼
Approximate Relationship (Eurocode 8).
Ct = 0,085 for moment resisting steel space frames
Ct = 0,075 for eccentrically braced steel frames
Ct = 0,050 for all other structures
𝑇! = 𝐶!𝐻!/!
H building height in m measured from
foundation or top of rigid basement.
Approximate Relationship (Eurocode 8).
d : elastic horizontal displacement of top of
building in m under gravity loads applied
horizontally.
𝑇! = 2 𝑑
Page 36
2.3.5 Automatic Lateral force analysis using ETABS
ETABS: Define > Static load cases
Figure 2.4: Apply the Equivalent Static Force Case
Figure 2.5: Modify the Equivalent Static Force Case
Note: The seismic forces should be applied only above the top of the basement
Page 37
Fundamental period (EN1998-1-1,Eq.4.6) T1=CtH3/4 (For heights up to 40m)
Value of Ct(EN1998-1-1,cl.4.3.3.2.2(3)) Ct = 0.085 (for moment resisting steel frames) Ct= 0.075 (for moment resisting concrete frames) Ct= 0.05 (for all other structures) (EN 1998-1-1:2004, cl. 4.3.3.2.2(3)) Ct= 0.075/√ΣAc(for concrete/masonry shear wall structures) (EN 1998-1-1:2004, Eq. 4.7) Ac= Σ[Ai·(0,2+(lwi/H2))] (EN 1998-1-1:2004, Eq. 4.8)
Fundamental period requirements (EN1998-1-1,Eq.4.6)
T1≤4TCT1≤2sec IF this
YES
LATERAL FORCE
ANALYSIS
RESPONSE SPECTRUM ANALYSIS
Correction factor λ(EN1998-1-
1,cl.4.3.3.2.2(1Ρ)) λ=0.85 if T1≤2TC and more than 2 storey λ=1.0 in all other case
Design spectrum Sd(T)(EN1998-1-
1,cl.3.2.2.5) 0≤T≤TB
TB≤T≤TcTC≤T≤TD
TD≤T
Seismic mass(EN1998-1-1,cl.3.2.4)
ΣGk,j/g”+”ΣψE,i.Qk,i/g (EN 1998-1-1:2004, Eq.3.17)
Base shear(EN1998-1-1,cl.4.3.3.2.2) Fb=Sd(T1).m.λ
(EN 1998-1-1:2004, Eq. 4.5)
Horizontal seismic forces (according to displacement of
the masses)
F! = F! ∙s! ∙m!
s! ∙m!
(EN 1998-1-1:2004, Eq. 4.10)
Horizontal seismic forces (according to height of the
masses)
F! = F! ∙z! ∙m!
z! ∙m!
(EN 1998-1-1:2004, Eq. 4.11)
NO
Page 38
2.3.6 User loads - Lateral force analysis using ETABS
Geometrical data
Span of the longitutinal direction Span of the transverse direction
Span of each beam
Span of each bracing
Height of each column
Total heigh of building
Area of floor for each storey
Number of floors
Number of beams IPE240 at each floor
Number of beams IPE180 at each floor
Number of columns HE280A at each floor
Number of TUBE sections D127-4 at each floor
Lx 15m:=
Ly 15m:=
Lb 5m:=
Lt 5.831m:=
hc 3m:=
H 9m:=
Af Ly Lx⋅ 225m2=:=
Nf 3:=
Nb 24:=
Ns 9:=
Nc 16:=
Nt 8:=
Page 39
Dead load
Weight of steel column HE280A
Weight of primary beams IPE240
Weight of secondary beams IPE180
Weight of steel beams TUBE-D127-4
Slab thickness
Weigth of concrete
Weight of slab
Weigth of finishes
Total dead load
Total dead load
Live load
Combination coefficient for variable action
Live load
Total live load
Total gravity load per storey (EN1998-1-1,cl.3.2.4(2)P)
Total gravity load per storey (EN1998-1-1,cl.3.2.4(2)P)
Seismic mass
gc 76.4kg m 1−⋅:=
gp 30.7kg m 1−⋅:=
gs 18.8kg m 1−⋅:=
gt 12.38kg m 1−⋅:=
hs 170mm:=
γ c 25kNm 3−⋅:=
gslab γ c hs⋅ 4.25 kNm 2−⋅⋅=:=
gfin 1kNm 2−⋅:=
Gk.storey gc Nc⋅ hc⋅ gp Nb⋅ Lb⋅+ gs Ns⋅ Lb⋅+ gt Nt⋅ Lt⋅+( )g gslab Af⋅+ gfin Af⋅+⎡⎣ ⎤⎦ 1.267 103× kN⋅=:=
Gk gc Nc⋅ hc⋅ gp Nb⋅ Lb⋅+ gs Ns⋅ Lb⋅+ gt Nt⋅ Lt⋅+( )g gslab Af⋅+ gfin Af⋅+⎡⎣ ⎤⎦ Nf⋅ 3.802 103× kN⋅=:=
ψEi 0.3:=
qk 2kN m 2−⋅:=
Qk qk Af⋅ 450 kN⋅=:=
FEd.storey Gk.storey ψEi Qk⋅( )+ 1.402 103× kN⋅=:=
FEd Gk ψEi Qk⋅( ) Nf⋅+ 4.207 103× kN⋅=:=
S_massFEdg
4.29 105× kg=:=
Page 40
Horizontal design response Spectrum (EN1998-1-1,cl.3.2.2.5)
Behaviour factor q (EN1998-1-1,cl.6.3)
Lower bound factor (EN1998-1-1,cl.3.2.2.5(4)P)
Seismic zone (CYS NA EN1998-1-1, zonation map)
Importance factor (CYS NA EN1998-1-1,cl. NA2.12)
Design ground acceleration on type A (EN1998-1-1,cl.3.2.1(3))
Value of Ct (EN1998-1-1,cl.4.3.3.2.2(3))
Fundamental period of vibration (EN1998-1-1,cl.4.3.3.2.2(3))
Type of soil (EN1998-1-1,cl.3.1.2(1))
Value of parameters describing the Type 1 elastic response spectrum (EN1998-1-1,table 3.2)
Soil factor, S
q 1.5:=
β 0.2:=
Seismic_zone "3":=
agR 0.15g Seismic_zone "1"if
0.2g Seismic_zone "2"if
0.25g Seismic_zone "3"if
2.452m
s2=:=
Importance_factor "II":=
γ I 0.8 Importance_factor "I"if
1.0 Importance_factor "II"if
1.2 Importance_factor "III"if
1.4 Importance_factor "IV"if
1=:=
ag γ I agR⋅ 2.452m
s2=:=
Value_Ct "OTHER":=
Ct 0.085 Value_Ct "MRSF"if
0.075 Value_Ct "MRCF"if
0.05 Value_Ct "OTHER"if
0.05=:=
T1 CtH
m
⎛⎜⎝
⎞⎟⎠
3
4
⋅
⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦s 0.26s=:=
Soil_type "B":=
S 1.0 Soil_type "A"if
1.2 Soil_type "B"if
1.15 Soil_type "C"if
1.35 Soil_type "D"if
1.2=:=
Page 41
Lower limit of the period, TB
Upper limit of the period, TC
Constant displacement value, TD
Corection factor λ (EN1998-1-1,cl.4.3.3.2.2(1)P)
Check the fundamental period of vibration requirements (EN1998-1-1,cl.4.3.3.2.1(2))
Design spectrum for elastic analysis (EN1998-1-1,cl.3.2.2.5(4)P)
TB 0.15s Soil_type "A"if
0.15s Soil_type "B"if
0.20s Soil_type "C"if
0.20s Soil_type "D"if
0.15s=:=
TC 0.40s Soil_type "A"if
0.50s Soil_type "B"if
0.60s Soil_type "C"if
0.80s Soil_type "D"if
0.5s=:=
TD 2.0s Soil_type "A"if
2.0s Soil_type "B"if
2.0s Soil_type "C"if
2.0s Soil_type "D"if
2s=:=
λ 0.85 T1 2TC≤ Nf 2>∧if
1 otherwise
0.85=:=
Check_1 if T1 4TC≤ T1 2s≤∧ "Lateral force analysis", "Response spectrum analysis", ( ):=
Check_1 "Lateral force analysis"=
S1e T1( ) ag S⋅23
T1TB
2.5q
23
−⎛⎜⎝
⎞⎟⎠
⋅+⎡⎢⎣
⎤⎥⎦
⋅:= S1e 0( ) 1.961 m s 2−⋅⋅=
S2e T1( ) ag S⋅2.5q
⋅:= S2e TB( ) 4.903m s 2−⋅⋅=
S3e T1( ) ag S⋅2.5q
⋅TCT1⋅ ag S⋅
2.5q
⋅TCT1⋅ β ag⋅≥if
β ag⋅( ) β ag⋅ ag S⋅2.5q
⋅TCT1⋅≥if
:= S3e TC( ) 4.903m s 2−⋅⋅=
S4e T1( ) ag S⋅2.5q
⋅TC TD⋅
T12
⋅⎛⎜⎜⎝
⎞⎟⎟⎠
ag S⋅2.5q
⋅TC TD⋅
T12
⋅ β ag⋅≥if
β ag⋅( ) ag S⋅2.5q
⋅TC TD⋅
T1( )2⋅ β ag⋅≤if
:=
Page 42
Design spectrum acceleration
Seismic base shear (EN1998-1-1,cl.4.3.3.2.2(1))
Seismic base shear on each bracing Note: 2 bracing on each direction
S4e T1( ) 72.642m
s2=
Se T( ) if T TB< S1e T( ), if T TC< S2e T( ), if T TD< S3e T( ), S4e T( ), ( ), ( ), ( ):=
T 0.01sec 0.02sec, 4sec..:=
0 1 2 3 40
2
4
6
8
Se T( )
T
Se S1e 0( ) 0 T1≤ TB≤if
S2e TB( ) TB T1≤ TC≤if
S3e TC( ) TC T1≤ TD≤if
S4e T1( ) TD T1≤ 4s≤if
4.903m
s2=:=
Fb S_mass Se⋅T1s
⋅ λ⋅ 464.519kN⋅=:=
Fb.bracingFb2
232.259kN⋅=:=
Page 43
Table 2.12: Summary table of the lateral force results
StoryHeigth
zi (m)
Mass mi (kN)
zi*miFb (kN)
F=Fb(zi*mi)/Σzi*mi
Moment M=F*zi (kNm)
Length of floor Lx=Ly
Accidental eccentricity ei=0.05L
Torsional moment M=F*ei (kNm)
Moment due to SRSS
MSRS=√Mx^2+My^2 (kNm)
STORY1 9 1402 12618 464.52 232.26 2090.34 15 0.75 174.195 246.3489315STORY2 6 1402 8412 464.52 154.84 929.04 15 0.75 116.13 164.232621STORY3 3 1402 4206 464.52 77.42 232.26 15 0.75 58.065 82.1163105
TOTAL 4206 25236 464.52 3251.64
Mass per storey
Heigth at roof level
Heigth at level 2
Heigth at level 1
Total mass:
Lateral force at roof level (EN1998-1-1,Eq.4.11)
Lateral force at level 2 (EN1998-1-1,Eq.4.11)
Lateral force at level 1 (EN1998-1-1,Eq.4.11)
Check lateral force per storey
mi FEd.storey 1.402 103× kN=:=
z3 9m:=
z2 6m:=
z1 3m:=
Σmi_zi FEd.storey z3⋅ FEd.storey z2⋅+ FEd.storey z1⋅+ 2.524 104× kNm⋅=:=
F3mi z3⋅
Σmi_ziFb⋅ 232.259kN⋅=:=
F2mi z2⋅
Σmi_ziFb⋅ 154.84kN⋅=:=
F1mi z1⋅
Σmi_ziFb⋅ 77.42kN⋅=:=
F F3 F2+ F1+ 464.519kN=:=
Check_2 if F Fb≠ "OK", "NOT OK", ( ):=
Check_2 "OK"=
Page 44
ETABS: Define > Static load case >
Figure 2.6: Define manually the lateral forces
Figure 2.7: Define manually the lateral forces/moments per storey
Page 45
2.3.7 Torsional effects
FLOW CHART OF TORSIONAL EFFECTS
Carry out Lateral force analysis/ Response spectrum analysis
𝑀! = 𝑒!𝐹!
𝑀! = 𝑒!𝐹!
𝑒! = −0.05 ∗ 𝐿!
𝑒! = +0.05 ∗ 𝐿!
𝑒! = +0.05 ∗ 𝐿!
𝑒! = −0.05 ∗ 𝐿!
SRSS rule
𝑀!"!! = 𝑀!! +𝑀!
!
Page 46
2.3.8 Summary of analysis process in seismic design situation
Importance class/Ductility class
I II III IV
DCL DCM DCH
DCM DCH
DCH
Ignore “topographic amplification effects”
Consider “topographic amplification effects”
IF Slopes <15o Cliffs height
<30m
Slopes <15o Cliffs height
<30m
Ignore Consider
Regular in plan: YES Regular in elevation YES
Regular in plan: NO Regular in elevation YES
Regular in plan: YES Regular in elevation NO
Regular in plan: NO Regular in elevation NO
Type of soil: A , B ,C ,D, E, S1, S2
Type 1 elastic response spectrum
0≤T≤TB
TB≤T≤TC
TC≤T≤TD TD≤T≤4s
LATERAL FORCE
MODAL ANALYSIS
Displacement ds=qd·de
P-Δ effects θ≤0.1 – Ignore
0.1≤θ≤0.2 Consider 0.2≤θ≤0.3 Consider θ≥0.3 Not Permitted
Interstorey drift drv≤0.005h - Brittle
drv≤0.0075h - Ductile drv≤0.010h - Other
Frame joint ΣMRC≥1.3ΣMRB
Storey ≥ 2
Page 47
3.0 Define static loads
Here define as many load cases for your model as you need e.g. dead loads, live loads, wind
loads, seismic loads, thermal loads etc. To be simple define only one dead load with self
weight multiplier 1(including finishes, dead, walls etc) and one live load.
Figure 3.1: Static load cases
Page 48
4.0 Seismic mass requirements according to EC8
Combination of the seismic action with other actions (EN 1998-1-1,cl.3.2.4):
1. Define the category of building (EN 1991,Table 6.1),
2. Define the reduce factor (EN 1991, Table A.1.1).
Combination of seismic mass
𝐆𝐤,𝐣 + 𝛙𝐄𝐢𝐐𝐤,𝐢 (ΕΝ1998-1-1,Eq. 3.17)
Combination coefficient for variable action is: ψ!" = ϕ ∙ ψ!" (ΕΝ1998-1-1,Eq. 4.2)
Table 4.1: Values of φ for calculating 𝛙𝐄𝐢 (CYS NA EN1998-1-1:2004)
Type of Variable
action
Storey φ
Categories A-C1
Roof
Storeys with correlated occupancies
Independently occupied storeys
1,0
0,8
0,5
Categories A-F1 1.0
Table 4.2: Values of ψ coefficients
Category Specific Use ψο ψ1 ψ2
A Domestic and residential 0.7 0.5 0.3
B Office 0.7 0.5 0.3
C Areas for Congregation 0.7 0.7 0.6
D Shopping 0.7 0.7 0.6
E Storage 1.0 0.9 0.8
F Traffic < 30 kN vehicle 0.7 0.7 0.6
G Traffic < 160 kN vehicle 0.7 0.5 0.3
H Roofs 0.7 0 0
Snow, altitude < 1000 m 0.5 0.2 0
Wind 0.5 0.2 0
Page 49
4.1 Mass Source Option
In ETABS, the user has the option of choosing one of three options for defining the source of
the mass of a structure. Click the Define menu > Mass Source command to bring up the
Define Mass Source form. The following options appear on the form:
1. From Self and Specified Mass:
Each structural element has a material property associated with it; one of the items specified
in the material properties is a mass per unit volume. When the ‘From Self and Specified
Mass’ box is checked, ETABS determines the building mass associated with the element
mass by multiplying the volume of each structural element times it’s specified mass per unit
volume. This is the default. It is also possible to assign additional mass to account for
partitions and cladding, etc. ETABS adds any additional mass assignments to the element
mass to derive a total mass. You cannot have a negative mass in ETABS.
2. From Loads:
This specifies a load combination that defines the mass of the structure. The mass is equal to
the weight defined by the load combination divided by the gravitational multiplier, g. This
mass is applied to each joint in the structure on a tributary area basis in all three translational
directions.
3. From Self and Specified Mass and Loads:
This option combines the first two options, allowing you to consider self- weight, specified
mass, and loads in the same analysis.
It is important to remember when using the ‘From Self and Specified Mass and Loads’
option, NOT to include the Dead Load Case in the ‘Define Mass Multiplier for Loads’
box. This will account for the dead load of the structure TWICE.
Page 50
Figure 4.1: Seismic source
Page 51
5.0 Wind loading on structure (EN1991-1-4:2004)
5.1 Calculation of Wind load according to EN1991-1-4:2004
Step by step procedure
Figure 5.1: Fundamental Basic wind velocity, vb,0
(CYS NA EN1991-1-4,Fig.1)
Season factor (CYS EN1991-1-4,NA 2.4)
cseason=1.0
Directional factor (CYSEN1991-1-4,NA 2.4)
cdir=1.0 (Conservative value for all direction)
Basic wind velocity (EN1991-1-4, Eq. 4.1)
vb=cdir.cseasonvb,0
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Page 52
Table 5.1: Terrain category and terrain parameters (EN1991-1-4, Tab.:4.1) Terrain category
Description z0 (m) zmin(m)
0 Sea, costal area exposed to the open sea. SEA 0.003 1
I Lakes or area with negligible vegetation and without obstacles.
COUNTRY
0.01 1
II
Area with low vegetation such as grass and isolated obstacles trees, buildings) with separations of at least 20 obstacle height.
0.05 2
III
Area with regular cover of vegetation or buildings or woth isolatd obstacles with seperations of maximum 20 obstacle height (such as villages, suburban terrain, permanent forest). TOWN
0.3 5
IV* Area in which at least 15% of the surface is covered with building and their average height exceeds 15m.
1.0 10
* For buildings in terrain category IV, displacement height hdis should be consider and information can be found in Aneex A.5 of EN1991-1-4:2005.
Roughness factor, cr(z) (EN1991-1-4,Eq.4.3-4.5)
cr(z)=kr . ln(z/z0) for zmin≤z≤zmax
cr(z)=cr . (zmin) for z≤zmin z0: is the roughness length
Maximum height, zmax (EN1991-1-4, cl. 4.3.2)
zmax=200m Orography factor co(z)
co(z)=1
Terrain factor, (EN1991-1-4,cl.4.4) kr=0.19(z0/z0,II)0.07
Mean wind velocity, vm(z) (EN1991-1-4 cl.4.3.1 )
vm(z)=cr(z).co(z).vb
Wind turbulence, Iv(z) (EN1991-1-4,Eq.4.7)
Iv(z)=σv/vm(z)=kl/co(z)ln(z/z0) for zmin≤z≤zmax Iv(z)=Iv(zmin) for z≤zmin Turbulence factor: kl=1.0 (NA CYS EN1991-1-4, cl. NA 2.10) Note: for co(z)=1 Iv(z) is not important
Peak velocity pressure, qpeak(z) (EN1991-1-4 Eq.4.8 )
qpeak(z)=[1+7 Iv(z)]0.5ρ vm2
(z)=ce(z)·0.5·ρ·vb2
Air density:ρ=1.25kg/m3
Page 53
Table 5.3: Values of external pressure coefficient for vertical walls of rectangular plan building
(EN1991-1-4, Tab.:4.1)
ZONE A B C D E
h/d cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1
5 -1.2 -1.4 -0.8 -1.1 -0.5 +0.8 +1.0 -0.7 1 -1.2 -1.4 -0.8 -1.1 -0.5 +0.8 +1.0 -0.5
≤0.25 -1.2 -1.4 -0.8 -1.1 -0.5 +0.7 +1.0 -0.3 Note: Values for cpe,1 are intended for the design of small elements and fixings with an element of 1m2 or less such as cladding elements and roofing elements. Values for cpe,10 may be used for the design of the overall load bearing structure of buildings. The external pressure coeffiecient cpe,1 and cpe,10 is using for loadaded area of 1m2 and 10m2 respectively.
Key for vertical walls – Flat Roof (EN1991-1-4, Fig.7.5)
Key for vertical walls –Mono&dual pitch Roof
(EN1991-1-4, Fig.7.5)
Pressure on surface &Wind force (EN1991-1-4, Eq. 5.1&5.5) we=qp(ze).(cpe +cpi) & Fw=cscd·Σwe·Aref
Table 5.2: Reference height ze, depending on h and b, and corresponding velocity pressure profile (EN1991-1-4, Fig. 7.4)
Page 54
5.2 Application of wind loading using ETABS
Table 5.4: Wind load assumptions
Data Symbol Value Units
Basic wind velocity vb,0 24 m/s
Terrain category - II -
Structural factor cscd 1 -
Turbulence factor kl 1 -
Orography factor co(z) 1 -
ETABS: Clink on
ETABS: Select from first drop-down menu
ETABS: Click on select “NONE” and draw rectangular cover all side of plan view
Draw walls in plan
Page 55
ETABS: Select the area of elevation A-A
ETABS: Assign > Shell/Area loads > Wind pressure coefficients
Figure 5.2: Wind load areas
Table 5.5: Wind pressure coefficient applied on walls
Wind pressure coefficient for load case WINDX
Windward load “Area D” Leeward load “Area E”
Side load “Area A & B” Side load “Area A & B”
Page 56
Wind pressure coefficient for load case WINDY
Windward load “Area D” Leeward load “Area E”
Side load “Area A & B” Side load “Area A & B”
Page 57
WIND LOADING ACCORDING TO EN1991-1-4:2005
Job No.:
Sheet No.: Date: December 2012 Check by:
CALCULATION OF WIND LOADING TO EN 1991-1-4:2005. Loading available for rectangular, clad buildings with flat roofs only.
Obstruction height, have = 7.5 m Distance to nearest adjacent building, x = 50 m Height of building, h = 9 m Longitudinal length of the building ,
d = 15 m
Transverse length of the building, b = 15 m Edge distance, (Wind direction - θ=90°) e = 15 Basic Wind Velocity, Vbo = 24 m/s ( Figure1)
Season Factor, Cseason = 1.0 (cl.NA2.4)
Directional Factor, Cdir = 1.0 (cl.NA2.4)
Basic Wind Velocity, Vb0=CdirCseasonVb,o Vb = 24 m/s (Eq.4.1)
Structural factor, CsCd = 1.0 (cl.6.2)
Orography factor, Co(z) = 1.0 cl.4.3.1(1))
Turbulence factor, kI = 1.0 (cl.NA2.10)
z0 zmin (Τable 4.1)
Terrain Category Define terrain category II 0.05 2
Max heigh, zmax = 200 m (cl. 4.3.2)
Height above ground, z = 100 m
Dispacement height, hdis = 4.5 m (Annex A.5)
Clear height of building,
h-hdis = 4.5
Define height z
5
Page 58
External Pressure Coefficients Walls Cpe
Wind direction θ=0°
Width b = 15 m Height h = 9 m Depth d = 15 m Edge distance, (Wind direction - θ=0°) e = 15 m Actual h/b (For zone D -‐ windward face) h/b = 0.60
Length in Zone A
Zones A & B exist
3 m
Length in Zone B
12 m
Length in Zone C
0 m
Wind direction θ=90°
Width b = 15 m
Height h = 9 m
Depth d = 15 m
Edge distance, (Wind direction - θ=90°) e = 15 m
Actual h/b (For zone D -‐ windward face) h/b = 0.60
Length in Zone A
Zones A & B exist
3 m
Length in Zone B
12 m
Length in Zone C
0 m
Table 7.1 values of Cpe for wind on
Front (θ=90°) Front (θ=0°) Zones (θ=90°) Zones (θ=0°)
D 0.747 0.747 A 3 m A -‐1.2 m E -‐0.567 -‐0.567 B 12 m B -‐0.8 m A -‐1.2 -‐1.2 C 0 m C 0 m
B -‐0.8 -‐0.8 C 0 0
Page 59
6.0 Load combination
Table 6.1: Load combination factors and coefficients
Data Symbol Value Reference
Permanent action γG 1.35 EN1990,cl.6.4.3.2
Variable action γQ 1.5 EN1990,cl.6.4.3.2
Office areas (Type B), ψ0 0.7 CYS NA EN1990:2002, Table A1.1
Roofs ψ0 0.7 CYS NA EN1990:2002, Table A1.1
Wind loads ψ0 0.5 CYS NA EN1990:2002, Table A1.1
Persistent and transient design situation – STR/GEO Equation 6.10 Ed=ΣγG Gk +γQ Qk1 + γQ ψ0,2 Qk2
Ultimate limit state (ULS)
Static load combination
STATIC 2. 1.35DL + 1.5LL STATIC 3. 1.35DL + 1.5LL + 0.75WINDX STATIC 4. 1.35DL + 1.5LL - 0.75WINDX STATIC 5. 1.35DL + 1.5LL + 0.75WINDY STATIC 6. 1.35DL + 1.5LL - 0.75WINDY STATIC 7. 1.35DL + 1.5WINDX + 1.05LL STATIC 8. 1.35DL - 1.5WINDX – 1.05LL STATIC 9. 1.35DL + 1.5WINDY + 1.05LL STATIC 10. 1.35DL - 1.5WINDY – 1.05LL
Seismic load combination for “Modal Analysis”
SEISMIC 2. DL + 0.3LL + EQX + 0.3EQY SEISMIC 3. DL + 0.3LL + EQX – 0.3EQY SEISMIC 4. DL + 0.3LL - EQX + 0.3EQY SEISMIC 5. DL + 0.3LL - EQX – 0.3EQY SEISMIC 6. DL + 0.3LL + EQY + 0.3EQX SEISMIC 7. DL + 0.3LL + EQY – 0.3EQX SEISMIC 8. DL + 0.3LL - EQY + 0.3EQX SEISMIC 9. DL + 0.3LL - EQY – 0.3EQX
Page 60
Seismic load combination for “Lateral force Analysis”
SEISMIC 10. DL + 0.3LL + EQXA + 0.3EQYA SEISMIC 11. DL + 0.3LL + EQXA – 0.3EQYA SEISMIC 12. DL + 0.3LL - EQXA + 0.3EQYA SEISMIC 13. DL + 0.3LL - EQXA – 0.3EQYA SEISMIC 14. DL + 0.3LL + EQYA + 0.3EQXA SEISMIC 15. DL + 0.3LL + EQYA – 0.3EQXA SEISMIC 16. DL + 0.3LL - EQYA + 0.3EQXA SEISMIC 17. DL + 0.3LL - EQYA – 0.3EQXA
SEISMIC 18. DL + 0.3LL + EQXB + 0.3EQYB SEISMIC 19. DL + 0.3LL + EQXB – 0.3EQYB SEISMIC 20. DL + 0.3LL - EQXB + 0.3EQYB SEISMIC 21. DL + 0.3LL - EQXB – 0.3EQYB SEISMIC 22. DL + 0.3LL + EQYB + 0.3EQXB SEISMIC 23. DL + 0.3LL + EQYB – 0.3EQXB SEISMIC 24. DL + 0.3LL - EQYB + 0.3EQXB SEISMIC 25. DL + 0.3LL - EQYB – 0.3EQXB
Serviceability limit state (SLS)
STATIC 1. DL + LL
Page 61
7.0 Design preferences
ETABS: Options > Preferences > Steel frame design
Figure 7.1: Steel frame design preferences
2
3
4
1
5
6
Page 62
Table 7.1: Steel frame design parameters
Note 1: Reliability class
Class section classification according to EN1998-1-1,cl.6.5.3(2)
1. Depending on the ductility class and the behavior factor q used in the design, the
requirements regarding the cross-sectional classes of the steel elements which
dissipate energy are indicated in table below (EN1998-1-1,cl.6.5.3(2).
Ductility class Reference q factor Cross-Section Class
Lower
limit
q factor Upper
limit
DCM 1.5< q ≤ 2 Class 1, 2 or 3
2.0< q ≤ 4 Class 1 or 2
DCH 4.0< q Class 1
Note 2: Frame type
See section 2.0 of this manual
Note 3: Gamma factors
Partial factors Values Reference
Resistance of cross-sections whatever the
class
γΜ0=1.00 EN1993-1-1,cl.6.1(1)
Resistance of members to instability assessed
by member checks
γΜ1=1.00 EN1993-1-1,cl.6.1(1)
Resistance of cross-sections in tension to
fracture
γΜ1=1.25 EN1993-1-1,cl.6.1(1)
Note 4: Behavior factor
See section 2.0 of this manual
Note 5: System Omega
Omega Factor (System Overstrength Factor) axial load member: (𝛀 = 𝑵𝒑𝒍,𝑹𝒅/𝑵𝑬𝒅)
Omega factor may different for each diagonal member.
Page 63
1. Run the design analysis with the Ω=1
2. Find the Npl,Rd and NEd of the bracing member and then overwrite the omega factor for
each diagonal member separately and then re-run the analysis.(Ω=1).
Note: Omega factor should be limited to the following for all diagonal members
Note 6: Vertical deflection limits
STEEL MEMBERS (CYS NA EN1993-1-1,table NA.1)
Vertical deflection Limits
wmax Cantilevers L/180
Beams carrying plaster or other brittle finish L/360
Other beams (except purlin and sheeting rails)
L/250
Purlins and sheeting rails To suit cladding
General use L/300
ETABS deflection limits
DL limit, L/ 360
Super DL+LL Limit, L/ 360
Live load Limit, L/ 360
Total Limit, L/ 360
Total Camper Limit, L/ 360
Check_16 if Ωmax 1.25Ωmin≤ "OK", "NOT OK", ( ):=
Page 64
8.0 Analysis and design requirements for Concentrically braced frames according to
EN1998-1-1,cl.6.7.2
Analysis requirements according to EN1998-1-1,cl.6.7.2 Beams & Columns
1. Under gravity load conditions, only beams and columns shall be considered to resist such loads, without taking into account the bracing members (EN1998-1-1,cl6.7.2(1)P).
Diagonal members
2. The diagonals shall be taken into account as follows in an elastic analysis of the structure for the seismic action: a) in frames with diagonal bracings, only the tension diagonals shall be taken into
account, b) in frames with V bracings, both the tension and compression diagonals shall be
taken into account (EN1998-1-1,cl6.7.2(2).
3. Taking into account of both tension and compression diagonals in the analysis of any type of concentric bracing is allowed provided that all of the following conditions are satisfied: a) a non-linear static (pushover) global analysis or non-linear time history analysis is
used,
b) both pre-buckling and post-buckling situations are taken into account in the modeling of the behavior of diagonals and,
c) background information justifying the model used to represent the behavior of diagonals is provided (EN1998-1-1,cl6.7.2(3).
Page 65
8.1 Steps of the design detail of Concentric steel frames
Table 8.1: Detail steel frame design
Design step
number
Description
Step 1 Design of slab under gravity loads (without CBF bracings) considering columns
as fixed supports
Step 2 Design columns under gravity loads (without CBF bracings)
Step 3 Design beams under gravity loads (without CBF bracings)
Step 4 Check concentric bracings under gravity loads combination
Step 5 Accidental torsional effects
Step 6 Second order effects (P-Δ) (P loads are those taken in the definition of the
seismic mass “m”)
Step 7 Check of beams and of concentric bracings under gravity loads combination
Step 8 Design of concentric bracing under seismic combination of loads with the
accidental torsional effects and P-Δ effects taken into account
Step 9 Check of beams and columns under seismic combination of loads with bracings
overstrength factors Ω and with second order effects taken into account
Step 10 Re-run the analysis with the modified overstrength factors Ω
Page 66
8.2 Classification of steel sections
Table 8.2: Section classification (EN1993-1-1,cl.5.5) Classes Analysis type Description
Class 1 Plastic analysis Section can form a plastic hinge with the rotation capacity
required from plastic analysis, without reduction of the resistance
Class 2 Plastic/ Elastic analysis Section can develop its plastic moment capacity, but has limited
rotation capacity.
Class 3 Elastic analysis Section in which the stress in the extreme compression fiber of the
section, assuming an elastic distribution of stresses, can reach the
yield strength, but local buckling is likely to prevent the
development of the plastic moment capacity.
Description of detail
requirements
Equations References
Reduction of yield and
ultimate strength of sections
EN10025-2
ε - Factor EN1993-1-1,Table 5.2
Depth of a part of section for
internal compression
(I-sections)
EN1993-1-1,Table 5.2
Section classification for web
element
EN1993-1-1,Table 5.2
fy. fy t 16mm<if
fy 10N mm 2−⋅− 16mm t< 40mm<if
fy 20N mm 2−⋅− 40mm t< 80mm<if
:=
fu. fu t 16mm≤if
fu 10N mm 2−⋅− 16mm t< 40mm≤if
fu 20N mm 2−⋅− 40mm t< 80mm≤if
:=
ε235fy
:=
cw h 2 tf⋅− 2 r⋅−:=
Class_type web "CLASS 1"cwtw
72 ε⋅≤if
"CLASS 2" 84 ε⋅cwtw
< 83 ε⋅≤if
"CLASS 3" 105 ε⋅cwtw
< 124 ε⋅≤if
:=
Page 67
Depth of a part of section for
oustand flange
(I-sections)
EN1993-1-1,Table 5.2
Section classification for
flange element
EN1993-1-1,Table 5.2
cfb tw− 2.r−( )
2:=
Class_type flange "CLASS 1"cftf
9 ε⋅≤if
"CLASS 2" 9 ε⋅cftf
< 10 ε⋅≤if
"CLASS 3" 10 ε⋅cftf
< 14 ε⋅≤if
:=
Page 68
8.3 Design of composite slab under gravity loads
Table 8.3: Detail design of composite slab (with steel sheeting) Partial factor Value References
Partial factor of longitudinal shear in composite slabs γvs = 1.25 CYS EN1994-1-
1cl.2.4.1.2(6)P
Partial factor for shear connector γv = 1.25 CYS EN1994-1-
1cl.2.4.1.2(5)P
Partial factor for steel reinforcement γs = 1.15 CYS EN1992-1-1,table 2.1
Partial factor of concrete γc = 1.5 CYS EN1992-1-1,table 2.1
Partial factor of structural steel γM0 = 1.0 CYS EN1993-1-1,cl 6.1(1)
Description of detail requirements Equations References
Minimum nominal thickness of profile steel sheets t ≥ 0.70mm CYS EN1994-1-1,cl.3.5(2)
Minimum depth of slab h ≥ 90mm EN1994-1-1,cl.9.2.1(2)
Depth of concrete slab above steel sheeting hc ≥ 50mm EN1994-1-1,cl.9.2.1(2)
Minimum steel reinforcement in both direction As.prov ≥80mm2/m EN1994-1-1,cl.9.2.1(4)
Spacing of the reinforcement bars s = min{2h,350mm} EN1994-1-1,cl.9.2.1(5)
Maximum height of steel decking hp ≤ 85mm EN1994-1-1,cl.6.6.4.2(3)
Minimum width per ribs b0 ≥ hp EN1994-1-1,cl.6.6.4.2(3)
Diameter of stud that welded in the sheeting d ≤ 20mm EN1994-1-1,cl.6.6.4.2(3)
Page 69
For holes provided in the sheeting, the diameter of the stud d ≤ 22mm EN1994-1-1,cl.6.6.4.2(3)
Maximum overall height of stud hsc ≤ hp +75mm EN1994-1-1,cl.6.6.4.1(2)
Design
stage Description of checks Equations References
Resistance verifications of metal decking at the construction stage
Construction Stage
Moment resistance of steel sheeting From manufacture data -
Concrete compressive strength fcd = fck / γc EN1994-1-1,cl.2.4.1.2(2)P
Design yield strength fyo,d = fyp / γM0 -
Bending resistance of metal decking MEd / MRd <1.0 EN1993-1-3,cl.6.1.1
Shear resistance of metal decking 𝑉!,!" =
!!!"#$
𝑡 𝑓!"𝛾!!
EN1993-1-3,cl.6.1.5(1)
Deflection of metal decking 𝛿!"# =
!"!
!"#!" (W in kN/m2) -
δmax ≤ min {L / 180,20mm) EN1994-1-1,cl.9.6(2)
Resistance verifications of composite slab at the composite stage
Composite Stage
Area of concrete Ac = b hc (b=1m) -
Compression design force of concrete Nc = 0.85 fcd Ac EN1994-1-1,cl.6.2.1.2
Tensile resistance of profiles steel sheeting Np = fyp,d Ap EN1994-1-1,cl.6.2.1.2
Page 70
Location of neutral axis Neutral axis=if{Np < Nc “Lie above steel sheeting”, “Lie
below steel sheeting”} EN1994-1-1,9.7.2(5) & (6)
Depth of concrete in compression xpl = Ape fyp,d / 0.85 b fcd EN1994-1-1,fig.9.6
Moment resistance (full shear connection) Mpl, Rd = Ap fyd (dp – 0.5 xpl) -
Bending resistance of slab MEd / Mpl,Rd <1.0 -
The design values of m and k Should be obtain from the manufacture -
Shear span (for UDL load) Ls = L / 4 EN1994-1-1,cl.9.7.3(5)
Shear span (for UDL & point load) Ls = 3L/8 EN1994-1-1,cl.9.7.3(5)
Shear resistance (in longitudinal direction) Vl,Rd = bdp /γvs [(mAp / bLs ) + k] EN1994-1-1,Eq. 9.7
Longitudinal shear resistance of slab VEd / Vl,Rd -
Coefficient factor k k = 1+(200 / dp)1/2 EN1992-1-1,cl.6.2.2(1)
Value of vmin vmin = 0.035k3/2 fck1/2 CYS EN1992-1-1,Eq.6.3
Design vertical shear resistance Vv,Rd = vmin bs dp 1 EN1992-1-1,Eq.6.2b
Vertical shear resistance check VEd / Vv,Rd < 1.0 -
Serviceability limit state (SLS) - Deflection
Calculation of deflection (simply supported slab) 𝛿!"# =!"!
!"#!" (W in kN/m2) -
Deflection limits (imposed load) L / 350 (not greater than 20mm)
Deflection limits (total load) L / 250 (not greater than 30mm) EN1992-1-1,cl.7.4.1(4)
Serviceability limit state (SLS) - Cracking
Minimum amount of steel ratio (un-propped) As = 0.2% Ac EN1994-1-1,cl.9.8.1(2)
Minimum amount of steel ratio (propped) As = 0.4% Ac EN1994-1-1,cl.9.8.1(2)
Page 71
Serviceability limit state (SLS) – Floor vibration
Floor vibration limits f = 18 / √δa SCI-P-076 : Design guide
on the vibration of floors
Note 1: Although in reality the slab is continuous, it is normally convenient to design it as simply supported. As a consequence of this, the beneficial effect of
compression from the hogging moment at the support is neglected, such that σcp = 0.
Page 72
8.4 Design of composite beam (with steel sheeting) under gravity loads
Table 8.4: Detail design of composite beam
Minimum height of stud EN1994-1-1,cl.6.6.1.2(1)
Nominal diameter of stud EN1994-1-1,cl.6.6.1.2(1)
Ultimate strength of shear connector EN1994-1-1,cl.6.6.4.2(1)
Check the minimum spacing of studs EN1994-1-1,cl.6.6.5.5(3)
Preliminary depth of beams
EN1994-1-1,cl.6.4.3(1)
Ultimate limit state
Bending Resistance of the steel section (EN1993-1-1,cl.6.2.5)
Moment resistance of steel
section Y-Y axis
Mc,Rd,y =Mpl,Rd,y = Wpl,y fy / γM0 EN1993-1-1,cl.6.2.5(2)
Vertical Shear resistance of the steel section (cl.6.2.2) & (EN1993-1-1,cl.6.2.6)
Factor for shear area η = 1.0 (conservative value) EN1993-1-1,cl.6.2.6(3g)
Shear area 1 Av = A -2 b tf + (tw + 2r) tf ≥ η hw tw EN1993-1-1,cl.6.2.6(3a)
Shear resistance of steel Vpl,Rd y = Av (fy / √3) / γM0 EN1993-1-1,cl.6.2.6(2)
hmin if hsc 4d≥ "OK", "NOT OK", ( ):=
dlim if 16mm d< 25mm< "OK", "NOT OK", ( ):=
fus 450N mm 2−⋅:=
slim if sprov 5 d⋅≥ sprov 6 h⋅<∧ "OK", "NOT OK", ( ):=
hmax 600mm fy 235N mm 2−⋅≤if
550mm 235N mm 2−⋅ fy< 275N mm 2−
⋅≤if
400mm 275 N⋅ mm 2−⋅ fy< 355N mm 2−
⋅≤if
270mm 355 N⋅ mm 2−⋅ fy< 460N mm 2−
⋅≤if
:=
Page 73
Construction
Stage
section Y-Y axis
Check if the verification of
shear buckling resistance
required or not
(EN1993-1-1,cl.6.2.6(6))
Bending and shear interaction check (cl.6.2.2.4)
Area of web Aw = hw tw EN1993-1-1,cl.6.2.8(5)
Coefficient of interaction vy=VEd / Vpl.Rd,y EN1993-1-1,cl.6.2.8(5)
Reduced yield strength ρ = [(2VEd / Vpl.Rd,y) – 1] 2 EN1993-1-1,cl.6.2.8(3)
Reduced design plastic
resistance moment Y-Y axis EN1993-1-1,cl.6.2.8(5)
Lateral torsional buckling of the steel beam
It is assumed that the steel beam is laterally restrained by the steel sheeting during construction. In order to provide restraint, the sheeting is
fixed to the beam either by the action of through-deck welding or by short-fired pins
Effective width of composite beam (cl.5.4.1.2(5))
Effective width of composite
beam
(EN1994-1-1cl. 5.4.1.2(5))
Plastic resistance moment of composite section with full shear connection (cl.6.2)
hwtw
72ε
η⋅<
Ma.pl.Rd.
Wpl.yρ Aw
2⋅
4tw−
⎛⎜⎜⎝
⎞⎟⎟⎠fy⋅
γM0vy 0.5>if
Ma.pl.Rd vy 0.5<if
:=
beff bo 2 minL12
L22
+Le8
, ⎛⎜⎝
⎞⎟⎠
⎛⎜⎝
⎞⎟⎠
+:=
Page 74
Composite
Stage
Tensile resistance of steel
section (EN1993-1-1,cl.6.2.3(2))
Compression resistance of
concrete slab
(EN1994-1-1,cl.6.2.1.2(1d)
Tensile resistance in web of
steel section -
Location of neutral axis (EN1994-1-1,cl.6.2.1.2(1))
Bending resistance with full
shear connection
(EN1994-1-1,cl.6.1.2)
Bending resistance
check checks (EN1993-1-1,cl.6.2.5(1))
Vertical Shear resistance of the composite steel section (cl.6.2.2) & (EN1993-1-1,cl.6.2.6)
Design of shear
resistance check (EN1993-1-1,cl.6.2.6(1)P)
Check if the verification of
shear buckling resistance (EN1993-1-1,cl.6.2.6(6))
Npl.afy A⋅
γM0:=
Nc.f 0.85 fcd⋅ beff⋅ hc⋅:=
Npl.w fy tw⋅ ha 2 tf⋅−( )⋅:=
Location_neutral axis "Lies in the concrete slab" Nc.f Npl.a>if
"Lies in the top flange of the beam" Nc.f Npl.a≤if
"Lies in the web of the beam" Nc.f Npl.w<if
:=
Mpl.Rd Npl.aha2
h+Npl.aNc.f
hc2
⋅−⎛⎜⎝
⎞⎟⎠
⋅ Location_neutral axis "Lies in the concrete slab"if
Npl.aha2
⋅ Nc.fhc2
hp+⎛⎜⎝
⎞⎟⎠
⋅+ Location_neutral axis "Lies in the top flange of the beam"if
Ma.pl.Rd Nc.fhc ha+ 2hp+
2
⎛⎜⎝
⎞⎟⎠
⋅+Nc.f
2
Npl.w
ha4
⋅− Location_neutral axis "Lies in the top flange of the beam"if
:=
Check_7 if MEd Mpl.Rd≤ "OK", "NOT OK", ( ):=
Check_8 if VEd Vpl.Rd≤ "OK", "NOT OK", ( ):=
Check_9 ifhwtw
72ε
η⋅< "Not required shear buckling resistance", "Required shear buckling resistance",
⎛⎜⎝
⎞⎟⎠
:=
Page 75
Composite
Stage
required or not
Design resistance of shear stud connector (cl.6.6.3.1(1))
Upper limit of reduction
factor kt
(EN1994-1-1,Table:6.2)
Reduction factor kt
Ribs transverse to the supporting beams
(EN1994-1-1,cl.6.6.4.2)
Limitation of kt (EN1994-1-1,cl.6.6.4.2(2))
Reduction factor kt
Ribs parallel to the supporting beams
(EN1994-1-1,cl.6.6.4.1)
Minimum height of shear stud (EN1994-1-1,cl.6.6.1.2(1))
Limitation of stud diameter (EN1994-1-1,cl.6.6.1.2(1))
Factor α
(EN1994-1-1,cl.6.6.3.1(1))
kt.max 0.85 nr 1 1mm ts≥∧ d 20mm<∧if
1.0 nr 1 1mm ts<∧ d 20mm<∧if
0.75 nr 1 1mm ts≥∧ 19mm d≤ 22mm<∧if
0.75 nr 1 1mm ts<∧ 19mm d≤ 22mm<∧if
0.70 nr 2 1mm ts≥∧ d 20mm<∧if
0.80 nr 2 1mm ts<∧ d 20mm<∧if
0.60 nr 2 1mm ts≥∧ 19mm d≤ 22mm<∧if
0.60 nr 2 1mm ts<∧ 19mm d≤ 22mm<∧if
:=
kt0.7
nr
bohp⋅
hschp
1−⎛⎜⎝
⎞⎟⎠
⋅:=
Check_10 if kt kt.max< "OK", "NOT OK", ( ):=
kt 0.6bohp⋅
hschp
1−⎛⎜⎝
⎞⎟⎠
⋅ 1.0≤:=
hmin if hsc 4d≥ "Ductile", "Not Ductile", ( ):=
dlim if 16mm d< 25mm< "Ductile", "Not ductile", ( ):=
α 0.2hscd
1+⎛⎜⎝
⎞⎟⎠
⋅ 3hscd
≤ 4≤if
1hscd
4>if
1=:=
Page 76
Composite
Stage
Design shear resistance of a
headed stud
(EN1994-1-1,cl.6.6.3.1(1))
Degree of shear connection (cl.6.6.1.2(1))
Ratio of the degree shear
connection (EN1994-1-1,cl.6.2.1.3(3))
Minimum degree of shear
connection for equal flange
(EN1994-1-1,cl.6.6.1.2(1))
Check the degree of shear
interaction within the limits (EN1994-1-1,cl.6.6.1.2(1))
Number of shear connector
required -
Stud spacing -
Check the minimum
spacing of studs (EN1994-1-1,cl.6.6.5.7(4))
Adequacy of the shear connection
(EN1994-1-1,cl.6.6.1.3(3))
Design of transverse reinforcement (cl.6.6.6.2) & (EN1992-1-1,cl.6.2.4)
Length under consideration -
PRd kt min0.8 fus⋅ π⋅
d2
4⋅
γ v
0.29α⋅ d2⋅ fck Ecm⋅⋅
γ v,
⎛⎜⎜⎜⎝
⎞⎟⎟⎟⎠
⋅:=
ηNc.fNpl.a
:=
ηmin 1355fy
N mm 2−⋅
⎛⎜⎜⎜⎝
⎞⎟⎟⎟⎠
0.75 0.03Lem
⋅−⎛⎜⎝
⎞⎟⎠
⋅− Le 25m<if
1.0 Le 25m>if
:=
Check_11 if η ηmin> η 0.4≥∧ "OK", "NOT OK", ( ):=
n2 Npl.a⋅
PRd:=
sprovLe
Nstud:=
slim if sprov 5 d⋅≥ sprov 6 h⋅<∧ "OK", "NOT OK", ( ):=
Check_12 if Mpl.Rd 2.5 Ma.pl.Rd⋅< "Uniform spacing", "Not uniform spacing", ( ):=
Δ xLe2
:=
Page 77
Longitudinal shear stress (EN1992-1-1,cl.6.2.4(3))
Strength reduction factor (EN1992-1-1,Eq.6.6N)
Area of transverse
reinforcement required
(EN1992-1-1,cl.6.2.4(4))
Check the crushing
compression in the flange (EN1992-1-1cl.6.2.4(4))
Serviceability limit state
Vertical deflection
Construction
Stage
Maximum deflection at
construction stage -
Vertical deflection limit (CYS NA EN1993-1-1,table
NA.1)
Composite
Stage
Short term elastic modular
ration
(EN1994-1-1,cl.7.2.1)
Second moment of area of the
composite section -
Deflection with full shear
connection -
Vibration of floor (Simplified analysis) (EN1990 A1.4.4)
vEdNpl.a2 hc⋅ Δ x⋅
:=
v 0.6 1fck
250 N⋅ mm 2−⋅
−⎛⎜⎜⎝
⎞⎟⎟⎠
⋅:=
As.reqvEd hc⋅ sf⋅
fydsin θf( )cos θf( )⋅
:=
Check_14 if vEd v fcd⋅ sin θf( )⋅ cos cos θf( )( )⋅≤ "OK", "NOT OK", ( ):=
δc5 Gk.c Qk.c+( )⋅ Le
4⋅
384 Es⋅ Iyy⋅:=
Check_15 if δcLe250
< "OK", "NOT OK", ⎛⎜⎝
⎞⎟⎠
:=
noEsEcm
:=
rA
beff hc⋅:=
IcA h 2 hp⋅+ hc+( )2⋅
4 1 no r⋅+( )⋅
beff hc3
⋅
12 no⋅+ Iyy+:=
δcom5 Gk Qk+( )⋅ Le( )4⋅
384 Es⋅ Ic⋅:=
Page 78
Total load on beam is EN1990,A1.4.4
Increase the inertia, Ic by 10% to allow for the
increased dynamic stiffness of the composite beam -
Instantaneous deflection caused by re-application of
the self weigth of the floor and the beam to the
composite beam -
Natural frequency
SCI P354
Check natural frequency limitation -
Fv Gk ψ1 Qk⋅+:=
Icl Iy Iy 0.1⋅( )+:=
δα
5 Fv Le⋅( )⋅ Le3
⋅
384 Es⋅ Icl⋅:=
f18 Hz⋅
δα
mm
:=
Check_17 if f 4Hz< "OK", "NOT OK", ( ):=
Page 79
8.5 Detail design of steel columns under gravity loads
Table 8.5: Detail design of composite beam
Partial factor Value References
Partial factor of cross-sections whatever the class
is γM0 = 1.0
CYS EN1993-1-1,cl 6.1(1)
Partial factor of member to instability assessed by
member checks γM1 = 1.0
CYS EN1993-1-1,cl 6.1(1)
Description of detail requirements Equations References
Design plastic resistance of the gross cross-section Npl,Rd = A fy / γM0 EN1993-1-1,cl.6.2.3(2)
Compression resistance of steel section Nc,Rd =A fy / γM0 EN1993-1-1,cl.6.2.4(1)
Bending interaction check
Moment resistance of steel section Y-Y axis Mc,Rd,y =Mpl,Rd,y = Wpl,y fy / γM0 EN1993-1-1,cl.6.2.5(2)
Moment resistance of steel section Z-Z axis Mc,Rd,z= Mpl,Rd,z = Wpl,z fy / γM0 EN1993-1-1,cl.6.2.5(2)
Shear interaction check
Factor for shear area η = 1.0 (conservative value) EN1993-1-1,cl.6.2.6(3g)
Shear area 1 Av = A -2 b tf + (tw + 2r) tf ≥ η hw tw EN1993-1-1,cl.6.2.6(3a)
Shear resistance of steel section Y-Y axis Vpl,Rd y = Av (fy / √3) / γM0 EN1993-1-1,cl.6.2.6(2)
Shear resistance of steel section Z-Z axis Vpl,Rd,z = 2b tf (fy / √3) / γM0 EN1993-1-1,cl.6.2.6(2)
Bending and shear interaction check
Area of web Aw = hw tw EN1993-1-1,cl.6.2.8(5)
Page 80
Coefficient of interaction vy=VEd / Vpl.Rd,y EN1993-1-1,cl.6.2.8(5)
Reduced yield strength ρ = [(2VEd / Vpl.Rd,y) – 1] 2 EN1993-1-1,cl.6.2.8(3)
Reduced design plastic resistance moment Y-Y axis EN1993-1-1,cl.6.2.8(5)
Coefficient of interaction vz=VEd / VRd,y EN1993-1-1,cl.6.2.8(5)
Reduced yield strength ρ = [(2VEd / Vpl.Rd,z) – 1] 2 EN1993-1-1,cl.6.2.8(3)
Reduced design plastic resistance moment Z-Z axis EN1993-1-1,cl.6.2.8(5)
Check combination of axial and bending EN1993-1-1,cl.6.2.1(7)
Bending and axial interaction check
Criteria 1 – Y-Y axis c1=NEd ≤ Npl,Rd EN1993-1-1,cl.6.2.9.1(4)
Criteria 2 – Y-Y axis c2=NEd ≤ (0.5 hw tw fy )/ γM0 EN1993-1-1,cl.6.2.9.1(4)
Check criteria c= max(cy1, cy2)
Factor a a = min {(A-2 b tf) / A) ,0.5} EN1993-1-1,cl.6.2.9.1(5)
Factor n n = NEd / Npl,Rd EN1993-1-1,cl.6.2.9.1(5)
Factor β EN1993-1-1,cl.6.2.9.1(6)
Reduced design value of the resistance to bending MN,y,Rd = Mpl,y,Rd (1-n)/(1-0,5a) if c>1.0 and
EN1993-1-1,cl.6.2.9.1(5)
Mc.Rd.y
Wpl.yρ Aw
2⋅
4tw−
⎛⎜⎜⎝
⎞⎟⎟⎠fy⋅
γM0vy 0.5>if
Mc.Rd.y vy 0.5<if
:=
Mc.Rd.z
Wpl.zρ Aw
2⋅
4tw−
⎛⎜⎜⎝
⎞⎟⎟⎠fy⋅
γM0vz 0.5>if
Mc.Rd.z vz 0.5<if
:=
Check_1 ifNEd
Npl.Rd
MEd.yMc.Rd.y
+MEd.z
Mc.Rd.z+ 1.0≤ "OK", "NOT OK",
⎛⎜⎝
⎞⎟⎠
:=
β 5n 5n 1≥if
1 otherwise
1=:=
Page 81
moments making allowance for the presence of
axial forces (Y-Y axis)
MN,y,Rd = Mpl,y,Rd if 0 ≤ c ≤ 1.0
Reduced design value of the resistance to bending
moments making allowance for the presence of
axial forces (Z-Z axis)
MN,z,Rd = Mpl,z,Rd for n<a and
MN,z,Rd = Mpl,z,Rd [1-(n-a/1-a)2] for n>a EN1993-1-1,cl.6.2.9.1(5)
Check combination of bi-axial bending EN1993-1-1,cl.6.2.9.1(6)
Buckling interaction check
Buckling length See: Figure 1: Effective length columns Design Guidance of EC3)
Elastic critical force for the relevant buckling mode based on the
gross cross sectional properties 𝑁!".! =
𝐸!𝐼!𝜋!
𝐿!".!! -
Non dimensional slenderness λ! =𝐴𝑓!𝑁!".!
EN1993-1-1,cl.6.3.1.2(1)
Buckling curve
EN1993-1-1,table 6.2
Imperfection factor a
EN1993-1-1,table 6.1
Check_1 ifMEd.y
MN.y.Rd
⎛⎜⎝
⎞⎟⎠
a MEd.zMN.z.Rd
⎛⎜⎝
⎞⎟⎠
β
+
⎡⎢⎢⎣
⎤⎥⎥⎦
1.0≤ "OK", "NOT OK",
⎡⎢⎢⎣
⎤⎥⎥⎦
:=
Buckling_class_Y
"a" tf 40mm<if
"b" 40mm tf< 100mm<if
hb
1.2>if
"b" tf 100mm≤if
"d" tf 100mm>if
hb
1.2≤if
:=
Page 82
Value to determine the reduction factor χ Φ = 0.5 [1 + α (λ – 0.2) + λ2 EN1993-1-1,cl.6.3.1.2(1)
Reduction factor χ χ =1
Φ + Φ! − λ!≤ 1,0 EN1993-1-1,cl.6.3.1.2(1)
Design buckling resistance of a compression member 𝑁!,!" =𝜒𝐴𝑓!𝛾!!)
EN1993-1-1,cl.6.3.1.1(3)
Buckling length See: Figure 1: Effective length columns Design Guidance of EC3)
Elastic critical force for the relevant buckling mode based on the
gross cross sectional properties 𝑁!".! =
𝐸!𝐼!𝜋!
𝐿!".!! -
Non dimensional slenderness λ! =𝐴𝑓!𝑁!".!
EN1993-1-1,cl.6.3.1.2(1)
Buckling curve
EN1993-1-1,table 6.2
Imperfection factor a
EN1993-1-1,table 6.1
αy 0.1 Buckling_class_Y "ao"if
0.21 Buckling_class_Y "a"if
0.34 Buckling_class_Y "b"if
0.49 Buckling_class_Y "c"if
0.76 Buckling_class_Y "d"if
:=
Buckling_class_Y
"a" tf 40mm<if
"b" 40mm tf< 100mm<if
hb
1.2>if
"b" tf 100mm≤if
"d" tf 100mm>if
hb
1.2≤if
:=
Page 83
Value to determine the reduction factor χ Φ = 0.5 [1 + α (λ – 0.2) + λ2 EN1993-1-1,cl.6.3.1.2(1)
Reduction factor χ χ =1
Φ + Φ! − λ!≤ 𝜒 ≤ 1,0 EN1993-1-1,cl.6.3.1.2(1)
Design buckling resistance of a compression member 𝑁!,!",! =𝜒𝐴𝑓!𝛾!!)
EN1993-1-1,cl.6.3.1.1(3)
Non dimensional slenderness EN1993-1-1,cl.6.3.1.2(1)
Check the bukling effects if can be ignored and only cross
section check is adequate
EN1993-1-1,cl.6.3.1.2(4)
Lateral torsional buckling interaction check
Elastic critical moment for lateral torsional buckling NCCI: SN003a-EN-EU
Effective length factor (Pinned End) k = 1.0 NCCI: SN003a
Factor for end warping kw = 1.0 NCCI: SN003a
Coefficient factor C1 (Load condition: UDL)
NCCI: SN003a
Coefficient factor C2 C2 = 1.554 NCCI: SN003a
Distance between the point of load application and the
shear centre (load applied on centre) zg = 0m NCCI: SN003a
αz 0.1 Buckling_class_Z "ao"if
0.21 Buckling_class_Z "a"if
0.34 Buckling_class_Z "b"if
0.49 Buckling_class_Z "c"if
0.76 Buckling_class_Z "d"if
:=
λ max λy λz, ( ):=
Check if λ 0.2< "Ignored buckling effects", "Consider buckling effects", ( ):=
Mcr C1π2 Es⋅ Izz⋅
k Lcr⋅( )2⋅
kkw
⎛⎜⎝
⎞⎟⎠
2 IwIzz⋅
k Lcr⋅( )2G It⋅
π2Es Izz⋅
+ C2 zg⋅( )2+⋅ C2 zg⋅−:=
C1 1.88 1.40ψ− 0.52ψ 2+:=
Check_5 if C1 2.7≤ "OK", "NOT OK", ( ):=
Page 84
Lateral torsional buckling curves
EN1993-1-1,table 6.4
Imperfection factors for lateral torsional buckling curves
EN1993-1-1,table 6.3
Non dimensional slenderness for lateral torsional buckling
EN1993-1-1,cl.6.3.2.2(1)
Value to determine the reduction factor χLT EN1993-1-1,cl.6.3.2.2(1)
Reduction factor for lateral-torsional buckling EN1993-1-1,cl.6.3.2.2(1)
Check if the lateral torsional buckling
can be ignored
EN1993-1-1,cl.6.3.2.2(4)
Moments due to the shift of the centroidal axis for
class sections 1,2 & 3
EN1993-1-
1,cl.6.3.3(4)/table 6.7
Characteristic resistance to normal force of the
critical cross-section
EN1993-1-
1,cl.6.3.3(4)/table 6.7
Characteristic moment resistance of the critical
cross-section
E1993-1-1,cl.6.3.3(4)/table
6.7)
Buckling_curve_Z "a"hb
2≤if
"b"hb
2>if
:=
αLT 0.21 Buckling_curve_Z "a"if
0.34 Buckling_curve_Z "b"if
0.49 Buckling_curve_Z "c"if
0.76 Buckling_curve_Z "d"if
:=
λLTWpl.y fy⋅
Mcr:=
φLT 0.5 1 αLT λLT 0.2−( )⋅+ λLT2
+⎡⎣
⎤⎦⋅:=
χLT1
φLT φLT2
λLT2
−+
:=
Check_6 if λLT λLTO< "Ignored torsional buckling effects", "Consider torsional buckling effects", ( ):=
Check_7 ifMEd.yMcr
λLTO2
< "Ignored torsional buckling effects", "Consider torsional buckling effects", ⎛⎜⎝
⎞⎟⎠
:=
ΔMEd.z 0:=
ΔMEd.y 0:=
NRk fy A⋅:=
My.Rk fy Wpl.y⋅:=
Mz.Rk fy Wpl.z⋅:=
Page 85
Ratio of end moments
EN193-1-1,Table B2)
Equivalent uniform moment factor
EN1993-1-1,table B.1&B.2
Interaction factors
EN1993-1-1,table B.1&B.2
Combined bending and axial compression
EN1993-1-1,Eq.6.61
ψyMEd.y1MEd.y2
1−MEd.y1MEd.y2
≤ 1≤if
MEd.y2MEd.y1
1−MEd.y2MEd.y1
≤ 1≤if
:=
ψzMEd.z1MEd.z2
1−MEd.z1MEd.z2
≤ 1≤if
MEd.z2MEd.z1
1−MEd.z2MEd.z1
≤ 1≤if
:=
Cmy 0.6 0.4ψy⋅+:=
Cmz 0.6 0.4ψz⋅+:=
kyy min Cmy 1 λy 0.2−( )NEd
χyNRkγM1⋅
⋅+⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
⋅⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
Cmy 1 0.8NEd
χyNRkγM1⋅
⋅+⎛⎜⎜⎜⎝
⎞⎟⎟⎟⎠
⋅, ⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
:=
kzz min Cmz 1 2λz 0.6−( )NEd
χzNRkγM1⋅
⋅+⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
⋅⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
Cmz 1 1.4NEd
χzNRkγM1⋅
⋅+⎛⎜⎜⎜⎝
⎞⎟⎟⎟⎠
⋅, ⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
:=
kyz 0.6kzz:=
kzy 0.6kyy:=
NEdxy NRk⋅
γM1
kyyMEd.y ΔM Ed.y+
χLTMy.RkγM1
⋅
⋅+ kyzMz.Ed ΔM Ed.z+
Mz.Rk
γM1
⋅+
Page 86
Combined bending and axial compression
EN1993-1-1,Eq.6.62
Note: This equations is applicable only for I and H sections with section class 1 and 2
Note 1: The shear area is for rolled I and H sections, load parallel to web
NEdχz NRk⋅
γM1
kzyMEd.y ΔM Ed.y+
χLTMy.RkγM1
⋅
⋅+ kzzMEd.z ΔM Ed.z+
Mz.Rk
γM1
⋅+
Page 87
8.6 Detail design rules of steel Concentric Braced Frames (CBF) according to Eurocode 8
8.6.1 Detail design rules of steel bracing according to Eurocode 8
Description Value References
Overstrength factor used in design γov = 1.25 CYS EN1998-1-1cl.6.2(3)P
Non-dimensional slenderness (X bracing) EN1998-1-1,cl.6.7.3(1)
Non-dimensional slenderness (one diagonal) λ ≤ 2.0 EN1998-1-1,cl.6.7.3(2)
Non-dimensional slenderness (V bracing) λ ≤ 2.0 EN1998-1-1,cl.6.7.3(3)
Non-dimensional slenderness (V,X & one bracing) EN1998-1-1,cl.6.7.3(4)
Yield resistance check EN1998-1-1,cl.6.7.3(5)
Check Ω factor EN1998-1-1,cl.6.7.3(8)
Check Ω factor EN1998-1-1,cl.6.7.3(8)
Ductility class require for seismic design
EN1998-1-1,cl.6.5.3(2)
Check_6 if 1.3 λy< 2< "OK", "NOT OK", ( ):=
Check_5 if Ns 3≥ "Consider limitation (As EC8)", "Ignore limitation (As EC3)", ( ):=
Check_15 if NEd Npl.Rd≤ "OK", "NOT OK", ( ):=
Ω.Npl.RdNEd
:=
Check_16 if Ωmax 1.25Ωmin≤ "OK", "NOT OK", ( ):=
Class_type_req "CLASS 1 , 2 or 3" 1.5 q< 2≤ Ductility_class "DCM"∧if
"CLASS 1 or 2" 2 q< 4≤ Ductility_class "DCM"∧if
"CLASS 1" q 4> Ductility_class "DCH"∧if
:=
Page 88
8.7 Detail design rules of steel columns and beams according to Eurocode 8
Description Value References
Overstrength factor used in design γov = 1.25 CYS EN1998-1-1cl.6.2(3)P
Yield resistance check EN1998-1-1,cl.6.7.3(5)
Check Ω factor
EN1998-1-1,cl.6.7.3(8)
Minimum resistance requirement, NEd
EN1998-1-1,cl.6.7.4(1)
Ductility class require for seismic design
EN1998-1-1,cl.6.5.3(2)
Check_15 if NEd Npl.Rd≤ "OK", "NOT OK", ( ):=
Ω.Npl.RdNEd
:=
NEd. NEd.G 1.1 γ ov⋅ Ω⋅ NEd.E⋅+:=
Class_type_req "CLASS 1 , 2 or 3" 1.5 q< 2≤ Ductility_class "DCM"∧if
"CLASS 1 or 2" 2 q< 4≤ Ductility_class "DCM"∧if
"CLASS 1" q 4> Ductility_class "DCH"∧if
:=
Page 89
8.8 Detail design rules of steel composite members according to Eurocode 8
Description Value References
Minimum concrete strength C20/25 – C40/50 CYS EN1998-1-1cl.7.2.1(1)
Steel reinforcement class B or C
EN1998-1-1,cl.7.2.2(2)
Minimum degree of connection η ≤ 0.8 EN1998-1-1,cl.7.6.2(3)
Reduction factor kt = 0.75
EN1998-1-1,cl.7.6.2(4)
Profiled steel sheeting with ribs transverse to the
supporting beams is used, the reduction factor
kt = kt * kr
EN1998-1-1,cl.7.6.2(6)
Yield strength of steel
EN1998-1-1,cl.7.6.2(8)
Ductility class require for seismic design
EN1998-1-1,cl.6.5.3(2)
fy "fy=355" 1.5 q< 4≤ Ductility_class "DCM"∧xd
0.27≤∧if
"fy=235" 1.5 q< 4≤ Ductility_class "DCM"∧ 0.27xd
< 0.36≤∧if
"fy=355" q 4> Ductility_class "DCH"∧xd
0.20≤∧if
"fy=235" q 4> Ductility_class "DCH"∧ 0.20xd
< 0.27≤∧if
:=
xx
Class_type_req "CLASS 1 , 2 or 3" 1.5 q< 2≤ Ductility_class "DCM"∧if
"CLASS 1 or 2" 2 q< 4≤ Ductility_class "DCM"∧if
"CLASS 1" q 4> Ductility_class "DCH"∧if
:=
Page 90
8.9 Detail design rules of steel moment resistance frames (MRF) according to Eurocode 8
8.9.1 Detail design rules for MRF - Design criteria
Description Value References
Below design criteria apply to (Bottom – Top) Single/Multi-story buildings EN1998-1-1cl.6.6.1(1)
Moment capacity (where fixed support is provided) ∑MRc ≥ 1.3MRb EN1998-1-1,cl.4.4.2.3(4)
8.9.2 Detail design rules of steel beam for MRF
Description Value References
Moment capacity verification 𝑀!"
𝑀!".!" ≤ 1.0 EN1998-1-1,cl.6.6.2.(2)
Design shear force
VEd = VEd.G + VEd.M
Where
VEd.M = (Mpl.Rd.A + Mpl.Rd.B)/L
EN1998-1-1,cl.6.6.2.(2)
Shear capacity verification 𝑉!"𝑉!".!"
≤ 0.5 EN1998-1-1,cl.6.6.2.(2)
Axial capacity verification 𝑁!"𝑁!".!"
≤ 0.15 EN1998-1-1,cl.6.6.2.(2)
Page 91
8.9.3 Detail design rules of steel column for MRF
Description Value References
Overstrength factor used in design γov = 1.25 CYS EN1998-1-1cl.6.2(3)P
Check Ω factor (derivate from all beam with
moment connection) Ω!"# =
!!".!"
!!".! MEd.E : Lateral force
EN1998-1-1cl.6.6.3(1P)
Design axial compression force NEd = NEd.G +1.1γvoΩ NEd.E NEd.E : Lateral force EN1998-1-1cl.6.6.3(1P)
Design bending moment MEd = MEd.G +1.1γvoΩ MEd.E MEd.E : Lateral force EN1998-1-1cl.6.6.3(1P)
Design shear force VEd = VEd.G +1.1γvoΩ VEd. VEd.E : Lateral force EN1998-1-1cl.6.6.3(1P)
Design shear force verification 𝑉!"𝑉!".!"
≤ 0.5 EN1998-1-1cl.6.6.3(4)
Page 92
9.0 Design of steel frames
9.1 Design of steel member overwrites data
Figure 9.1: Steel design result of the member
Overwrites
Page 93
Figure 9.2: Steel frame design overwrites for Eurocode 3
3
2
1
4
7
8
9
10
11
12
5
6
Page 94
Table 9.1: Steel frame design overwrites for Eurocode 3
Explanation of Steel frame design overwrites for Eurocode 3
Note No. Parameter Values
1 Effective length factor
2 Moment coefficient
kyy
kzz
Page 95
3 Bending Coefficient (C1)
4 Moment coefficient
5 Overstrength factor
used in design1
6 Omega gamma
factor γov = 1.25
7 Compressive/Tensile
capacity
8 Major bending
capacity, Mc3Rd
9 Minor bending
capacity, Mc2Rd
10 Buckling resistance
moment
Ω.Npl.RdNEd
:=
Page 96
11 Major shear capacity, Vc3Rd
12 Minor shear
capacity, Vc2Rd
Notes: 1Ω is not calculated automatically by the program. Rather, its value can be overwritten by the user through design Preference and Overwrites.
Page 97
9.2 Design of columns / beams using ETABS – Gravity load analysis only
STEP 1: Analyze > Run Analysis STEP 2: Design > Steel frame design > Select design combo… Note: Under gravity load conditions, only beams and columns shall be considered to resist such loads, without taking into account the bracing members (EN1998-1-1,cl6.7.2(1)P). Design combination at ULS
STATIC 1. 1.35DL + 1.5LL STATIC 10. 1.00DL + 0.3LL
Figure 9.3: Gravity load combination at ULS
Design combination at SLS
DSTLD 1. DL + LL DSTLD 2. DL
Page 98
Figure 9.4: Gravity load combination at SLS
Figure 9.5: Steel design under gravity load ONLY
Write click on each member in order to check it individually Column name: C2 Storey level: Storey 1
Page 99
Figure 9.6: Steel design result of the member
Figure 9.7: Ultimate moment results under worst case combination
ETABS: Display > Show tables
Worst case combination
Page 100
Take the ultimate moment and shear force from the above table and place them into the Excel
spreadsheet or Mathcad file in order to verify the steel design results of ETABS.
Table 9.2: Summarize of design values required to carry out the design of steel member
Design value Symbol Results
(kN)
Design axial force for gravity load combination (G+0.3Q) NEd.GV 344.75
Design moment at y-y at end 1 (seismic load combination) MEd.GV.y1 -1.293
Design moment at y-y at end 2 (seismic load combination) MEd.GV.y2 3.195
Design moment at z-z at end 1 (seismic load combination) MEd.GV.z1 -0.173
Design moment at z-z at end 2 (seismic load combination) MEd.GV.z2 -0.142
Shear forces at y-y at end (seismic load combination) VEd.GV.y -0.01
Shear force at z-z at end 1 (seismic load combination) VEd.GV.z -1.63
Press the button summary
Page 101
Design results of ETABS
ETABS/HAND Description of
comparison Results
ETABS Equation 6.62 in EC3
0.160
HAND (see section 9.3) 0.135
Page 102
ETABS/HAND N.c.Rd N.t.Rd N.pl.Rd
ETABS 2675.75 2675.75 2675.75
HAND (see section 9.3) 2675.75 2675.75 2675.75
ETABS/HAND Curve Alpha LambarBar Phi Chi Nb.Rd
y-y z-z y-y z-z y-y z-z y-y z-z y-y z-z y-y z-z
ETABS “b” “c” 0.340 0.490 0.268 0.454 0.548 0.66 0.976 0.868 2610 2322
HAND (see section 9.3) “b” “b” 0.340 0.340 0.248 0.42 0.539 0.625 0.983 0.918 2630 2534
Page 103
ETABS/HAND M.c.Rd M.v.Rd
M.b.rd y-y z-z y-y z-z
ETABS 305.8 142.45 305.8 142.45 302.05
HAND (see section 9.3) 305.8 142.45 305.8 142.45 305.80
ETABS/HAND Curve AlphaLT LambdaBarLT PhiLT ChiLT C1 Mcr
ETABS a 0.21 0.255 0.538 0.988 2.532 4694
HAND (see section 9.3) b 0.34 0.24 0.535 0.986 2.532 4679
ETABS/HAND kyy kyz kzy kzz
ETABS 0.442 0.582 0.964 0.970
HAND (see section 9.3) 0.441 0.576 0.265 0.96
Page 104
ETABS/HAND V.c.Rd
V.pl.Rd η y-y z-z
ETABS 504 1234 504 1.2
HAND (see section 9.3) 504 1156 504 1.0
Page 105
9.3 Design of steel column (Gravity design situation) – Hand calculations
1. Rolled I - section 2. Limit to class 1 and 2 section 3. Column not susceptible to torsional deformations
Length of column
Total axial load on column, NEd
Shear force y-y axis
Shear force z-z axis
Design moment y-y axis
Design moment y-y axis
Maximum moment
Design moment z-z axis
Design moment z-z axis
Maximum moment
Section properties:
Depth of section,h: Width of section,b:
Thickness of web, tw:
Thickness of flange, tf :
Thickness of element
Second moment of area z-z:
Second moment of area y-y:
Cross section area, A:
Radius of section:
Heigth of web, hw
hc 3m:=
NEd 344.798kN:=
VEd.y 0.011kN:=
VEd.z 1.626kN:=
MEd.y1 3.195kNm⋅:=
MEd.y2 1.293− kNm⋅:=
MEd.y maxMEd.y1 MEd.y2, ( ) 3.195kNm⋅⋅=:=
MEd.z1 0.142− kNm⋅:=
MEd.z2 0.173− kNm⋅:=
MEd.z maxMEd.z1 MEd.z2, ( ) 0.142− kNm⋅⋅=:=
h 270mm:=
b 280mm:=
tw 8mm:=
tf 13mm:=
t max tw tf, ( ) 13mm⋅=:=
Izz 47630000mm4:=
Iyy 1.367 108⋅ mm4:=
A 9730mm2:=
r 24mm:=
hw h 2tf− 2r− 196mm⋅=:=
Page 106
Area of the web
Warping Constant, Iw:
Torsional Constant, IT:
Plastic Modulus, Wply
Plastic Modulus, Wplz
Elastic modulus, E:
Yield strength of steel , fy:
Ultimate strength, fu:
Shear modulus
Reduction of yield and ultimate strength of sections EN10025-2
Partial safety factor
Resistance of cross-sections whatever the class (CYS EN1993-1-1,cl 6.1(1))
Resistance of members to instability (CYS EN1993-1-1,cl 6.1(1))
Resistance of cross-section in tension (CYS EN1993-1-1,cl.6.1(1))
Section classification
For section classification the coefficient ε is:
For a flange element:
Aw hw tw⋅ 1.568 103× mm2⋅=:=
Iw 753.7 109⋅ mm6⋅:=
It 635000mm4:=
Wpl.y 1112000mm3:=
Wpl.z 518000mm3:=
Es 210kNmm 2−⋅:=
fy 275N mm 2−⋅:=
fu 430N mm 2−⋅:=
G 81kNmm 2−⋅:=
fy fy t 16mm≤if
fy 10N mm 2−⋅− 16mm t< 40mm≤if
fy 20N mm 2−⋅− 40mm t< 80mm≤if
:=
fy 275 N mm 2−⋅⋅=
fu fu t 16mm≤if
fu 10N mm 2−⋅− 16mm t< 40mm≤if
fu 20N mm 2−⋅− 40mm t< 80mm≤if
:=
fu 430 N mm 2−⋅⋅=
γM0 1:=
γM1 1:=
γM2 1.25:=
ε235fy
N mm 2−⋅
0.924=:=
Page 107
For a web element:
Tension resistance (cl.6.2.3)
Design plastic resistance of the cross section (EN1993-1-1,cl.6.2.3(2)
Design ultimate resistance (EN1993-1-1,cl.6.2.3(2b))
Design tension resistance (EN1993-1-1,cl.6.2.3(2))
Check tension capacity
cfb tw− 2.r−( )
2112mm⋅=:=Class_type flange "CLASS 1"
cftf
9 ε⋅≤if
"CLASS 2" 9 ε⋅cftf
< 10 ε⋅≤if
"CLASS 3" 10 ε⋅cftf
< 14 ε⋅≤if
:=
Class_type flange "CLASS 2"=
cw h 2 tf⋅− 2 r⋅− 196mm⋅=:=
Class_type web "CLASS 1"cwtw
72 ε⋅≤if
"CLASS 2" 84 ε⋅cwtw
< 83 ε⋅≤if
"CLASS 3" 105 ε⋅cwtw
< 124 ε⋅≤if
:= Class_type web "CLASS 1"=
Class_type if Class_type flange Class_type web Class_type flange, "ADD MANUALY", ( ):=
Class_type "ADD MANUALY"=
Npl.RdA fy⋅
γM02.676 103× kN⋅=:=
Nu.Rd0.9A fy⋅
γM21.927 103× kN⋅=:=
Nt.Rd min Nu.Rd Npl.Rd, ( ) 1.927 103× kN⋅=:=
Check1 ifNEd
Nt.Rd1.0≤ "OK", "NOT OK",
⎛⎜⎝
⎞⎟⎠
:=
Check1 "OK"=
Page 108
Compression resistance (cl.6.2.4)
Compression resistance of steel section (EN1993-1-1,cl.6.2.4(1))
Check compression capacity (EN1993-1-1,cl.6.2.4(1)P)
Bending resistance (cl.6.2.5) Moment resistance of steel section at Y-Y (EN1993-1-1,cl.6.2.5(2)
Moment resistance of steel section at Z-Z (EN1993-1-1,cl.6.2.5(2)
Shear resistance (cl.6.2.6)
Factor for shear area (EN1993-1-1,cl.6.2.6(g))
Shear area of steel section (EN1993-1-1,cl.6.2.6(3))
Shear resistance of steel section Y-Y (EN1993-1-1,cl.6.2.6(2))
Shear area of steel section (EN1993-1-1,cl.6.2.6(3))
Shear resistance of steel section Z-Z (EN1993-1-1,cl.6.2.6(2))
Nc.Rd Npl.Rd 2.676 103× kN⋅=:=
Check2 ifNEd
Nc.Rd1.0≤ "OK", "NOT OK",
⎛⎜⎝
⎞⎟⎠
:=
Check2 "OK"=
Mc.Rd.yWpl.y fy⋅
γM0305.8kNm⋅⋅=:=
Mc.Rd.zWpl.z fy⋅
γM0142.45kNm⋅⋅=:=
η 1:=
Avy A 2 b⋅ tf⋅− tw 2r+( ) tf⋅+:=
Av Avy Avy η tw⋅ hw⋅>if
η tw⋅ hw⋅ Avy η tw⋅ hw⋅<if
:= Av 3.178 103× mm2⋅=
Vpl.Rd.y Avfy 3( ) 1−⋅
γM0⋅ 504.575kN⋅=:=
Avz 2 b⋅ tf⋅ 7.28 103× mm2⋅=:=
Vpl.Rd.z 2 b⋅ tf⋅fy 3( ) 1−⋅
γM0⋅ 1.156 103× kN⋅=:=
Page 109
Check if the verification of shear buckling resistance required or not (EN1993-1-1,cl.6.2.6(6))
Bending and shear interaction check (cl.6.2.8)
Strong axis Y-Y
Interaction check 1
Reduced yield strength
Reduced design plastic resistance moment (EN1993-1-1,cl.6.2.8(5))
Weak axis Z-Z
Interaction check 1
Reduced yield strength
Reduced design plastic resistance moment (EN1993-1-1,cl.6.2.8(5))
Check ifhwtw
72ε
η⋅< "Not required shear buckling resistance", "Required shear buckling resistance",
⎛⎜⎝
⎞⎟⎠
:=
Check "Not required shear buckling resistance"=
vyVEd.yVpl.Rd.y
2.18 10 5−×=:=
ρ2VEd.yVpl.Rd.y
1−⎛⎜⎝
⎞⎟⎠
2
1=:=
Mc.Rd.y
Wpl.yρ Aw
2⋅
4tw−
⎛⎜⎜⎝
⎞⎟⎟⎠fy⋅
γM0vy 0.5>if
Mc.Rd.y vy 0.5<if
:=
Mc.Rd.y 305.8kNm⋅⋅=
vzVEd.zVpl.Rd.z
1.407 10 3−×=:=
ρ2VEd.zVpl.Rd.z
1−⎛⎜⎝
⎞⎟⎠
2
0.994=:=
Mc.Rd.z
Wpl.zρ Aw
2⋅
4tw−
⎛⎜⎜⎝
⎞⎟⎟⎠fy⋅
γM0vz 0.5>if
Mc.Rd.z vz 0.5<if
:=
Mc.Rd.z 142.45kNm⋅⋅=
Page 110
Check combination of axial and bending (EN1993-1-1,cl.6.2.1(7))
Unity factor
Bending and axial force interaction check (cl.6.2.9)
Factor a
Factor n
Factor β
Coefficient 1
Coefficient 2
Coefficient check
Strong axis Y-Y Reduced design value of the resistance to
bending moments making allowance for the presence of axial forces (EN1993-1-1,cl.6.2.9.1(5))
Check_1 ifNEd
Npl.Rd
MEd.yMc.Rd.y
+MEd.z
Mc.Rd.z+ 1.0≤ "OK", "NOT OK",
⎛⎜⎝
⎞⎟⎠
:=
NEdNpl.Rd
MEd.yMc.Rd.y
+MEd.zMc.Rd.z
+ 0.138=
Check_1 "OK"=
a minA 2b tf⋅−( )
A0.5,
⎡⎢⎣
⎤⎥⎦
0.252=:=
nNEdNpl.Rd
0.129=:=
β 5n 5n 1≥if
1 otherwise
1=:=
c1NEd
0.25Npl.Rd0.515=:=
c2NEd
0.5hw tw⋅ fy⋅1.599=:=
c max c1 c2, ( ) 1.599=:=
MN.y.RdMc.Rd.y 1 n−( )⋅
1 0.5a−c 1>if
Mc.Rd.y 0 c≤ 1≤if
:=
MN.y.Rd 304.764kNm⋅⋅=
Page 111
Weak axis Z-Z Reduced design value of the resistance to bending moments making allowance for the presence of axial forces (EN1993-1-1,cl.6.2.9.1(5))
Check combination of bi-axial bending (EN1993-1-1,cl.6.2.9.1(6))
Unity factor
Bucking interaction check (cl.6.3)
Strong axis Y-Y
Status of effective length
Effective length factor (Guidance of EC3)
Buckling length of column (fixed end)
Euler Buckling at y-y axis (EN1993-1-1,cl.6.3.1.2(1)
MN.z.Rd Mc.Rd.z n a≤if
Mc.Rd.z 1n a−1 a−⎛⎜⎝
⎞⎟⎠
2−
⎡⎢⎣
⎤⎥⎦
⋅ n a≥if
:=
MN.z.Rd 142.45kNm⋅⋅=
Check_1 ifMEd.y
MN.y.Rd
⎛⎜⎝
⎞⎟⎠
a MEd.zMN.z.Rd
⎛⎜⎝
⎞⎟⎠
β
+
⎡⎢⎢⎣
⎤⎥⎥⎦
1.0≤ "OK", "NOT OK",
⎡⎢⎢⎣
⎤⎥⎥⎦
:=
MEd.yMN.y.Rd
⎛⎜⎝
⎞⎟⎠
a MEd.zMN.z.Rd
⎛⎜⎝
⎞⎟⎠
β
+ 0.316=
Check_1 "OK"=
Effective_Length " Pinned Fixed":=
k 0.7 Effective_Length "Fixed Fixed"if
0.85 Effective_Length "Partial restraint"if
0.85 Effective_Length " Pinned Fixed"if
1 Effective_Length "Pinned Pinned"if
0.85=:=
Lcr k hc 2.55m=:=
NcryEs Iyy⋅ π
2⋅
Lcr2
4.357 104× kN⋅=:=
Page 112
Slenderness parameter at y-y axis (for class 1,2 and 3 cross-section) (EN1993-1-1,cl.6.3.1.2(1)
Buckling curve (EN1993-1-1,table 6.2)
Imperfection factor (EN1993-1-1,table 6.1)
Value to determine the reduction factor χ (EN1993-1-1,cl.6.3.1.2(1))
Reduction factor χ (EN1993-1-1,cl.6.3.1.2(1))
Reduction factor χ check
Design buklcing resistance (EN1993-1-1,cl.6.3.1.1(3))
Buckling resistance of compression member check (EN1993-1-1,cl.6.3.1.1(1))
λyA fy⋅
Ncry0.248=:=
Buckling_class_Y
"a" tf 40mm<if
"b" 40mm tf< 100mm<if
hb
1.2>if
"b" tf 100mm≤if
"d" tf 100mm>if
hb
1.2≤if
:=
Buckling_class_Y "b"=
αy 0.1 Buckling_class_Y "ao"if
0.21 Buckling_class_Y "a"if
0.34 Buckling_class_Y "b"if
0.49 Buckling_class_Y "c"if
0.76 Buckling_class_Y "d"if
:=
αy 0.34:=
φ y 0.5 1 αy λy 0.2−( )⋅+ λy2
+⎡⎣
⎤⎦⋅ 0.539=:=
χy1
φ y φ y2
λy2
−+
0.983=:=
Check1 if χy 1.0≤ "OK", "NOT OK", ( ):=
Check1 "OK"=
Nb.Rd.yχy A⋅ fy⋅
γM12.63 103× kN⋅=:=
Check2 ifNEd
Nb.Rd.y"OK", "NOT OK",
⎛⎜⎝
⎞⎟⎠
:=
Check2 "OK"=
Page 113
Weak axis Z-Z
Buckling length of column (fixed end)
Euler Buckling at y-y axis (EN1993-1-1,cl.6.3.1.2(1)
Slenderness parameter at y-y axis (for class 1,2 and 3 cross-section) (EN1993-1-1,cl.6.3.1.2(1)
Check if the buckling may be ignored (EN1993-1-1,cl.6.3.1.2(4))
Slenderness parameter
MinimumEuler Buckling
Buckling curve (EN1993-1-1,table 6.2)
Imperfection factor (EN1993-1-1,table 6.1)
Lcr k hc⋅ 2.55m=:=
NcrzEs Izz⋅ π
2⋅
Lcr2
1.518 104× kN⋅=:=
λzA fy⋅
Ncrz0.42=:=
λ max λy λz, ( ):=
Ncr min Ncry Ncrz, ( ):=
Check_2 if λ 0.2<NEdNcr
0.04<∧ "Ignored buckling effects", "Consider buckling effects", ⎛⎜⎝
⎞⎟⎠
:=
Check_2 "Consider buckling effects"=
Buckling_class_Z
"a" tf 40mm<if
"b" 40mm tf< 100mm<if
hb
1.2>if
"b" tf 100mm≤if
"d" tf 100mm>if
hb
1.2≤if
:=
Buckling_class_Z "b"=
αz 0.1 Buckling_class_Z "ao"if
0.21 Buckling_class_Z "a"if
0.34 Buckling_class_Z "b"if
0.49 Buckling_class_Z "c"if
0.76 Buckling_class_Z "d"if
:=
αz 0.34:=
Page 114
Value to determine the reduction factor χ (EN1993-1-1,cl.6.3.1.2(1))
Reduction factor χ (EN1993-1-1,cl.6.3.1.2(1))
Reduction factor χ check
Design buklcing resistance (EN1993-1-1,cl.6.3.1.1(3))
Buckling resistance of compression member check (EN1993-1-1,cl.6.3.1.1(1))
Lateral torsional buckling check (cl.6.3.2)
Effective length factor, k (SN003a-EN-EU)
Factor for end warping, kw (SN003a-EN-EU)
Ratio of the smaller and larger moment
Coefficient factor C1 (SN003a-EN-EU)
Coefficient factor C1 check (SN003a-EN-EU)
Coefficient factor C2 (SN003a-EN-EU)
Distance between the point of load application and the shear centre
φ z 0.5 1 αz λz 0.2−( )⋅+ λz2
+⎡⎣
⎤⎦⋅ 0.625=:=
χz1
φ z φ z2
λz2
−+
0.918=:=
Check_3 if χz 1.0≤ "OK", "NOT OK", ( ):=
Check_3 "OK"=
Nb.Rd.zχz A⋅ fy⋅
γM12.457 103× kN⋅=:=
Check_4 ifNEd
Nb.Rd.z"OK", "NOT OK",
⎛⎜⎝
⎞⎟⎠
:=
Check_4 "OK"=
k 0.85=
kw 1.0:=
ψMEd.y2MEd.y1
0.405−=:=
C1 1.88 1.40ψ− 0.52ψ 2+ 2.532=:=
Check_5 if C1 2.7≤ "OK", "NOT OK", ( ):=
Check_5 "OK"=
C2 1.554:=
zg 0m:=
Page 115
Elastic critical moment for lateral torsional buckling (SN003a-EN-EU)
Lateral torsional buckling curve (EN1993-1-1,table 6.4)
Imperfection factor for lateral torsional (EN1993-1-1,table 6.3)
Non dimensional slenderness (EN1993-1-1,cl.6.3.2.2(1))
Value to determine the reduction factor (EN1993-1-1,cl.6.3.2.2(1))
Reduction factor for lateral-torsional buckling (EN1993-1-1,cl.6.3.2.2(1))
Parameter λ LTO (EN1993-1-1,cl.6.3.2.3(1))
Design buckling resistance moment (EN1993-1-1,cl.6.3.2.1(3))
Mcr C1π2 Es⋅ Izz⋅
Lcr( )2⋅
kkw
⎛⎜⎝
⎞⎟⎠
2 IwIzz⋅
Lcr( )2G It⋅
π2Es Izz⋅
+ C2 zg⋅( )2+⋅ C2 zg⋅− 4.679 103× kNm⋅⋅=:=
Buckling_curve_Z "b"hb
2≤if
"c"hb
2>if
:=
Buckling_curve_Z "b"=
αLT 0.21 Buckling_curve_Z "a"if
0.34 Buckling_curve_Z "b"if
0.49 Buckling_curve_Z "c"if
0.76 Buckling_curve_Z "d"if
:=
αLT 0.34=
λLTWpl.y fy⋅
Mcr0.256=:=
φLT 0.5 1 αLT λLT 0.2−( )⋅+ λLT2
+⎡⎣
⎤⎦⋅ 0.542=:=
χLT1
φLT φLT2
λLT2
−+
0.98=:=
Check_6 if χLT 1≤ χLT1
λLT2
≤∧ "OK", "NOT OK", ⎛⎜⎜⎝
⎞⎟⎟⎠
:=
Check_6 "OK"=
λLTO 0.4:=
Mb.Rd χLTWpl.y⋅fyγM1⋅ 299.741kNm⋅⋅=:=
Check_7 ifMEd.yMb.Rd
1≤ "OK", "NOT OK", ⎛⎜⎝
⎞⎟⎠
:=
Page 116
Check if the lateral torsional buckling be ignored (EN1993-1-1,cl.6.3.2.2(4))
Combine bending and axial compression cl.6.3.3
Moments due to the shift of the centroidal axis for class sections 1,2 & 3 (EN1993-1-1,cl.6.3.3(4)/table 6.7)
Characteristic resistance to normal force of the critical cross-section (EN1993-1-1,cl.6.3.3(4)/table 6.7)
Characteristic moment resistance of the critical cross-section (EN1993-1-1,cl.6.3.3(4)/table 6.7)
Ratio of end moments (EN1993-1-1,Table B2)
Equivalent uniform moment factor
Equivalent uniform moment factor
Check_7 "OK"=
Check_8 if λLT λLTO<MEd.yMcr
λLTO2
<∧ "Ignored torsional buckling effects", "Consider torsional buckling effects", ⎛⎜⎝
⎞⎟⎠
:=
Check_8 "Ignored torsional buckling effects"=
ΔMEd.z 0:=
ΔMEd.y 0:=
NRk fy A⋅ 2.676 103× kN⋅=:=
My.Rk Mc.Rd.y 305.8kNm⋅⋅=:=
Mz.Rk Mc.Rd.z 142.45kNm⋅⋅=:=
ψyMEd.y1MEd.y2
1−MEd.y1MEd.y2
≤ 1≤if
MEd.y2MEd.y1
1−MEd.y2MEd.y1
≤ 1≤if
:=
ψzMEd.z1MEd.z2
1−MEd.z1MEd.z2
≤ 1≤if
MEd.z2MEd.z1
1−MEd.z2MEd.z1
≤ 1≤if
:=
Cmy 0.6 0.4ψy⋅+ 0.438=:=
Cmz 0.6 0.4ψz⋅+ 0.928=:=
Page 117
Interaction factors (EN1993-1-1,table B.1&B.2)
EN1993-1-1,Equation 6.61
Unity factor
EN1993-1-1,Equation 6.62
Unity factor
kyy min Cmy 1 λy 0.2−( )NEd
χyNRkγM1⋅
⋅+⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
⋅⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
Cmy 1 0.8NEd
χyNRkγM1⋅
⋅+⎛⎜⎜⎜⎝
⎞⎟⎟⎟⎠
⋅, ⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
0.441=:=
kzz min Cmz 1 2λz 0.6−( )NEd
χzNRkγM1⋅
⋅+⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
⋅⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
Cmz 1 1.4NEd
χzNRkγM1⋅
⋅+⎛⎜⎜⎜⎝
⎞⎟⎟⎟⎠
⋅, ⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
0.96=:=
kyz 0.6kzz 0.576=:=
kzy 0.6kyy 0.265=:=
Check_9 ifNEd
χy NRk⋅
γM1
kyyMEd.y ΔM Ed.y+
χLTMy.RkγM1
⋅
⋅+ kyzMEd.z ΔM Ed.z+
Mz.Rk
γM1
⋅+ 1.0≤ "OK", "NOT OK", ⎛⎜⎜⎜⎝
⎞⎟⎟⎟⎠
:=
NEdχy NRk⋅
γM1
kyyMEd.y ΔM Ed.y+
χLTMy.RkγM1
⋅
⋅+ kyzMEd.z ΔM Ed.z+
Mz.Rk
γM1
⋅+ 0.135=
Check_9 "OK"=
Check_10 ifNEd
χz NRk⋅
γM1
kzyMEd.y ΔM Ed.y+
χLTMy.RkγM1
⋅
⋅+ kzzMEd.z ΔM Ed.z+
Mz.Rk
γM1
⋅+ 1.0≤ "OK", "NOT OK", ⎛⎜⎜⎜⎝
⎞⎟⎟⎟⎠
:=
NEdχz NRk⋅
γM1
kzyMEd.y ΔM Ed.y+
χLTMy.RkγM1
⋅
⋅+ kzzMEd.z ΔM Ed.z+
Mz.Rk
γM1
⋅+ 0.142=
Check_10 "OK"=
Page 118
9.4 Design of steel column (Seismic design situationn)
Column name: C2 Storey level: Storey 1
Page 119
Step 1: Option > Preferences > Steel frame design
Step 2: Design > Steel frame design > Select design combo…
Figure 9.7: Lateral/gravity load combination at ULS
Modify the existing “System Omega”. The omega factor is equal to the minimum section overstrength factor of concentric bracing. See below:
Note: the minimum value of Ω is calculate over all the diagonals of the braced frame system
Page 120
Figure 9.8: Gravity load combination at SLS
Ultimate limit state (ULS)
Static load combination
STATIC 1. 1.35DL + 1.5LL STATIC 2. 1.35DL + 1.5LL + 0.75WINDX STATIC 3. 1.35DL + 1.5LL - 0.75WINDX STATIC 4. 1.35DL + 1.5LL + 0.75WINDY STATIC 5. 1.35DL + 1.5LL - 0.75WINDY STATIC 6. 1.35DL + 1.5WINDX + 1.05LL STATIC 7. 1.35DL - 1.5WINDX – 1.05LL STATIC 8. 1.35DL + 1.5WINDY + 1.05LL
Page 121
STATIC 9. 1.35DL - 1.5WINDY – 1.05LL STATIC 10. DL + 0.3LL
Seismic load combination for “Modal Analysis”
SEISMIC 1. DL + 0.3LL + EQX + 0.3EQY SEISMIC 2. DL + 0.3LL + EQX – 0.3EQY SEISMIC 3. DL + 0.3LL - EQX + 0.3EQY SEISMIC 4. DL + 0.3LL - EQX – 0.3EQY SEISMIC 5. DL + 0.3LL + EQY + 0.3EQX SEISMIC 6. DL + 0.3LL + EQY – 0.3EQX SEISMIC 7. DL + 0.3LL - EQY + 0.3EQX SEISMIC 8. DL + 0.3LL - EQY – 0.3EQX
Serviceability limit state (SLS)
DSTLD 1. DL + LL DSTLD 2. LL
ETABS: Display > Show Tables
Table 9.3a: Analysis results of gravity load combination (STATIC 10: G + 0.3Q)
Story Column Load Loc P V2 V3 T M2 M3
STORY1 C2 STATIC10 0 -‐245.17 -‐0.28 -‐0.27 0 -‐0.43 0.001 STORY1 C2 STATIC10 1.38 -‐244.13 -‐0.28 -‐0.27 0 -‐0.055 0.389
Select all combinations
Page 122
STORY1 C2 STATIC10 2.76 -‐243.1 -‐0.28 -‐0.27 0 0.321 0.776 Note: P = NEd.G
Table 9.3b: Analysis results of seismic action (MODAL EQX / EQY)
Story Column Load Loc P V2 V3 T M2 M3
STORY1 C2 EQX 0 38.99 29.66 0.49 -‐0.001 0.884 58.02 STORY1 C2 EQX 1.38 38.99 29.66 0.49 -‐0.001 0.202 17.094 STORY1 C2 EQX 2.76 38.99 29.66 0.49 -‐0.001 -‐0.48 -‐23.833 STORY1 C2 EQX 0 33.61 26.3 1.15 0.001 1.917 51.189 STORY1 C2 EQX 1.38 33.61 26.3 1.15 0.001 0.332 14.928 STORY1 C2 EQX 2.76 33.61 26.3 1.15 0.001 1.256 21.431 STORY1 C2 EQY 0 3.55 2.72 8.97 0.003 14.692 5.227 STORY1 C2 EQY 1.38 3.55 2.72 8.97 0.003 2.313 1.468 STORY1 C2 EQY 2.76 3.55 2.72 8.97 0.003 10.076 2.297 STORY1 C2 EQY 0 2.6 1.89 10.93 0.002 17.899 3.709 STORY1 C2 EQY 1.38 2.6 1.89 10.93 0.002 2.813 1.097 STORY1 C2 EQY 2.76 2.6 1.89 10.93 0.002 -‐12.273 -‐1.516 Note: P = NEd.E
Results of Seismic load combination (SEISMIC 1-8)
Select all the seismic load combinations Sort out the highest values of P, V and M
Page 123
Table 9.4: Analysis result of design values of V and M based on worst case seismic design
combination
Story Column Load Loc P V2 V3 T M2 M3
STORY1 C2 SEISMIC1 MIN 0 -‐279.84 -‐27.4 -‐4.11 -‐0.002 -‐6.755 -‐52.756 STORY1 C2 SEISMIC1 MIN 1.38 -‐278.8 -‐27.4 -‐4.11 -‐0.002 -‐1.081 -‐14.979 STORY1 C2 SEISMIC1 MIN 2.76 -‐277.77 -‐27.4 -‐4.11 -‐0.002 -‐3.958 -‐21.344
Table 9.5: Summarize of design values required to carry out the design of steel member
Design value Symbol Results
(kN/kNm)
Design axial force for gravity load combination (G+0.3Q) NEd.G 245
Design axial force for the design seismic action alone NEd.E 39
Design moment at y-y at end 1 (seismic load combination) MEd.SC.y1 52.8
Design moment at y-y at end 2 (seismic load combination) MEd.SC.y2 21.3
Design moment at z-z at end 1 (seismic load combination) MEd.SC.z1 6.8
Design moment at z-z at end 2 (seismic load combination) MEd.SC.z2 4.0
Shear forces at y-y at end (seismic load combination) VEd.SC.y 27.4
Shear force at z-z at end 1 (seismic load combination) VEd.SC.z 4.1
Page 124
9.4.1 Design of steel column (Seismic design situation – Hand calculation)
Detail design of steel column using Eurocode 3 and Eurocode 8
1. Rolled I - section 2. Limit to class 1 and 2 section 3. Column not susceptible to torsional deformations Design data
Length of column Overstrength factor (EN1998-1-1,cl.6.1.3(2))
Omega factor of bracing members at storey 1
Behavior factor q
Ductlity class
Total axial force due to the non-seismic actions (G+ψ EiQ)
Total axial force due to the non-seismic actions (seismic)
Design shear force due to Eurocode requirement (EN1998-1-1,cl.6.7.4(1))
Design shear force due to Eurocode requirement (EN1998-1-1,cl.6.7.4(1))
Design moment y-y axis (seismic combination)
Design moment y-y axis (seismic combination)
Design moment y-y axis (seismic combination)
Design moment y-y axis (seismic combination)
Maximum moment
Maximum moment
hc 3m:=
γ ov 1.25:=
Ω 2.5:=
q 4:=
Ductility_class "DCM":=
NEd.G 245.17kN:=
NEd.E 39kN:=
VEd.y 4.11kN:=
VEd.z 27.4kN:=
MEd.y1 52.76kNm⋅:=
MEd.y2 21.34kNm⋅:=
MEd.z1 6.75kNm⋅:=
MEd.z2 3.96kNm⋅:=
MEd.y maxMEd.y1 MEd.y2, ( ) 52.76kNm⋅⋅=:=
MEd.z maxMEd.z1 MEd.z2, ( ) 6.75 kNm⋅⋅=:=
Page 125
Design shear force due to Eurocode requirement (EN1998-1-1,cl.6.7.4(1))
Section properties:
Depth of section,h: Width of section,b:
Thickness of web, tw: Thickness of flange, tf :
Thickness of element Second moment of area z-z: Second moment of area y-y:
Cross section area, A:
Radius of section,r:
Heigth of web, hw
Area of the web
Warping Constant, Iw:
Torsional Constant, IT:
Plastic Modulus, Wply
Plastic Modulus, Wplz
Elastic modulus, E:
Yield strength of steel , fy:
Ultimate strength, fu:
Shear modulus
NEd NEd.G 1.1 γ ov⋅ Ω⋅ NEd.E⋅+ 379.233kN⋅=:=
h 270mm:=
b 280mm:=
tw 8mm:=
tf 13mm:=
t max tw tf, ( ) 13mm⋅=:=
Izz 47630000mm4:=
Iyy 1.367 108⋅ mm4:=
A 9730mm2:=
r 24mm:=
hw h 2tf− 2r− 196mm⋅=:=
Aw hw tw⋅ 1.568 103× mm2⋅=:=
Iw 753.7 109⋅ mm6⋅:=
It 635000mm4:=
Wpl.y 1112000mm3:=
Wpl.z 518000mm3:=
Es 210kNmm 2−⋅:=
fy 275N mm 2−⋅:=
fu 430N mm 2−⋅:=
G 81kNmm 2−⋅:=
Page 126
Reduction of yield and ultimate strenght of sections EN10025-2
Partial safety factor
Resistance of cross-sections whatever the class (CYS EN1993-1-1,cl 6.1(1))
Resistance of members to instability (CYS EN1993-1-1,cl 6.1(1))
Resistance of cross-section in tension (CYS EN1993-1-1,cl.6.1(1))
Section classification
For section classification the coefficient ε is:
For a flange element:
fy fy t 16mm≤if
fy 10N mm 2−⋅− 16mm t< 40mm≤if
fy 20N mm 2−⋅− 40mm t< 80mm≤if
:=
fy 275 N mm 2−⋅⋅=
fu fu t 16mm≤if
fu 10N mm 2−⋅− 16mm t< 40mm≤if
fu 20N mm 2−⋅− 40mm t< 80mm≤if
:=
fu 430 N mm 2−⋅⋅=
γM0 1:=
γM1 1:=
γM2 1.25:=
ε235fy
N mm 2−⋅
0.924=:=
cfb tw− 2.r−( )
2112mm⋅=:=
Class_type flange "CLASS 1"cftf
9 ε⋅≤if
"CLASS 2" 9 ε⋅cftf
< 10 ε⋅≤if
"CLASS 3" 10 ε⋅cftf
< 14 ε⋅≤if
:=
Class_type flange "CLASS 2"=
Page 127
Note: The column now has to be check using the resistance verification checks of Eurocode
3 as shown in section 9.3 of this document.
For a web element:
Requirements on cross-sectional class of dissipative elements depending on Ductility class (EN1998-1-1,cl.6.5.3(2))
Section classification rule for EC8 (EN1998-1-1,cl.6.5.3(2))
cw h 2 tf⋅− 2 r⋅− 196mm⋅=:=
Class_type web "CLASS 1"cwtw
72 ε⋅≤if
"CLASS 2" 84 ε⋅cwtw
< 83 ε⋅≤if
"CLASS 3" 105 ε⋅cwtw
< 124 ε⋅≤if
:=Class_type web "CLASS 1"=
Class_type if Class_type flange Class_type web Class_type flange, "ADD MANUALY", ( ):=
Class_type "ADD MANUALY"=
Class_type_req "CLASS 1 , 2 or 3" 1.5 q< 2≤ Ductility_class "DCM"∧if
"CLASS 1 or 2" 2 q< 4≤ Ductility_class "DCM"∧if
"CLASS 1" q 4> Ductility_class "DCH"∧if
:=
Class_type_req "CLASS 1 or 2"=
Page 128
9.5 Design of composite beams - Hand calculations
ETABS: Define > Wall/Slab/Deck sections
Figure 9.9: Define deck section Comflor60 -Corus
Figure 9.10: Modified “Stiffness Modifiers” (crack-sections)
Page 129
ETABS: Analyze > Run analysis
ETABS: Display > Show Tables >
Select all combinations
Page 130
Assumptions - Design and analysis
This design process is envisaging a analyzed to determine the forces and moments in the individual structural members. Simple design approach: This method applies to structures in which the connections between members will not develop any significant restraint moments. Members forces and moments are calculated on the basic of the following assumptions: 1. Simply supported beam. 2. The steel sheeting with ribs is placed transverse to the beam. 3. Limited only to I abd H rolled sections with equal flanges 4. Ignored any contribution of steel sheeting to the transverse reinforcements
Length of beam
Spacing of the secondary beams (LHS)
Spacing of the secondary beams (RHS)
Loading length
Slab design data
Comfloor 60
Overall depth of slab
Steel sheeting deck profile (Comflor 60)
Depth of concrete slab above steel sheeting
Rib width at top
Rib width at bottom
Le 5m:=
L1 5m:=
L2 5m:=
LL12
L22
+ 5m=:=
h 150mm:=
hp 60mm:=
hc h hp− 90mm⋅=:=
b1 131mm:=
b2 180mm:=
Page 131
Distance between shear connector (Assume single shear connector)
Space of each troughs
Thickness of steel sheeting
Structural steel properties
Depth of section, h:
Width of section,b:
Thickness of web, tw:
Thickness of flange, tf :
Thickness of element
Radius of section,r:
Heigth of web, hw
Area of the web
Radious of gyration
Second moment of area z-z:
Second moment of area y-y:
Cross section area, A:
Torsional Constant, IT:
Warping Constant, Iw:
Plastic Modulus, Wply
Plastic Modulus, Wplz
Yield strength
Ultimate strength
Modulus of Elasticity
Shear modulus
bob1 b2+
2155.5mm⋅=:=
e 300mm:=
ts 1mm:=
ha 240mm:=
b 120mm:=
tw 6.2mm:=
tf 9.8mm:=
t max tw tf, ( ) 9.8mm⋅=:=
r 15mm:=
hw ha 2tf− 2r− 190.4mm⋅=:=
Aw hw tw⋅ 1.18 103× mm2⋅=:=
iz 26.9507mm:=
Izz 2840000mm4:=
Iyy 38920000mm4:=
A 3910mm2:=
It 130000mm4:=
Iw 753.7 109⋅ mm6⋅:=
Wpl.y 367000mm3:=
Wpl.z 73900mm3:=
fy 275N mm 2−⋅:=
fu 430N mm 2−⋅:=
Es 210kNmm 2−⋅:=
G 81kNmm 2−⋅:=
Page 132
Concrete properties
Yield strength of reinforcement
Cylinder strength
Modulus of Elasticity
Shear connector properties
Diameter Overall height before welding
Ultimate strength of shear connector
Number of stud per in one rib
Material partial factors for resistance
Resistance of cross-sections whatever the class (CYS EN1993-1-1,cl 6.1(1))
Resistance of members to instability (CYS EN1993-1-1,cl 6.1(1))
Partial factor for concrete (EN 1992 1-1 Table 2.1N)
Partial factor for reinforcing steel (EN 1992 1-1 Table 2.1N)
Partial factor for design shear resistance of a headed stud (CYS EN1994-1-1,cl.2.4.1.2(5)P)
Partial factor for design shear resistance of a composite slab (CYS EN1994-1-1,cl.2.4.1.2(6)P)
Partial factor for permanent action
Partial factor for variable action
Design value of the cylinder compressive strength of concrete (EN1992-1-1,cl.
fyk 500N mm 2−⋅:=
fck 25N mm 2−⋅:=
Ecm 31kNmm 2−⋅:=
d 19mm:=
hsc 95mm:=
fus 450N mm 2−⋅:=
nr 1:=
γM0 1.0:=
γM1 1.0:=
γ c 1.5:=
γ s 1.15:=
γ v 1.25:=
γ vs 1.25:=
γG 1.35:=
γQ 1.5:=
fcdfckγ c
16.667N mm 2−⋅⋅=:=
Page 133
Design value of the yield strength of structural steel
Loading at construction stage
Dead load
Weight of steel deck (Comfloor 60)
Weight of wet concrete
Weight of steel beam (IPE240)
Live load
Construction live load
Total load at construction stage
Moment at construction stage
Shear force at construction stage
Design moments and shear forces
Shear force at composite stage
Design moment at composite stage
Shear force at composite stage
Design moment at composite stage
fydfykγ s
434.783N mm 2−⋅⋅=:=
gk.deck 0.114kNm 2−⋅:=
gk.c.wet 2.79kNm 2−⋅:=
gk.b 0.8kNm 1−⋅:=
qk 0.75kNm 2−⋅:=
FEd γG gk.deck L⋅ gk.c.wet L⋅+ gk.b+( )⋅ γQ qk⋅ L⋅+ 26.307kNm 1−⋅⋅=:=
MEd.cFEd L
2⋅
882.209kNm⋅⋅=:=
VEd.cFEd L⋅
265.767kN⋅=:=
VEd.c 65.767kN⋅=
MEd.c 82.209kNm⋅⋅=
VEd 55.5kN:=
MEd 132kNm⋅:=
Page 134
Ultimate limit state verification
Construction stage
Section classification (EN19931-1,cl.5.6(6))
Reduction of yield and ultimate strength of sections EN10025-2
For section classification the coefficient ε is:
For a flange element:
fy fy t 16mm≤if
fy 10N mm 2−⋅− 16mm t< 40mm≤if
fy 20N mm 2−⋅− 40mm t< 80mm≤if
:=
fy 275 N mm 2−⋅⋅=
fu fu t 16mm≤if
fu 10N mm 2−⋅− 16mm t< 40mm≤if
fu 20N mm 2−⋅− 40mm t< 80mm≤if
:=
fu 430 N mm 2−⋅⋅=
ε235fy
N mm 2−⋅
0.924=:=
cfb tw− 2.r−( )
241.9mm⋅=:=
Class_type flange "CLASS 1"cftf
9 ε⋅≤if
"CLASS 2" 9 ε⋅cftf
< 10 ε⋅≤if
"CLASS 3" 10 ε⋅cftf
< 14 ε⋅≤if
:=
Class_type flange "CLASS 1"=
Page 135
For a web element:
Bending Resistance of the steel section (EN1993-1-1,cl.6.2.5)
Design resistance for bending (EN1993-1-1,cl.6.2.5(2))
Bending resistance check checks (EN1993-1-1,cl.6.2.5(1))
Vertical Shear resistance of the steel section (cl.6.2.2) & (EN1993-1-1,cl.6.2.6)
Factor for shear area (EN1993-1-1,cl.6.2.6(g))
Shear area of steel section (EN1993-1-1,cl.6.2.6(3))
Shear resistance of steel section Y-Y (EN1993-1-1,cl.6.2.6(2))
cw ha 2 tf⋅− 2 r⋅− 190.4mm⋅=:=
Class_type web "CLASS 1"cwtw
72 ε⋅≤if
"CLASS 2" 84 ε⋅cwtw
< 83 ε⋅≤if
"CLASS 3" 105 ε⋅cwtw
< 124 ε⋅≤if
:= Class_type web "CLASS 1"=
Class_type if Class_type flange Class_type web Class_type flange, "ADD MANUALY", ( ):=
Class_type "CLASS 1"=
Ma.pl.RdWpl.y fy⋅
γM0100.925kNm⋅⋅=:=
Check_1 if MEd.c Ma.pl.Rd≤ "OK", "NOT OK", ( ):=
Check_1 "OK"=
η 1:=
Av1 A 2 b⋅ tf⋅− tw 2r+( ) tf⋅+:=
Av Av1 Av1 η tw⋅ hw⋅>if
η tw⋅ hw⋅ Av1 η tw⋅ hw⋅<if
:= Av 1.913 103× mm2⋅=
Vpl.Rd Avfy 3( ) 1−⋅
γM0⋅ 303.691kN⋅=:=
Page 136
Design of shear resistance check (EN1993-1-1,cl.6.2.6(1)P)
Check if the verification of shear buckling resistance required or not (EN1993-1-1,cl.6.2.6(6))
Bending and shear interaction check (cl.6.2.2.4)
Strong axis Y-Y
Interaction check 1
Reduced yield strength
Reduced design plastic resistance moment (EN1993-1-1,cl.6.2.8(5))
Lateral torsional buckling resistance of steel beam (EN1993-1-1,cl.6.3.2)
Status of effective length
Effective length factor (Guidance of EC3)
Check_2 if VEd Vpl.Rd≤ "OK", "NOT OK", ( ):=
Check_2 "OK"=
Check_3 ifhwtw
72ε
η⋅< "Not required shear buckling resistance", "Required shear buckling resistance",
⎛⎜⎝
⎞⎟⎠
:=
Check_3 "Not required shear buckling resistance"=
vyVEdVpl.Rd
0.183=:=
ρ2VEdVpl.Rd
1−⎛⎜⎝
⎞⎟⎠
2
0.403=:=
Ma.pl.Rd.
Wpl.yρ Aw
2⋅
4tw−
⎛⎜⎜⎝
⎞⎟⎟⎠fy⋅
γM0vy 0.5>if
Ma.pl.Rd vy 0.5<if
:=
Ma.pl.Rd 100.925kNm⋅⋅=
Effective_Length "Pinned Pinned":=
k 0.7 Effective_Length "Fixed Fixed"if
0.85 Effective_Length "Partial restraint"if
0.85 Effective_Length " Pinned Fixed"if
1 Effective_Length "Pinned Pinned"if
1=:=
Page 137
Effective length (pinned)
Factor for end warping, kw (SN003a-EN-EU)
Coefficient factor C1 (SN003a-EN-EU)
Coefficient factor C2 (SN003a-EN-EU)
Distance between the point of load application and the shear centre
Elastic critical moment for lateral torsional buckling (SN003a-EN-EU)
Lateral torsional buckling curve (EN1993-1-1,table 6.4)
Imperfection factor for lateral torsional (EN1993-1-1,table 6.3)
Non dimensional slenderness (EN1993-1-1,cl.6.3.2.2(1))
Parameter introducing the effect of biaxial bending (EN1994-1-1,cl.6.3.2.3(1))
Parameter λ LTO (EN1993-1-1,cl.6.3.2.3(1))
Lcr k Le⋅ 5m=:=
kw 1.0:=
C1 1.348:=
C2 0.454:=
zg 0m:=
Mcr C1π2 Es⋅ Izz⋅
Lcr( )2⋅
kkw
⎛⎜⎝
⎞⎟⎠
2 IwIzz⋅
Lcr( )2G It⋅
π2Es Izz⋅
+ C2 zg⋅( )2+⋅ C2 zg⋅− 176.744kNm⋅⋅=:=
Buckling_curve_Z "b"hb
2≤if
"c"hb
2>if
:=
Buckling_curve_Z "b"=
αLT 0.21 Buckling_curve_Z "a"if
0.34 Buckling_curve_Z "b"if
0.49 Buckling_curve_Z "c"if
0.76 Buckling_curve_Z "d"if
:=
αLT 0.34=
λLTWpl.y fy⋅
Mcr0.756=:=
β 0.75:=
λLTO 0.4:=
Page 138
Value to determine the reduction factor (EN1993-1-1,cl.6.3.2.2(1))
Reduction factor for lateral-torsional buckling (EN1993-1-1,cl.6.3.2.2(1))
Design plastic resistance (EN1993-1-1,cl.6.3.2.1)
Section verification for lateral torsional buckling (EN1993-1-1,cl.6.3.2.1(1))
Composite stage
Effective width of composite beam (cl.5.4.1.2(5))
Total effective width at mid-span (EN1994-1-1cl. 5.4.1.2(5))
Plastic resistance moment of composite section with full shear connection (cl.6.2)
Tensile resistance of steel section (EN1993-1-1,cl.6.2.3(2))
Compression resistance of concrete slab (EN1994-1-1,cl.6.2.1.2(1d)
Tensile resistance in web of steel section
φLT 0.5 1 αLT λLT λLTO−( )⋅+ β λLT2
⋅⎛⎝
⎞⎠+⎡
⎣⎤⎦⋅ 0.775=:=
χLT1
φLT φLT2
β λLT2
−+
0.841=:=
Check_5 if χLT 1≤ χLT1
λLT2
≤∧ "OK", "NOT OK", ⎛⎜⎜⎝
⎞⎟⎟⎠
:=
Check_5 "OK"=
Mb.Rd χLTWpl.y fy⋅
γM1⋅ 84.882kNm⋅⋅=:=
Check_6 ifMEd.cMb.Rd
1< "OK", "NOT OK", ⎛⎜⎝
⎞⎟⎠
:=
Check_6 "OK"=
beff bo 2 minL12
L22
+Le8
, ⎛⎜⎝
⎞⎟⎠
⎛⎜⎝
⎞⎟⎠
+:=
Npl.afy A⋅
γM01.075 103× kN⋅=:=
Nc.f 0.85 fcd⋅ beff⋅ hc⋅ 1.792 103× kN⋅=:=
Npl.w fy tw⋅ ha 2 tf⋅−( )⋅:=
Page 139
Location of neutral axis (EN1994-1-1,cl.6.2.1.2(1))
Bending resistance with full shear connection (EN1994-1-1,cl.6.1.2)
Bending resistance check checks (EN1993-1-1,cl.6.2.5(1))
Vertical Sheat resistance of the composite steel section (cl.6.2.2) & (EN1993-1-1,cl.6.2.6)
Shear resistance of steel section Y-Y (EN1993-1-1,cl.6.2.6(2))
Design of shear resistance check (EN1993-1-1,cl.6.2.6(1)P)
Location_neutral axis "Lies in the concrete slab" Nc.f Npl.a>if
"Lies in the top flange of the beam" Nc.f Npl.a≤if
"Lies in the web of the beam" Nc.f Npl.w<if
:=
Location_neutral axis "Lies in the concrete slab"=
Mpl.Rd Npl.aha2
h+Npl.aNc.f
hc2
⋅−⎛⎜⎝
⎞⎟⎠
⋅ Location_neutral axis "Lies in the concrete slab"if
Npl.aha2
⋅ Nc.fhc2
hp+⎛⎜⎝
⎞⎟⎠
⋅+ Location_neutral axis "Lies in the top flange of the beam"if
Ma.pl.Rd Nc.fhc ha+ 2hp+
2
⎛⎜⎝
⎞⎟⎠
⋅+Nc.f
2
Npl.w
ha4
⋅− Location_neutral axis "Lies in the top flange of the beam"if
:=
Mpl.Rd 261.285kNm⋅⋅=
Check_7 if MEd Mpl.Rd≤ "OK", "NOT OK", ( ):=
Check_7 "OK"=
Vpl.Rd 303.691kN⋅=
Check_8 if VEd Vpl.Rd≤ "OK", "NOT OK", ( ):=
Check_8 "OK"=
Page 140
Check if the verification of shear buckling resistance required or not (EN1993-1-1,cl.6.2.6(6))
Design resistance of shear stud connector (cl.6.6.3.1(1))
For sheeting with ribs transverse to the beam For sheeting parallel to the beam see Equation 6.22 of EC4
Upper limit of reduction factor kt (EN1994-1-1,Table:6.2)
Reduction factor kt (EN1994-1-1,cl.6.6.4.2)
Limitation of kt (EN1994-1-1,cl.6.6.4.2(2))
Minimum height of shear stud (EN1994-1-1,cl.6.6.1.2(1))
Check_9 ifhwtw
72ε
η⋅< "Not required shear buckling resistance", "Required shear buckling resistance",
⎛⎜⎝
⎞⎟⎠
:=
Check_9 "Not required shear buckling resistance"=
kt.max 0.85 nr 1 1mm ts≥∧ d 20mm<∧if
1.0 nr 1 1mm ts<∧ d 20mm<∧if
0.75 nr 1 1mm ts≥∧ 19mm d≤ 22mm<∧if
0.75 nr 1 1mm ts<∧ 19mm d≤ 22mm<∧if
0.70 nr 2 1mm ts≥∧ d 20mm<∧if
0.80 nr 2 1mm ts<∧ d 20mm<∧if
0.60 nr 2 1mm ts≥∧ 19mm d≤ 22mm<∧if
0.60 nr 2 1mm ts<∧ 19mm d≤ 22mm<∧if
:=
kt.max 0.75=
kt 0.6bohp⋅
hschp
1−⎛⎜⎝
⎞⎟⎠
⋅:=
kt kt kt kt.max<if
kt.max otherwise
0.75=:=
hmin if hsc 4d≥ "Ductile", "Not Ductile", ( ):=
hmin "Ductile"=
Page 141
Limitation of stud diameter (EN1994-1-1,cl.6.6.1.2(1))
Factor α (EN1994-1-1,cl.6.6.3.1(1))
Design shear resistance of a headed stud (EN1994-1-1,cl.6.6.3.1(1))
Degree of shear connection (cl.6.6.1.2(1))
Ratio of the degree shear connection (EN1994-1-1,cl.6.2.1.3(3))
Minimum degree of shear connection for equal flange (EN1994-1-1,cl.6.6.1.2(1))
Check the degree of shear interaction within the limits (EN1994-1-1,cl.6.6.1.2(1))
Number of shear connector required
Numper of stud provided
Stud spacing
dlim if 16mm d< 25mm< "Ductile", "Not ductile", ( ):=
dlim "Ductile"=
α 0.2hscd
1+⎛⎜⎝
⎞⎟⎠
⋅ 3hscd
≤ 4≤if
1hscd
4>if
1=:=
PRd kt min0.8 fus⋅ π⋅
d2
4⋅
γ v
0.29α⋅ d2⋅ fck Ecm⋅⋅
γ v,
⎛⎜⎜⎜⎝
⎞⎟⎟⎟⎠
⋅ 55.298kN⋅=:=
ηNc.fNpl.a
1.667=:=
ηmin 1355fy
N mm 2−⋅
⎛⎜⎜⎜⎝
⎞⎟⎟⎟⎠
0.75 0.03Lem
⋅−⎛⎜⎝
⎞⎟⎠
⋅− Le 25m<if
1.0 Le 25m>if
:=
ηmin 0.225=
Check_11 if η ηmin> η 0.4≥∧ "OK", "NOT OK", ( ):=
Check_11 "OK"=
n2 Npl.a⋅
PRd38.889=:=
Nstud 40:=
sprovLe
Nstud0.125m=:=
Page 142
Check the minimum spacing of studs (EN1994-1-1,cl.6.6.5.7(4))
Adequacy of the shear connection (EN1994-1-1,cl.6.6.1.3(3))
Design of transverse reinforcement (cl.6.6.6.2) & (EN1992-1-1,cl.6.2.4)
Length under consideration
Longitudinal shear stress (EN1992-1-1,cl.6.2.4(3))
Strength reduction factor (EN1992-1-1,Eq.6.6N)
Angle between the diagonal strut (EN1992-1-1,cl.6.2.4(4))
Assume spacing of the bars
Area of transverse reinforcement required (EN1992-1-1,cl.6.2.4(4))
Area of transverse reinforcement provided
Check the crushing compression in the flange (EN1992-1-1cl.6.2.4(4))
slim if sprov 5 d⋅≥ sprov 6 h⋅<∧ "OK", "NOT OK", ( ):=
slim "OK"=
Check_12 if Mpl.Rd 2.5 Ma.pl.Rd⋅< "Uniform spacing", "Not uniform spacing", ( ):=
Check_12 "Not uniform spacing"=
Δ xLe2
2.5m=:=
vEdNpl.a2 hc⋅ Δ x⋅
:=
v 0.6 1fck
250 N⋅ mm 2−⋅
−⎛⎜⎜⎝
⎞⎟⎟⎠
⋅:=
θf 45deg:=
sf 200mm:=
As.reqvEd hc⋅ sf⋅
fydsin θf( )cos θf( )⋅
:=
As.prov 193mm2:=
Check_13 if As.req As.prov≤ "OK", "NOT OK", ( ):=
Check_13 "OK"=
Check_14 if vEd v fcd⋅ sin θf( )⋅ cos cos θf( )( )⋅≤ "OK", "NOT OK", ( ):=
Check_14 "OK"=
Page 143
Serviceability limit state verification
Construction stage
Dead load at composite stage
Live load at composite stage
Maximum deflection at construction stage
Vertical deflection limit (CYS NA EN1993-1-1,table NA.1)
Short term elastic modular ration (EN1994-1-1,cl.7.2.1)
Second moment of area of the composite section, Ic
Deflection with full shear connection
Vertical deflection limit (CYS NA EN1993-1-1,table NA.1)
Gk 10.88kNm 1−⋅:=
Qk 5.0kNm 1−⋅:=
δcon5 Gk Qk+( )⋅ Le
4⋅
384 Es⋅ Iyy⋅15.812mm⋅=:=
Check_15 if δconLe250
< "OK", "NOT OK", ⎛⎜⎝
⎞⎟⎠
:=
Check_15 "OK"=
noEsEcm
:=
rA
beff hc⋅:=
IyA h 2 hp⋅+ hc+( )2⋅
4 1 no r⋅+( )⋅
beff hc3
⋅
12 no⋅+ Iyy+ 1.563 10 4−
× m4=:=
δcom5 Gk Qk+( )⋅ Le( )4⋅
384 Es⋅ Iy⋅3.938mm⋅=:=
Check_16 if δcomLe200
< "OK", "NOT OK", ⎛⎜⎝
⎞⎟⎠
:=
Check_16 "OK"=
Page 144
Vibration (Simplified analysis):
Loading:
Permanent load
Imposed load
For category B building
Total weigth floor, Fv
Increase the inertia, Ic by 10% to allow for the increased dynamic stiffness of the composite beam, Icl
Instantaneous deflection caused by re-application of the self weight of the floor and the beam to the composite beam, δ α
Natural frequncy, f
Check beam vibration (SCI-P-076)
Gk 10.88 kNm 1−⋅⋅=
Qk 5 kNm 1−⋅⋅=
ψ1 0.5:=
Fv Gk ψ1 Qk⋅+:=
Icl Iy Iy 0.1⋅( )+:=
δα
5 Fv Le⋅( )⋅ Le3
⋅
384 Es⋅ Icl⋅3.016mm⋅=:=
f18
δα
mm
⎛⎜⎜⎝
⎞⎟⎟⎠
Hz 10.364Hz⋅=:=
Check_17 if f 4 Hz⋅> "OK", "NOT OK", ( ):=
Check_17 "OK"=
Page 145
9.5 Design of steel bracing
9.5.1 Main configuration of design of steel bracing
Basic theory: Tension only, utilises two members at each storey but only the tension element is assumed to resist wind load and seismic load, the compression element is assumed to buckle and offer no resistance to lateral movement. Eurocode 8 requirement: The diagonals shall be taken into account as follows in an elastic analysis of the structure for the seismic action:
a) in frames with diagonal bracings, only the tension diagonals shall be taken into
account, b) in frames with V bracings, both the tension and compression diagonals shall be taken
into account (EN1998-1-1,cl6.7.2(2).
Taking into account of both tension and compression diagonals in the analysis of any type of concentric bracing is allowed provided that all of the following conditions are satisfied:
a) a non-linear static (pushover) global analysis or non-linear time history analysis is used,
b) both pre-buckling and post-buckling situations are taken into account in the modeling of the behavior of diagonals and,
c) background information justifying the model used to represent the behavior of diagonals is provided (EN1998-1-1,cl6.7.2(3).
Page 146
Figure 9.11: Method of design bracing in this manual
Steps for designing steel bracing member:
1. Delete the compression member.
2. Leave the tension members only.
3. Run the design of steel frame.
4. Find the suitable section and ensure that the section pass all the checks.
5. Ensure that the compression member has been placed at the construction drawings.
Ignore compression members
Compression members Tension members
Direction of shear
Page 147
9.5.2 Simplified design of frames with X bracing (Extract from Design guidance to EC8)
In a standard design, the following simplified approach may be used:
• The analysis of the structure is realized considering that only one diagonal in each X
bracing is present, the other diagonal being considered as already buckled and unable to
provide strength. This corresponds to an underestimation of both the stiffness and the
strength of the structural system at the initial (pre-buckling) stage, but to a safe-side
estimate at the post-buckling stage.
• The beams and columns are capacity designed according to the real yield strength of the
diagonals, for bending with increased axial force and bending moment from the analysis
for the combination of the design seismic action with gravity loads.
However, this simplified approach could be dangerous for the stability of the structure, if it does
not take into account that action effects of compression in columns and beams at the pre-buckling
stage are higher than in the post-buckling stage envisaged in the analysis. Indeed, if the buckling
loads of the diagonal are closed to their yield load in tension, the initial shear resistance Vinit of
the X bracing is underestimated by a model where only one diagonal is considered present. If
low-slenderness diagonals are used, Vinit can be close to double the value of Vpl.Rd computed with
the hypothesis of one active yielded diagonal. The only way to prevent this unsafe situation is to
design slender diagonal having their buckling load at most around 0.5Npl.Rd. This condition is
behind the prescribed lower bound limit value of 1.3 for the slenderness λ. The prescribed upper
bound limit max λ=2, is justified by the aim to avoid shock effects during the load reversal in
diagonals.
Page 148
9.5.3 Model in ETABS
Figure 9.12: Amendment model
Assume that the steel bracing resist the lateral force at the +X direction
Assume that the steel bracing resist the lateral force at the -X direction
Page 149
Assume that the steel bracing resist the lateral force at the -Y direction
Assume that the steel bracing resist the lateral force at the +Y direction
Page 150
STEP 2: Design > Steel frame design > Select design combo…
Figure 9.13: Lateral/gravity load combination at ULS
Figure 9.14: Gravity load combination at SLS
Page 151
Ultimate limit state (ULS)
Static load combination
STATIC 11. 1.35DL + 1.5LL + 0.75WINDX STATIC 12. 1.35DL + 1.5LL - 0.75WINDX STATIC 13. 1.35DL + 1.5LL + 0.75WINDY STATIC 14. 1.35DL + 1.5LL - 0.75WINDY STATIC 15. 1.35DL + 1.5WINDX + 1.05LL STATIC 16. 1.35DL - 1.5WINDX – 1.05LL STATIC 17. 1.35DL + 1.5WINDY + 1.05LL STATIC 18. 1.35DL - 1.5WINDY – 1.05LL
Seismic load combination for “Modal Analysis”
SEISMIC 9. DL + 0.3LL + EQX + 0.3EQY SEISMIC 10. DL + 0.3LL + EQX – 0.3EQY SEISMIC 11. DL + 0.3LL - EQX + 0.3EQY SEISMIC 12. DL + 0.3LL - EQX – 0.3EQY SEISMIC 13. DL + 0.3LL + EQY + 0.3EQX SEISMIC 14. DL + 0.3LL + EQY – 0.3EQX SEISMIC 15. DL + 0.3LL - EQY + 0.3EQX SEISMIC 16. DL + 0.3LL - EQY – 0.3EQX
Serviceability limit state (SLS)
DSTLD 3. DL + LL
Page 152
Figure 9.15: Design steel bracing member
Write click on member Brace name: D3 Storey level: Storey 1
Page 153
Table 9.6: Design value of brace D3
Story Brace Load Loc P V2 V3 T M2 M3
STORY1 D3 SEISMIC1 MIN 0 -‐361.83 -‐1.41 -‐0.05 -‐0.044 -‐0.173 -‐1.792 STORY1 D3 SEISMIC2 MIN 0 -‐361.83 -‐1.41 -‐0.05 -‐0.044 -‐0.173 -‐1.792 STORY1 D3 SEISMIC3 MIN 0 -‐361.83 -‐1.41 -‐0.05 -‐0.044 -‐0.173 -‐1.792 STORY1 D3 SEISMIC4 MIN 0 -‐361.83 -‐1.41 -‐0.05 -‐0.044 -‐0.173 -‐1.792 STORY1 D3 SEISMIC1 MIN 2.915 -‐361.06 -‐0.13 -‐0.05 -‐0.044 -‐0.054 0.443 STORY1 D3 SEISMIC2 MIN 2.915 -‐361.06 -‐0.13 -‐0.05 -‐0.044 -‐0.054 0.443 STORY1 D3 SEISMIC3 MIN 2.915 -‐361.06 -‐0.13 -‐0.05 -‐0.044 -‐0.054 0.443 STORY1 D3 SEISMIC4 MIN 2.915 -‐361.06 -‐0.13 -‐0.05 -‐0.044 -‐0.054 0.443
Page 154
Worst case combination
Modify the default steel design data if needed
Page 155
Table 9.7: Summarize of design values required to carry out the design of steel member
Design value Symbol Results
(kN/kNm)
Design axial force for the worse case design load combination NEd 361.83
Design moment at y-y at end 1 (worse case combination) MEd.y1 -1.792
Design moment at y-y at end 2 (worse case combination) MEd.y2 0.443
Design moment at z-z at end 1 (worse case combination) MEd.z1 -0.173
Design moment at z-z at end 2 (worse case combination) MEd.z2 -0.054
Shear forces at y-y at end (worse case combination) VEd.y -0.05
Shear force at z-z at end 1 (worse case combination) VEd.z -1.41
Modify the omega factors if needed
Modify the effective length factor if needed
Page 156
9.5.4 Design of steel bracing (Gravity/Seismic design situation) – Hand calculation
1. Rolled I - section 2. Limit to class 1 and 2 section
Design data
Overstrength factor (EN1998-1-1,cl.6.1.3(2))
Behavior factor q
Ductlity class
Number of storeys
Length of bracing
Total axial load on column, NEd
Shear force y-y axis
Shear force z-z axis
Design moment y-y axis
Design moment y-y axis
Maximum moment
Design moment z-z axis
Design moment z-z axis
Maximum moment
Section properties:
Depth of section,d: Width of section,b:
Thickness of web, tw:
Thickness of flange, tf :
Thickness of element
γ ov 1.25:=
q 4:=
Ductility_class "DCM":=
Ns 3:=
hc 5.831m:=
NEd 361.83kN:=
VEd.y 0.05kN:=
VEd.z 1.41kN:=
MEd.y1 1.792kNm⋅:=
MEd.y2 0.443kNm⋅:=
MEd.y maxMEd.y1 MEd.y2, ( ) 1.792kNm⋅⋅=:=
MEd.z1 0.173− kNm⋅:=
MEd.z2 0.054− kNm⋅:=
MEd.z maxMEd.z1 MEd.z2, ( ) 0.054− kNm⋅⋅=:=
d 120mm:=
b 120mm:=
tw 16mm:=
tf 16mm:=
t max tw tf, ( ) 16mm⋅=:=
Page 157
Second moment of area z-z:
Second moment of area y-y:
Cross section area, A:
Warping Constant, Iw:
Torsional Constant, IT:
Plastic Modulus, Wply
Plastic Modulus, Wplz
Elastic modulus, E:
Yield strength of steel , fy:
Ultimate strength, fu:
Shear modulus
Reduction of yield and ultimate strenght of sections EN10025-2
Partial safety factor
Resistance of cross-sections whatever the class (CYS EN1993-1-1,cl 6.1(1))
Resistance of members to instability (CYS EN1993-1-1,cl 6.1(1))
Resistance of cross-section in tension (CYS EN1993-1-1,cl.6.1(1))
Izz 12280000mm4:=
Iyy 12280000mm4:=
A 6656mm2:=
Iw 0 mm6⋅:=
It 18000000mm4:=
Wpl.y 261600mm3:=
Wpl.z 261600mm3:=
Es 210kNmm 2−⋅:=
fy 275N mm 2−⋅:=
fu 430N mm 2−⋅:=
G 81kNmm 2−⋅:=
fy fy t 16mm≤if
fy 10N mm 2−⋅− 16mm t< 40mm≤if
fy 20N mm 2−⋅− 40mm t< 80mm≤if
:=
fy 275 N mm 2−⋅⋅=
fu fu t 16mm≤if
fu 10N mm 2−⋅− 16mm t< 40mm≤if
fu 20N mm 2−⋅− 40mm t< 80mm≤if
:=
fu 430 N mm 2−⋅⋅=
γM0 1:=
γM1 1:=
γM2 1.25:=
Page 158
Section classification
For section classification the coefficient ε is:
Requirements on cross-sectional class of dissipative elements depending on Ductility class (EN1998-1-1,cl.6.5.3(2))
Section classification rule for EC8 (EN1998-1-1,cl.6.5.3(2))
ε235fy
N mm 2−⋅
0.924=:=
cf d 2tf− 88mm⋅=:=
Class_type_flange "CLASS 1"cft
33 ε⋅≤if
"CLASS 2" 33 ε⋅cft
< 38 ε⋅≤if
"CLASS 3" 38 ε⋅cft
< 42 ε⋅≤if
:=
Class_type_flange "CLASS 1"=
cw d 2tw− 88mm⋅=:=
Class_type_web "CLASS 1"cwt
72 ε⋅≤if
"CLASS 2" 72 ε⋅cwt
< 83 ε⋅≤if
"CLASS 3" 83 ε⋅cwt
< 124 ε⋅≤if
:=
Class_type_web "CLASS 1"=
Class_type if Class_type_flange Class_type_web Class_type_flange, "ADD MANUALY", ( ):=
Class_type "CLASS 1"=
Class_type_req "CLASS 1 , 2 or 3" 1.5 q< 2≤ Ductility_class "DCM"∧if
"CLASS 1 or 2" 2 q< 4≤ Ductility_class "DCM"∧if
"CLASS 1" q 4> Ductility_class "DCH"∧if
"CLASS 1 or 2"=:=
Class_type_req "CLASS 1 or 2"=
Page 159
Tension resistance (cl.6.2.2)
Design plastic resistance of the cross section (EN1993-1-1,cl.6.2.3(2a))
Modified plastic resistance of cross section as described in "Design Guidance to EC8" (cl.6.10.2)
Design ultimate resistance (EN1993-1-1,cl.6.2.3(2b))
Design tension resistance (EN1993-1-1,cl.6.2.3(2))
Check tension capacity (EN1993-1-1,cl.6.2.3(1)P)
Compression resistance (cl.6.2.3)
Compression resistance of steel section (EN1993-1-1,cl.6.2.4(1))
Check compression capacity (EN1993-1-1,cl.6.2.4(1)P)
Bending resistance (cl.6.2.5) Moment resistance of steel section at Y-Y (EN1993-1-1,cl.6.2.5(2)
Moment resistance of steel section at Z-Z (EN1993-1-1,cl.6.2.5(2)
Sheat resistance (cl.6.2.6)
Factor for shear area (EN1993-1-1,cl.6.2.6(g))
Shear area of steel section (EN1993-1-1,cl.6.2.6(3))
Shear area of steel section (EN1993-1-1,cl.6.2.6(3))
Shear resistance of steel section Y-Y (EN1993-1-1,cl.6.2.6(2))
Npl.RdA fy⋅
γM01.83 103× kN⋅=:=
Npl.Rd 0.5Npl.Rd⋅ 915.2kN⋅=:=
Nu.Rd0.9A fy⋅
γM21.318 103× kN⋅=:=
Nt.Rd min Nu.Rd Npl.Rd, ( ) 915.2kN⋅=:=
Check_1 ifNEd
Nt.Rd1.0≤ "OK", "NOT OK",
⎛⎜⎝
⎞⎟⎠
:=
Check_1 "OK"=
Nc.Rd Npl.Rd 915.2kN⋅=:=
Check_2 ifNEd
Nc.Rd1.0≤ "OK", "NOT OK",
⎛⎜⎝
⎞⎟⎠
:=
Check_2 "OK"=
Mc.Rd.yWpl.y fy⋅
γM071.94kNm⋅⋅=:=
Mc.Rd.zWpl.z fy⋅
γM071.94kNm⋅⋅=:=
η 1:=
AvyA b⋅b d+
3.328 103× mm2⋅=:=
AvzA d⋅b d+
3.328 103× mm2⋅=:=
Vpl.Rd.y Avyfy 3( ) 1−⋅
γM0⋅ 528.391kN⋅=:=
Page 160
Shear resistance of steel section Z-Z (EN1993-1-1,cl.6.2.6(2))
Check if the verification of shear buckling resistance required or not (EN1993-1-1,cl.6.2.6(6))
Bending and shear interaction check (cl.6.2.8)
Strong axis Y-Y
Interaction check 1
Reduced yield strength
Reduced design plastic resistance moment (EN1993-1-1,cl.6.2.8(5))
Weak axis Z-Z
Interaction check 1
Reduced yield strength
Vpl.Rd.z Avzfy 3( ) 1−⋅
γM0⋅ 528.391kN⋅=:=
Check_3 ifdt
72ε
η⋅< "Not required shear buckling resistance", "Required shear buckling resistance", ⎛⎜
⎝⎞⎟⎠
:=
Check_3 "Not required shear buckling resistance"=
vyVEd.yVpl.Rd.y
9.463 10 5−×=:=
ρ2VEd.yVpl.Rd.y
1−⎛⎜⎝
⎞⎟⎠
2
1=:=
Mc.Rd.y
Wpl.yρ A2⋅
4t−
⎛⎜⎝
⎞⎟⎠fy⋅
γM0vy 0.5>if
Mc.Rd.y vy 0.5<if
:=
Mc.Rd.y 71.94kNm⋅⋅=
vzVEd.zVpl.Rd.z
2.668 10 3−×=:=
ρ2VEd.zVpl.Rd.z
1−⎛⎜⎝
⎞⎟⎠
2
0.989=:=
Page 161
Reduced design plastic resistance moment (EN1993-1-1,cl.6.2.8(5))
Check combination of axial and bending (EN1993-1-1,cl.6.2.1(7))
Unity factor
Bending and axial force interaction check (cl.6.2.9)
Factor a
Factor a
Factor n
Factor β
Factor α
Mc.Rd.z
Wpl.zρ A2⋅
4t−
⎛⎜⎝
⎞⎟⎠fy⋅
γM0vz 0.5>if
Mc.Rd.z vz 0.5<if
:=
Mc.Rd.z 71.94kNm⋅⋅=
Check_4 ifNEd
Npl.Rd
MEd.yMc.Rd.y
+MEd.z
Mc.Rd.z+ 1.0≤ "OK", "NOT OK",
⎛⎜⎝
⎞⎟⎠
:=
NEdNpl.Rd
MEd.yMc.Rd.y
+MEd.zMc.Rd.z
+ 0.42=
Check_4 "OK"=
aw minA 2b tw⋅−( )
A0.5,
⎡⎢⎣
⎤⎥⎦
0.423=:=
af minA 2d tf⋅−( )
A0.5,
⎡⎢⎣
⎤⎥⎦
0.423=:=
nNEdNpl.Rd
0.395=:=
β1.66
1 1.13n2−
1.66
1 1.13n2−
6≤if
6 otherwise
2.016=:=
a β 2.016=:=
Page 162
Strong axis Y-Y Reduced design value of the resistance to
bending moments making allowance for the presence of axial forces (EN1993-1-1,cl.6.2.9.1(5))
Weak axis Z-Z Reduced design value of the resistance to bending moments making allowance for the presence of axial forces (EN1993-1-1,cl.6.2.9.1(5))
Check combination of axial and bending (EN1993-1-1,cl.6.2.1(7))
Unity factor
Bucking interaction check (cl.6.3)
Strong axis Y-Y
Status of effective length
Effective length factor (Guidance of EC3)
MN.y.RdMc.Rd.y 1 n−( )⋅
1 0.5aw−:=
MN.y.Rd MN.y.Rd MN.y.Rd Mc.Rd.y≤if
Mc.Rd.y MN.y.Rd Mc.Rd.y>if
:=
MN.y.Rd 55.168kNm⋅⋅=
MN.z.RdMc.Rd.z 1 n−( )⋅
1 0.5af−:=
MN.z.Rd MN.z.Rd MN.z.Rd Mc.Rd.z≤if
Mc.Rd.z MN.z.Rd Mc.Rd.z>if
:=
MN.z.Rd 55.168kNm⋅⋅=
Check_5 ifNEd
Npl.Rd
MEd.yMc.Rd.y
+MEd.z
Mc.Rd.z+ 1.0≤ "OK", "NOT OK",
⎛⎜⎝
⎞⎟⎠
:=
NEdNpl.Rd
MEd.yMc.Rd.y
+MEd.zMc.Rd.z
+ 0.42=
Check_5 "OK"=
Effective_Length "Pinned Pinned":=
ky 0.7 Effective_Length "Fixed Fixed"if
0.85 Effective_Length "Partial restraint"if
0.85 Effective_Length " Pinned Fixed"if
1 Effective_Length "Pinned Pinned"if
1=:=
Page 163
Buckling length of column (fixed end)
Euler Buckling at y-y axis (EN1993-1-1,cl.6.3.1.2(1)
Slenderness parameter at y-y axis (for class 1,2 and 3 cross-section) (EN1993-1-1,cl.6.3.1.3(1)
Check for X bracing (EN1998-1-1,cl.6.7.3(4))
Check for X bracing (EN1998-1-1,cl.6.7.3(1))
Type of the section
Buckling curve (EN1993-1-1,table 6.2)
Imperfection factor (EN1993-1-1,table 6.1)
Value to determine the reduction factor χ (EN1993-1-1,cl.6.3.1.2(1))
Reduction factor χ (EN1993-1-1,cl.6.3.1.2(1))
Reduction factor χ check
Lcry ky hc 5.831m=:=
NcryEs Iyy⋅ π
2⋅
Lcry2
748.568kN⋅=:=
λyA fy⋅
Ncry1.564=:=
Check_6 if Ns 3≥ "Consider limitation (As EC8)", "Ignore limitation (As EC3)", ( ):=
Check_6 "Consider limitation (As EC8)"=
Check_7 if 1.3 λy< 2< "OK", "NOT OK", ( ):=
Check_7 "OK"=
Section "Hot finished":=
Buckling_curve "a" Section "Hot finished"if
"c" Section "Cold formed"if
:=
Buckling_curve "a"=
αy 0.21 Buckling_curve "a"if
0.49 Buckling_curve "c"if
:=
αy 0.21=
φ y 0.5 1 αy λy 0.2−( )⋅+ λy2
+⎡⎣
⎤⎦⋅ 1.866=:=
χy1
φ y φ y2
λy2
−+
0.347=:=
Check_8 if χy 1.0≤ "OK", "NOT OK", ( ):=
Check_8 "OK"=
Page 164
Design buklcing resistance (EN1993-1-1,cl.6.3.1.1(3))
Buckling resistance of compression member check (EN1993-1-1,cl.6.3.1.1(1))
Weak axis Z-Z
Status of effective length
Effective length factor (Guidance of EC3)
Buckling length of column (fixed end)
Euler Buckling at y-y axis (EN1993-1-1,cl.6.3.1.2(1)
Slenderness parameter at y-y axis (for class 1,2 and 3 cross-section) (EN1993-1-1,cl.6.3.1.3(1)
Check for X bracing (EN1998-1-1,cl.6.7.3(4))
Check for X bracing (EN1998-1-1,cl.6.7.3(1))
Type of the section
Nb.Rd.yχy A⋅ fy⋅
γM1634.758kN⋅=:=
Check_9 ifNEd
Nb.Rd.y"OK", "NOT OK",
⎛⎜⎝
⎞⎟⎠
:=
Check_9 "OK"=
Effective_Length "Pinned Pinned":=
kz 0.7 Effective_Length "Fixed Fixed"if
0.85 Effective_Length "Partial restraint"if
0.85 Effective_Length " Pinned Fixed"if
1 Effective_Length "Pinned Pinned"if
1=:=
Lcrz kzhc 5.831m=:=
NcrzEs Izz⋅ π
2⋅
Lcrz2
748.568kN⋅=:=
λzA fy⋅
Ncrz1.564=:=
Check_10 if Ns 3≥ "Consider limitation (As EC8)", "Ignore limitation (As EC3)", ( ):=
Check_10 "Consider limitation (As EC8)"=
Check_11 if 1.3 λz< 2< "OK", "NOT OK", ( ):=
Check_11 "OK"=
Section "Hot finished":=
Page 165
Buckling curve (EN1993-1-1,table 6.2)
Value to determine the reduction factor χ (EN1993-1-1,cl.6.3.1.2(1))
Reduction factor χ (EN1993-1-1,cl.6.3.1.2(1))
Reduction factor χ check
Design buklcing resistance (EN1993-1-1,cl.6.3.1.1(3))
Buckling resistance of compression member check (EN1993-1-1,cl.6.3.1.1(1))
Lateral torsional buckling check (cl.6.3.2)
Effective length factor, k (SN003a-EN-EU)
Factor for end warping, kw (SN003a-EN-EU)
Ratio of the smaller and larger moment
Coefficient factor C1 (SN003a-EN-EU)
Buckling_curve "a" Section "Hot finished"if
"c" Section "Cold formed"if
:=
Buckling_curve "a"=
αz 0.21 Buckling_curve "a"if
0.49 Buckling_curve "c"if
:=
αz 0.21=
φ z 0.5 1 αz λz 0.2−( )⋅+ λz2
+⎡⎣
⎤⎦⋅ 1.866=:=
χz1
φ z φ z2
λz2
−+
0.347=:=
Check_12 if χz 1.0≤ "OK", "NOT OK", ( ):=
Check_12 "OK"=
Nb.Rd.zχz A⋅ fy⋅
γM1634.758kN⋅=:=
Check_13 ifNEd
Nb.Rd.z"OK", "NOT OK",
⎛⎜⎝
⎞⎟⎠
:=
Check_13 "OK"=
kz 1=
kw 1.0:=
ψMEd.y2MEd.y1
0.247=:=
C1 1.88 1.40ψ− 0.52ψ 2+ 1.566=:=
Page 166
Coefficient factor C1 check (SN003a-EN-EU)
Coefficient factor C2 (SN003a-EN-EU)
Distance between the point of load application and the shear centre
Elastic critical moment for lateral torsional buckling (SN003a-EN-EU)
Imperfection factor for lateral torsional CHS sections (EN1993-1-1,table 6.3)
Non dimensional slenderness (EN1993-1-1,cl.6.3.2.2(1))
Value to determine the reduction factor (EN1993-1-1,cl.6.3.2.2(1))
Reduction factor for lateral-torsional buckling (EN1993-1-1,cl.6.3.2.2(1))
Parameter λ LTO (EN1993-1-1,cl.6.3.2.3(1))
Design buckling resistance moment (EN1993-1-1,cl.6.3.2.1(3))
Check_14 if C1 2.7≤ "OK", "NOT OK", ( ):=
Check_14 "OK"=
C2 1.554:=
zg 0m:=
Mcr C1π2 Es⋅ Izz⋅
Lcrz( )2⋅
kzkw
⎛⎜⎝
⎞⎟⎠
2 IwIzz⋅
Lcrz( )2G It⋅
π2Es Izz⋅
+ C2 zg⋅( )2+⋅ C2 zg⋅− 1.636 103× kNm⋅⋅=:=
αLT 0.76:=
λLTWpl.y fy⋅
Mcr0.21=:=
φLT 0.5 1 αLT λLT 0.2−( )⋅+ λLT2
+⎡⎣
⎤⎦⋅ 0.526=:=
χLT1
φLT φLT2
λLT2
−+
0.992=:=
Check_15 if χLT 1≤ χLT1
λLT2
≤∧ "OK", "NOT OK", ⎛⎜⎜⎝
⎞⎟⎟⎠
:=
Check_15 "OK"=
λLTO 0.4:=
Mb.Rd χLTWpl.y⋅fyγM1⋅ 71.389kNm⋅⋅=:=
Check_16 ifMEd.yMb.Rd
1≤ "OK", "NOT OK", ⎛⎜⎝
⎞⎟⎠
:=
Page 167
Check if the lateral torsional buckling be ignored (EN1993-1-1,cl.6.3.2.2(4))
Combine bending and axial compression cl.6.3.3
Moments due to the shift of the centroidal axis for class sections 1,2 & 3 (EN1993-1-1,cl.6.3.3(4)/table 6.7)
Characteristic resistance to normal force of the critical cross-section (EN1993-1-1,cl.6.3.3(4)/table 6.7)
Characteristic moment resistance of the critical cross-section (EN1993-1-1,cl.6.3.3(4)/table 6.7)
Ratio of end moments (EN1993-1-1,Table B2)
Equivalent uniform moment factor
Equivalent uniform moment factor
Check_16 "OK"=
Check_17 if λLT λLTO<MEd.yMcr
λLTO2
<∧ "Ignored torsional buckling effects", "Consider torsional buckling effects", ⎛⎜⎝
⎞⎟⎠
:=
Check_17 "Ignored torsional buckling effects"=
ΔMEd.z 0:=
ΔMEd.y 0:=
NRk fy A⋅ 1.83 103× kN⋅=:=
My.Rk fy Wpl.y⋅ 71.94kNm⋅⋅=:=
Mz.Rk fy Wpl.z⋅ 71.94kNm⋅⋅=:=
ψyMEd.y1MEd.y2
1−MEd.y1MEd.y2
≤ 1≤if
MEd.y2MEd.y1
1−MEd.y2MEd.y1
≤ 1≤if
:=
ψzMEd.z1MEd.z2
1−MEd.z1MEd.z2
≤ 1≤if
MEd.z2MEd.z1
1−MEd.z2MEd.z1
≤ 1≤if
:=
Cmy 0.6 0.4ψy⋅+ 0.699=:=
Cmz 0.6 0.4ψz⋅+ 0.725=:=
kyy min Cmy 1 λy 0.2−( )NEd
χyNRkγM1⋅
⋅+⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
⋅⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
Cmy 1 0.8NEd
χyNRkγM1⋅
⋅+⎛⎜⎜⎜⎝
⎞⎟⎟⎟⎠
⋅, ⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
1.018=:=
Page 168
Interaction factors (EN1993-1-1,table B.1&B.2)
EN1993-1-1,Equation 6.61
Unity factor
EN1993-1-1,Equation 6.62
Unity factor
kzz min Cmz 1 2λz 0.6−( )NEd
χzNRkγM1⋅
⋅+⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
⋅⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
Cmz 1 1.4NEd
χzNRkγM1⋅
⋅+⎛⎜⎜⎜⎝
⎞⎟⎟⎟⎠
⋅, ⎡⎢⎢⎢⎣
⎤⎥⎥⎥⎦
1.303=:=
kyz 0.6kzz 0.782=:=
kzy 0.6kyy 0.611=:=
Check_18 ifNEd
χy NRk⋅
γM1
kyyMEd.y ΔM Ed.y+
χLTMy.RkγM1
⋅
⋅+ kyzMEd.z ΔM Ed.z+
Mz.Rk
γM1
⋅+ 1.0≤ "OK", "NOT OK", ⎛⎜⎜⎜⎝
⎞⎟⎟⎟⎠
:=
NEdχy NRk⋅
γM1
kyyMEd.y ΔM Ed.y+
χLTMy.RkγM1
⋅
⋅+ kyzMEd.z ΔM Ed.z+
Mz.Rk
γM1
⋅+ 0.595=
Check_18 "OK"=
Check_19 ifNEd
χz NRk⋅
γM1
kzyMEd.y ΔM Ed.y+
χLTMy.RkγM1
⋅
⋅+ kzzMEd.z ΔM Ed.z+
Mz.Rk
γM1
⋅+ 1.0≤ "OK", "NOT OK", ⎛⎜⎜⎜⎝
⎞⎟⎟⎟⎠
:=
NEdχz NRk⋅
γM1
kzyMEd.y ΔM Ed.y+
χLTMy.RkγM1
⋅
⋅+ kzzMEd.z ΔM Ed.z+
Mz.Rk
γM1
⋅+ 0.584=
Check_19 "OK"=
Page 169
Eurocode 8 requirements
Yield resistance (EN1998-1-1,cl.6.7.3(5))
Yield resistance check (EN1998-1-1,cl.6.7.3(5))
Check omega factor (EN1998-1-1,cl.6.7.3(8))
Axial force at storey 3
Axial force at storey 2
Area of steel section (RHS 100X100X10)
Design plastic resistance of the cross section Storey 3: RHS 100X100X10 (EN1993-1-1,cl.6.2.3(2a))
Omega factor
Omega factor
Omega factor
Minimum omega
Minimum omega
Check Ω factor (EN1998-1-1,cl.6.7.3(8))
Check_20 if NEd Npl.Rd≤ "OK", "NOT OK", ( ):=
Check_20 "OK"=
NEd.3 162.34kN:=
NEd.2 317.56kN:=
A 3600mm2:=
Npl.Rd.30.5A fy⋅
γM0495 kN⋅=:=
Ωstorey1Npl.RdNEd
2.529=:=
Ωstorey2Npl.RdNEd.2
2.882=:=
Ωstorey3Npl.Rd.3NEd.3
3.049=:=
Ωmin min Ωstorey1 Ωstorey2, Ωstorey3, ( ):=
Ωmin 2.529=
Ωmax maxΩstorey1 Ωstorey2, Ωstorey3, ( ):=
Ωmax 3.049=
Check_21 if Ωmax 1.25Ωmin≤ "OK", "NOT OK", ( ):=
Check_21 "OK"=
Page 170
10.0 Modal response spectrum analysis
10.1 Set the analysis options
1. ETABS: Analyze > Set analysis Options
Calculate the number of modes:
Figure 10.1: Set the modal analysis parameters
Page 171
10.2 Evaluate the analysis results of the structure according to the modal analysis
requirements
2. ETABS: Display > Show Tables
Figure 10.2: Modal response spectrum results
Page 172
10.2.1 Assess the modal analysis results based on the EN1998
The requirements of the sum of effective modal masses for the modes taken into account
amounts to at least 90% of the total mass of the structure is satisfied (EN1998-1-
1,cl.4.3.3.3.1(3)).
Page 173
Effective mass of mode 6 = 97% > 90% “OK”
11.0 Second order effects (P – Δ effects) according to EN1998-1-1,cl.4.4.2.2
The criterion for taking into account the second order effect is based on the interstorey drift
sensitivity coefficient θ, which is define with equation (EN 1998-1-1,cl.4.4.2.2(2)).
Θ =P!"! ∙ d!V!"! ∙ h
dr: is the interstorey drift
h: is the storey height.
Vtot: is the total seismic storey shear.
Ptot: is the total gravity load at and above storey considered in the seismic design situation
(G+0.3Q).
Table 11.1: Consequences of value of P-Δ coefficient θ on the analysis
θ≤0,1 No need to consider P-Δ effects
0,1≤θ≤0,2 P-Δ effects may be taken into account approximately by
amplifying the effects of the seismic actions by !!!!
0,2≤θ≤0,3 P-Δ effects must be accounted for by an analysis including
second order effects explicity
θ≥0,3 Not permitted
Important note: If the above expression is not satisfied, second order effects, should be
enable in ETABS.
ETABS: Analyze > Set analysis option > > Set the parameters
Page 174
11.1 Displacement calculation according to EN1998-1-1,cl.4.4.2.2
d! = q ∗ d!
ds : is the displacement of a point of the structural system induced by the design seismic action.
qd : is the displacement behaviour factor, assumed equal to q unless otherwise specified. de : is the displacement of the same point of the structural system, as determined by a linear
analysis based on the design response spectrum.
11.2 Interstorey drift
Interstorey drift is the design interstorey drift, evaluated as the difference of the average lateral
displacements ds at the top and bottom of the storey under consideration and calculated in
accordance with EN1993-1-1,cl.4.3.4.
d! =d!.!"# − d!.!"#
2
Page 175
11.3 Calculation of second order effect using ETABS
3. ETABS: Run the model
4. ETABS: Display > Show tables
Select the design combinations
Static load case combination (include wind load)
STATIC 2. 1.35DL + 1.5LL + 0.75WINDX STATIC 3. 1.35DL + 1.5LL - 0.75WINDX STATIC 4. 1.35DL + 1.5LL + 0.75WINDY STATIC 5. 1.35DL + 1.5LL - 0.75WINDY STATIC 6. 1.35DL + 1.5WINDX + 1.05LL STATIC 7. 1.35DL - 1.5WINDX – 1.05LL STATIC 8. 1.35DL + 1.5WINDY + 1.05LL STATIC 9. 1.35DL - 1.5WINDY – 1.05LL
Seismic load case combination
SEISMIC 1. DL + 0.3LL + EQX + 0.3EQY SEISMIC 2. DL + 0.3LL + EQX – 0.3EQY SEISMIC 3. DL + 0.3LL - EQX + 0.3EQY SEISMIC 4. DL + 0.3LL - EQX – 0.3EQY SEISMIC 5. DL + 0.3LL + EQY + 0.3EQX SEISMIC 6. DL + 0.3LL + EQY – 0.3EQX SEISMIC 7. DL + 0.3LL - EQY + 0.3EQX SEISMIC 8. DL + 0.3LL - EQY – 0.3EQX
Page 176
Figure 11.1: Displacement due to lateral load
11.3.1 Interstorey drift displacement
For floor with the non use of diaphragm, the maximum displacement can be found in this table
For floor with the use of diaphragm, the maximum displacement can be found in this table
Page 177
Table 11.2: Displacement due to lateral load
Storey no. Max Displacement at X Max Displacement at Y
Storey 3
Storey 2
Storey 1
Sort smallest to largest in order to find the maximum displacement
or Sort largest to smallest in order to find the maximum displacement
Consider the maximum value
Do this process for all storeys separately as
showing below
Page 178
Table 11.3: Drift displacement
Storey
Displacement Direction x
dx.e (mm)
Displacement Direction y
dy.e (mm)
Behaviour factor q
Displacement dsx (mm)
cl.4.4.2.2
Displacement dsy (mm)
cl.4.4.2.2
Interstorey drift drx (mm)
Interstorey drift dry (mm)
Storey 3 11.742 11.7452 4 46.968 46.9808 6.7754 6.7776
Storey 2 8.3543 8.3564 4 33.4172 33.4256 9.0274 9.0296
Storey 1 3.8406 3.8416 4 15.3624 15.3664 7.6812 7.6832
d!" = q ∗ d!"
d!" = q ∗ d!" d!" =
d!".!"# − d!".!"#2
d!" =d!".!"# − d!".!"#
2
11.3.2 Total gravity load Ptot
ETABS: Display > Show tables
Select the design combinations
Static load case combination
STATIC 10. DL + 0.3LL
Page 179
Export the results in Excel sheet
Filter the value of the bottom storey
Page 180
Story Load Loc P
STORY3 STATIC10 Bottom 1402.76 STORY2 STATIC10 Bottom 2804.93 STORY1 STATIC10 Bottom 4207.11
11.3.2 Total seismic storey shear Vtot
ETABS: Display > Show tables
Record the total gravity load (G+ψEiQ) of each storey
Select the design combinations
Seismic load case combination
SEISMIC 1. DL + 0.3LL + EQX + 0.3EQY SEISMIC 2. DL + 0.3LL + EQX – 0.3EQY SEISMIC 3. DL + 0.3LL - EQX + 0.3EQY SEISMIC 4. DL + 0.3LL - EQX – 0.3EQY SEISMIC 5. DL + 0.3LL + EQY + 0.3EQX SEISMIC 6. DL + 0.3LL + EQY – 0.3EQX SEISMIC 7. DL + 0.3LL - EQY + 0.3EQX SEISMIC 8. DL + 0.3LL - EQY – 0.3EQX
Page 181
Export the results in Excel sheet
Sort smallest to largest in order to find the maximum shear force
or Sort largest to smallest in order to find the maximum shear force Consider the worst load
combination
Do this process for all storeys separately as
showing below
Page 182
Story Load Loc P VX
STORY1 SEISMIC1 MAX Bottom 4207.11 663.91 STORY2 SEISMIC1 MAX Bottom 2804.93 550.8 STORY3 SEISMIC1 MAX Bottom 1402.76 330
Repeat the above procedure in order to obtain the Vtot at Y-direction
Story Load Loc P VY
STORY1 SEISMIC5 MAX Bottom 4207.11 663.91 STORY2 SEISMIC5 MAX Bottom 2804.93 550.8 STORY3 SEISMIC5 MAX Bottom 1402.76 330
Filter the value of the bottom storey
Filter the values using the worst case combination
Record the total seismic shear of each storey for Vtot at X-direction
Page 183
Table 11.4: Second order effects check (EN1993-1-1,cl.4.4.2.2(2))
Storey
Displacement Direction x
dx.e (mm)
Displacement Direction y
dy.e (mm)
Behaviour factor q
Displacement dsx (mm)
cl.4.4.2.2
Displacement dsy (mm)
cl.4.4.2.2
Interstorey drift drx (mm)
Interstorey drift dry (mm)
Storey 3 11.742 11.7452 4 46.968 46.9808 6.7754 6.7776
Storey 2 8.3543 8.3564 4 33.4172 33.4256 9.0274 9.0296
Storey 1 3.8406 3.8416 4 15.3624 15.3664 7.6812 7.6832
Total gravity load
Ptot (kN)
Total seismic
storey shear Vtotx (kN)
Total seismic
storey shear Vtoty (kN)
Height of each storey (mm)
Interstorey drift sensitivity coefficient θ
at X direction
Interstorey drift sensitivity coefficient θ
at Y direction
663.91 663.91 663.91 3000 OK OK
550.8 550.8 550.8 3000 OK OK
330 330 330 3000 OK OK
Θ =P!"! ∙ d!"V!"!# ∙ h
≤ 0.10 Θ =P!"! ∙ d!"V!"!# ∙ h
≤ 0.10
Page 184
12.0 Damage limitation according to EN1998-1-1,cl.4.4.3
The “damage limitation requirement” is considered to have been satisfied, if, under a seismic
action having a larger probability of occurrence than the design seismic action corresponding
to the “no-collapse requirement” in accordance with 2.1(1)P and 3.2.1(3), the interstorey
drifts are limited in accordance with 4.4.3.2.
The damage limitation requirements should be verified in terms of the interstorey drift (dr)
(EN 1998-1-1,cl.4.4.3.2) using the equation below:
d! ∙ v ≤ 0.005 ∙ h
dr: is the difference of the average lateral displacement ds in CM at the top and bottom of storey.
v: is the reduction factor which takes into account the lower return period of the seismic action.
h: is the storey height
Table 12.1: Damage limitation (EN1998-1-1,cl.4.4.3)
For non-structural elements of brittle material attached to the structure drv≤0.005h
For building having ductile non structural elements drv≤0.0075h
For building having non-structural elements fixed in a way so as not to
interfere with structural deformation drv≤0.010h
Table 12.2: Reduction factor of limitation to interstorey drift (CYA NA EN1998-1-
1,cl.NA.2.15)
Importance class Reduction factor v
I 0.5
II 0.5
III 0.4
IV 0.4
Page 185
12.1 Calculation of damage limitation
Table 12.3: Interstorey drift (see table 11.3)
Storey
Displacement Direction x
dx.e (mm)
Displacement Direction y
dy.e (mm)
Behaviour factor q
Displacement dsx (mm)
cl.4.4.2.2
Displacement dsy (mm)
cl.4.4.2.2
Interstorey drift drx (mm)
Interstorey drift dry (mm)
Storey 3 11.742 11.7452 4 46.968 46.9808 6.7754 6.7776
Storey 2 8.3543 8.3564 4 33.4172 33.4256 9.0274 9.0296
Storey 1 3.8406 3.8416 4 15.3624 15.3664 7.6812 7.6832
Reduction factor
v cl.4.4.3.2(2)
Heigh of each storey (mm)
Damage limitation check
X-‐direction
Damage limitation check
Y-‐direction
0.4 3000 OK OK
0.4 3000 OK OK
0.4 3000 OK OK
d! ∙ v ≤ 0.005 ∙ h d! ∙ v ≤ 0.005 ∙ h
Page 186
ANNEX - A
ANNEX A.1 - Assumptions made in the design algorithm (Manual of ETABS – EC3 &
EC8)
1. Load combination
• The automated load combinations are based on the STR ultimate limit states and the
characteristic serviceability limit states.
2. Axial force check
• Tubular sections are assumed to be hot finished for selecting the appropriate buckling
curve from EC3 Table 6.2. This is non conservative if cold formed sections are used.
3. Bending moment check
• The load is assumed to be applied at the shear center for the calculation of the elastic
critical moment.
• Any eccentric moment due to load applied at other locations is not automatically
accounted for.
4. Shear Force Check
• Plastic design is assumed such that Vc,Rd is calculated in accordance with EC3
6.2.6(2).
• The shear area, Av is taken from the input frame section property, rather than using
the equations defined in EC3 6.2.6(3).
• Transverse stiffeners exist only at the supports and create a non-rigid end post for the
shear buckling check. No intermediate stiffeners are considered.
Page 187
• The contribution from the flanges is conservatively ignored for the shear buckling
capacity.
5. Combined Forces Check
• The interaction of bending and axial force is checked in accordance with EC3
6.2.1(7), which may be conservative compared to EC3 6.2.9.
• The calculation of the equivalent uniform moment factors, Cm, assumes uniform
loading, which is conservative.
A1.1:Limitation made in the design algorithm (Manual of ETABS – EC3&EC8)
6. General
• Class 4 sections are not designed (EC3 5.5) and should be considered using other
methods.
• The effects of torsion are not considered in the design (EC3 6.2.7) and should be
considered using other methods.
7. Axial Force Check
• The net area is not determined automatically. This can be specified on a member-by-
member basis using the Net Area to Total Area Ratio overwrite.
• The axial buckling check does not consider torsional or torsional-flexural buckling.
8. Combined Forces Check
• The effect of high shear is checked only for Class 1 or 2 I-sections when combined
with bending. Other section shapes and classes require independent checks to be
carried out.
Page 188
ANNEX –B: Steel design flowcharts
w1 = Initial part of the deflection under permanent loads wc = Precamber in the unloaded structural member w2 = due to Permanent load w3 = due to Variable load
STEEL MEMBERS
(CYS NA EN1993-1-1,table NA.1) Vertical deflection Limits
wmax Cantilevers L/180
Beams carrying plaster or other brittle finish L/360 Other beams (except purlin and sheeting rails) L/250 Purlins and sheeting rails To suit
cladding General use L/300
Vertical deflection (EN1993-1-1,cl.7.2.1)
BASIS OF STRUCTURAL DESIGN (EN1990:2002)
u = Overall horizontal displacement over the building height H
ui = Horizontal displacement over height Hi
STEEL MEMBERS (CYS NA EN1993-1-1,table NA.2)
Horizontal deflection Limits wmax
Top of columns in single storey buildings, exept portal frames H/300
Columns in portal frame buildings, not supporting crane runways To suit cladding
In each storey of the building with more than one storey Storey height/300
On the multi-storey building as a whole Building height/500
Horizontal deflection (EN1993-1-1,cl.7.2.2)
Page 189
STEEL MEMBERS (CYS NA EN1993-1-1,table NA.3)
Design situation Limits natural frequency
Floors over which people walk regularly 5Hz
Floor which is jumped or danced on in a rhythmical manner 9Hz
Dynamic effects (vibration of floors) (EN1993-1-1,cl.7.2.3)
Effective length (Design Guidance of EC3)
Figure 1: Effective length columns (Design Guidance of EC3)
End restraints Fixed/Fixed Partial restrain
in direction Pined/Fixed Pinned/Pined
Free in
position/Fixed Free/Fixed
Effective length
factor, ky,z 0.7L 0.85L 0.85L 1.0L 1.2L 2.0L
Page 190
𝑀!.!" =𝑊!",!𝑓!𝛾!!
𝑀!.!" =𝑊!",!"#𝑓!𝛾!!
Bending resistance (EN1993-1-1,cl. 6.2.5)
Class 1 or 2 Class 3
𝑴𝑬𝒅 ≤ 𝑴𝒄.𝑹𝒅
Compression resistance (EN1993-1-1,cl. 6.2.4)
Class 1 or 2and3
𝛮!.!" =𝛢𝑓!𝛾!!
𝑵𝑬𝒅 ≤ 𝑵𝒄,𝑹𝒅
Fastener holes in tension flange may be ignored if:
𝑨𝒇,𝒏𝒆𝒕𝟎.𝟗𝒇𝒖/𝜸𝑴𝟐 ≥ 𝑨𝒇𝒇𝒚/𝜸𝑴𝟎
Page 191
Shear resistance (EN1993-1-1,cl. 6.2.6)
Rolled I and H sections
(load parallel to web)
CHS
𝐴! = 𝐴 − 2𝑏𝑡! + 𝑡! + 2𝑟 𝑡!
𝐴! = 2𝐴/𝜋
RHS
𝐴! = 𝐴ℎ/(𝑏 +ℎ)Load parallel to
depth
𝐴! = 𝐴𝑏/(𝑏 +ℎ)Load parallel to
width
𝑽𝑬𝒅 ≤ 𝑽𝒄,𝑹𝒅
𝐴! = ℎ! ∙ 𝑡!
𝐴!/𝐴! ≥ 0.6
𝜏!" =𝑉!"𝐴!
𝑉!,!" =𝜏!"
𝑓!/( 3𝛾!!)
Elastic design
𝑽𝑬𝒅𝑽𝒄.𝑹𝒅
≤ 𝟏.𝟎
Plastic design
𝑉!".!" =𝐴!(𝑓!/ 3)
𝛾!!
Rolled C channel sections
(load parallel to web)
but ≥𝜂ℎ!𝑡!
𝜂= 1.0 (conservative
value)
Ignore Shear buckling resistance for webs without intermediate stiffeners
𝒉𝒘𝒕𝒘
> 72𝜺𝜼
Page 192
Combine Bending and shear (EN1993-1-1,cl. 6.2.8)
Shear design resistance NO
Reduction of resistances
(effect on Mc,Rd)
YES NO Reduction of
resistances (no effect on Mc,Rd)
𝑉!" ≤ 0.5 ∙ 𝑉!".!"
𝜌 = 1 −2𝑉!"𝑉!",!"
− 1!
𝑉!".!" =𝐴!(𝑓!/ 3)
𝛾!!
𝑓!" = 1 − 𝜌 𝑓!
Reduced design plastic resistance moment
𝐴! = ℎ!𝑡!
𝑴𝒚.𝑽,𝑹𝒅 =(𝑾𝒑𝒍,𝒚 −
𝝆𝑨𝒘𝟐
𝟒𝒕𝒘)𝒇𝒚
𝜸𝑴𝟎 ≤ 𝑴𝒚,𝒄,𝑹𝒅
If torsion present:
𝜌 = 1 −2𝑉!"𝑉!",!,!"
− 1!
For an I and H sections
𝑉!",!,!" = 1 −𝜏!,!"
1.25 𝑓!/ 3 /𝛾!!𝑉!",!"
Page 193
Bending & Axial force (EN1993-1-1,cl. 6.2.9)
Doubly symmetrical I and H sections
Z-Z axis
Doubly symmetrical I and H sections
Y-Y axis
𝑁!" ≤0.5 ∙ ℎ! ∙ 𝑡! ∙ 𝑓!
𝛾!!
𝑁!" ≤ 0.25𝑁!".!"
𝑀!,!,!" = 𝑀!",!,!"(1 − 𝑛)/(1 − 0,5𝑎)
MN,y,Rd≤ Mpl,y,Rd
𝑛 =𝑁!"𝑁!",!"
𝑎 =𝐴 − 2𝑏𝑡!
𝐴≤ 0,5
𝑁!" ≤ℎ! ∙ 𝑡! ∙ 𝑓!
𝛾!!
𝑛 =𝑁!"𝑁!",!"
𝑎 =𝐴 − 2𝑏𝑡!
𝐴≤ 0,5
𝑀!,!,!" = 𝑀!",!,!" 1 −𝑛 − 𝑎1 − 𝑎
!
𝑛 > 𝑎
𝑀!,!,!" = 𝑀!",!,!"
𝑛 < 𝑎
NO YES
Ignored axial force
Consider axial force
NO YES
Ignored axial force
Consider axial force
Class 1 or 2
𝑵𝑬𝒅
𝑵𝑹𝒅+𝑴𝒚,𝑬𝒅
𝑴𝒚,𝑹𝒅+𝑴𝒛,𝑬𝒅
𝑴𝒛,𝑹𝒅≤ 𝟏.𝟎
Page 194
For RHS Y-Y axis Z-Z axis
𝑁!" ≤ℎ! ∙ 𝑡! ∙ 𝑓!
𝛾!!
NO YES
Ignored axial force
Consider axial force
Hollow section Welded box section
𝑎! = (𝐴 − 2𝑏𝑡)/𝐴) ≤ 0.5
𝑎! = (𝐴 − 2ℎ𝑡)/𝐴) ≤ 0.5
𝑎! = (𝐴 − 2𝑏𝑡!)/𝐴) ≤ 0.5
𝑎! = (𝐴 − 2ℎ𝑡!)/𝐴) ≤ 0.5
𝑀!,!,!" =𝑀!",!,!" 1 − 𝑛1 − 0.5𝑎!
≤ 𝑀!",!,!"
𝑀!,!,!" =𝑀!",!,!" 1 − 𝑛1 − 0.5𝑎!
≤ 𝑀!",!,!"
Bending & Axial force (EN1993-1-1,cl. 6.2.9)
Class 1 or 2
𝑴𝒚,𝑬𝒅
𝑴𝑵,𝒚,𝑹𝒅
𝒂
+𝑴𝒛,𝑬𝒅
𝑴𝑵,𝒛,𝑹𝒅
𝜷
≤ 𝟏.𝟎
I and H section CHS RHS
𝑎 = 2 𝛽 = 5𝑛 ≥ 1
𝑛 = 𝑁!"/𝑁!",!"
𝑎 = 2 𝛽 = 5𝑛 ≥ 1
𝑛 = 𝑁!"/𝑁!",!"
𝑎 = 𝛽 =1.66
1 − 1.13𝑛!
but𝑎 = 𝛽 ≤ 6
Page 195
Buckling resistance in compression (EN1993-1-1,cl. 6.3.1.1)
𝑁!,!" =𝜒𝐴𝑓!𝛾!!)
Class 1 or 2and3
𝑵𝑬𝒅 ≤ 𝑵𝒃,𝑹𝒅
Φ = 0,5 1 + 𝑎 𝜆 − 0,2 + 𝜆!
λ =𝐴𝑓!𝑁!"
Buckling curve ao a b c d Imperfection factor a 0,13 0,21 0,34 0,49 0,76
χ =1
Φ + Φ! − λ!≤ 𝜒 ≤ 1,0
Slenderness for flexural buckling
𝑁!" =!!!"!!
for ideal strut
Cross-section Limits Buckling about axis
Buckling curve
Rolled I sections
h/b>1.2 tf≤40mm y-y a
z-z b
40mm<tf≤100mm y-y b z-z c
h/b≤1.2 tf≤ 100mm y-y b
z-z c
tf> 100mm y-y d z-z d
U-T and solid section any C L-sections any b
Hollow sections
Hot finished any a Cold formed any c
𝜆 ≤ 0.2 𝑁!"/𝑁!" ≤ 0.04
NO (consider buckling effects)
YES (ignored buckling effects)
Page 196
Buckling resistance in bending (EN1993-1-1,cl. 6.3.2)
𝑀!,!" =𝜒!"𝑊!𝑓!𝛾!!
Class 1 or 2and3
𝑴𝑬𝒅
𝑴𝒃.𝑹𝒅≤ 𝟏.𝟎
λ!" =𝑊!𝑓!𝑀!"
Slenderness for flexural buckling
λ! = 𝜋𝐸𝑓!= 93,9𝜀 𝜀 =
235𝑓!
Class 1 or 2 Class 3
Wy=Wpl,y Wy=Wel,y
χ!" =1
Φ!" + Φ!"! − λ!"
!≤ 𝜒!" ≤ 1,0
Φ!" = 0,5 1 + 𝑎!" 𝜆!" − 0,2 + 𝜆!"!
Buckling curve a b c d Imperfection factor aLT 0,21 0,34 0,49 0,76
Cross-section Limits Buckling curve
Rolled I-sections h/b≤2 h/b>2
a b
Welded I-sections h/b≤2 h/b>2
c d
Other cross-sections - d
See following pages for calculation of Mcr and λL
Page 197
Calculation process of Mcr (www.access-steel.com - Document SN003a&b)
𝛭!" = 𝐶!𝜋!𝐸𝐼!(𝑘𝐿!")!
𝑘𝑘!
! 𝐼!𝐼!+(𝑘𝐿!")!𝐺𝐼!𝜋!𝐸𝐼!
+ 𝐶!𝑧!!− 𝐶!𝑧!
Step 1: Define the properties of member Term Description Values
L Distance between point of lateral restraint
Lcr=kl
E Young’s modulus 210000 N/mm2
G Shear modulus 80770 N/mm2
Iz Second moment of area about the weak axis
From section table
It Torsion constant Iw Warping constant k Effective length factor 1.0 unless justified otherwise kw Factor for end warping 1.0 unless justified otherwise zg Distance between the point of
load application and the shear centre
+/-(h/2) or 0 if the load is applied through the shear
centre
Step 2: Calculate the coefficient C1 and C2
Loading and support conditions
C 2 Ψ=M1/M2 C1
Pinned UDL 0,454 1.00 1,00 Fixed UDL 1,554 0.75 1.14
Pinned central P 0,630 0.50 1,31 Fixed central P 1,645 0.25 1,62
0 1,77 -0.25 2,05 -0.50 2,33 -0.75 2,57 -1.00 2,55
Pinned UDL 1,127 Pinned, central P 1,348
𝛭!" =𝜋!𝐸𝐼!𝐿!"!
𝐼!𝐼!+𝐿!"!𝐺𝐼!𝜋!𝐸𝐼!
!.!
Point of application of the load is through the shear centre
YES zg=0
NO zg
Page 198
Alternative method to calculate the Mcr and λLT
𝝀𝑳𝑻 =𝟏𝑪𝟏𝑼𝑽𝝀𝒛 𝜷𝒘
Non-dimensional slenderness
Simply supported rolled I, H and C section
!!!= 1.0(conservative value)
𝑈 = 0.9(conservative value)
𝑉 = 1.0 (conservative value)
𝜆! =𝑘𝐿𝑖!
K=1.0 for beams k=1.0 for free cantilever k=0.9 for lateral restraint to top flange k=0.8 for torsional restraint k=0.7 for lateral and torsional restraint
βw = 1.0 (conservative value)
Page 199
Member combined bending and axial compression (EN1993-1-1,cl. 6.3.3)
𝑵𝑬𝒅𝝌𝒚𝑵𝑹𝒌𝜸𝑴𝟏
+ 𝒌𝒚𝒚𝑴𝒚,𝑬𝒅
𝝌𝑳𝑻𝑴𝒚,𝑹𝒌
𝜸𝑴𝟏
+ 𝒌𝒚𝒛𝑴𝒛,𝑬𝒅𝑴𝒛,𝑹𝒌𝜸𝑴𝟏
≤ 𝟏.𝟎
𝑵𝑬𝒅𝝌𝒛𝑵𝑹𝒌𝜸𝑴𝟏
+ 𝒌𝒛𝒚𝑴𝒚,𝑬𝒅
𝝌𝑳𝑻𝑴𝒚,𝑹𝒌
𝜸𝑴𝟏
+ 𝒌𝒛𝒛𝑴𝒛,𝑬𝒅𝑴𝒛,𝑹𝒌𝜸𝑴𝟏
≤ 𝟏.𝟎
Class 1 and 2 Class 3
Method 2:Interaction factor kij for members not susceptible to torsional deformations (Recommended by CYS NA EN 1993-1-1,cl.NA2.20 – Table B.1)
Interaction factors Type of sections Plastic cross-sectional properties
Class 1 and 2 Elastic cross-sectional properties
Class 3
kyy I-sections
RHS-sections
𝑪𝒎𝒚 𝟏 + 𝝀𝒚 − 𝟎.𝟐𝑵𝑬𝒅
𝝌𝒚𝑵𝑹𝒌/𝜸𝑴𝟏
≤ 𝑪𝒎𝒚 𝟏 + 𝟎.𝟖𝑵𝑬𝒅
𝝌𝒚𝑵𝑹𝒌/𝜸𝑴𝟏
𝑪𝒎𝒚 𝟏 + 𝟎.𝟔𝝀𝒚𝑵𝑬𝒅
𝝌𝒚𝑵𝑹𝒌/𝜸𝑴𝟏
≤ 𝑪𝒎𝒚 𝟏 + 𝟎.𝟔𝑵𝑬𝒅
𝝌𝒚𝑵𝑹𝒌/𝜸𝑴𝟏
kyz I-sections
RHS-sections 0.6kzz kzz
kzy I-sections
RHS-sections 0.6kyy 0.8kyy
kzz
I-sections
𝑪𝒎𝒛 𝟏 + 𝟐𝝀𝒛 − 𝟎.𝟔𝑵𝑬𝒅
𝝌𝒛𝑵𝑹𝒌/𝜸𝑴𝟏
≤ 𝑪𝒎𝒚 𝟏 + 𝟏.𝟏𝟒𝑵𝑬𝒅
𝝌𝒛𝑵𝑹𝒌/𝜸𝑴𝟏
𝑪𝒎𝒛 𝟏 + 𝟎.𝟔𝝀𝒛𝑵𝑬𝒅
𝝌𝒛𝑵𝑹𝒌/𝜸𝑴𝟏
≤ 𝑪𝒎𝒚 𝟏 + 𝟎.𝟔𝑵𝑬𝒅
𝝌𝒛𝑵𝑹𝒌/𝜸𝑴𝟏
RHS-sections
𝑪𝒎𝒛 𝟏 + 𝝀𝒛 − 𝟎.𝟐𝑵𝑬𝒅
𝝌𝒛𝑵𝑹𝒌/𝜸𝑴𝟏
≤ 𝑪𝒎𝒛 𝟏 + 𝟎.𝟖𝑵𝑬𝒅
𝝌𝒛𝑵𝑹𝒌/𝜸𝑴𝟏
Page 200
Method 2:Interaction factor kij for members susceptible to torsional deformations (Recommended by CYS NA EN 1993-1-1,cl.NA2.20 – Table B.2)
Interaction factors
Plastic cross-sectional properties Class 1 and 2
Elastic cross-sectional properties Class 3
kyy Kyy from Table B.1 Kyy from Table B.1 kyz Kyz from Table B.1 Kyz from Table B.1
kzz
𝟏 −𝟎.𝟏𝝀𝒛
𝑪𝒎𝑳𝑻 − 𝟎.𝟐𝟓𝑵𝑬𝒅
𝝌𝒛𝑵𝑹𝒌/𝜸𝑴𝟏
≥ 𝟏 −𝟎.𝟏
𝑪𝒎𝑳𝑻 − 𝟎.𝟐𝟓𝑵𝑬𝒅
𝝌𝒛𝑵𝑹𝒌/𝜸𝑴𝟏
for𝜆! < 0.4:
𝒌𝒛𝒚 = 𝟎.𝟔 + 𝝀𝒛
≤ 𝟏 −𝟎.𝟏𝝀𝒛
𝑪𝒎𝑳𝑻 − 𝟎.𝟐𝟓𝑵𝑬𝒅
𝝌𝒛𝑵𝑹𝒌/𝜸𝑴𝟏
𝟏 −𝟎.𝟎𝟓𝝀𝒛
𝑪𝒎𝑳𝑻 − 𝟎.𝟐𝟓𝑵𝑬𝒅
𝝌𝒛𝑵𝑹𝒌/𝜸𝑴𝟏
≥ 𝟏 −𝟎.𝟎𝟓
𝑪𝒎𝑳𝑻 − 𝟎.𝟐𝟓𝑵𝑬𝒅
𝝌𝒛𝑵𝑹𝒌/𝜸𝑴𝟏
Page 201
Summary design of steel member in bending
Choose yield strength of section, fy from table 3.1 in
EN 1993-1-1
Get starinε from table 5.2 in EN 1993-1-1
Substitute the value of εinto the class limits in table 5.2 to
work out the class of the flange and web
Take the latest favourable class from the flange outstand,
web in bending and web in compression results
Use the required value of W for the defined class to work
out Mc,Rd
Cross-section Resistance check
Design step Results
fy
ε
Flange Class
Web class
Overall Section Class
Mc,Rd
Steel grade
fy (N/mm2)
Nominal thickness of element t (mm) t≤16 16≤t≤40 40≤t≤63 63≤t≤80
S275 275 265 255 245 S355 355 345 335 325
𝜀 =235𝑓!
fy 235 275 355 420 ε 1.00 0.92 0.81 0.75
Flange under compression: c=(b-tw-2r)/2 c/tf
Web under pure bending: c=(h-2tf-2r) c/tw
Mc,Rd = Mpl,Rd = Wpl,yfy/γM0 Class 1 & 2 Mc,Rd = Mel,Rd = Wel,minfy/γM0 Class 3 Mc,Rd = Weff,minfy/γM0 Class 4
Class 1 or 2 Class 3 Class 4
Page 202
Summary design of steel member in shear
Calculate the shear area of the section, Av
Calculate the design plastic shear resistance, Vpl,Rd
Shear resistance check
Design step Results
Av
Vpl,Rd
VEd≤Vc,Rd
Steel grade
fy (N/mm2)
Nominal thickness of element t (mm) t≤16 16≤t≤40 40≤t≤63 63≤t≤80
S275 275 265 255 245 S355 355 345 335 325
𝑉!".!" =𝐴!(𝑓!/ 3)
𝛾!!
Page 203
Summary of buckling resistance in bending
Calculate the design bending moment and shear
Section classification
Design step Results
MEd &VEd
Wy&fy
Calculate critical length Lcr
Calculate Critical moment Mcr
Calculate non-dimensional slenderness λLT
λLT
Calculate imperfection factor αLT
αLT
Calculate reduction factor φLT
φLT
Calculate modified/reduction factor for lateral-torsional
buckling χLTorχLT,mod
χLTχLT,mod
Buckling resistance check 𝑴𝑬𝒅
𝑴𝒃,𝑹𝒅≤ 𝟏.𝟎
Calculate buckling resistance Mb,Rd
Mb,Rd
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