PROJECT : PAGE : CLIENT : DESIGN BY : JOB NO. : DATE : REVIEW BY : WF Simply Supported Beam Design with Torsional Loading Based on AISC 360-10/16 INPUT DATA & DESIGN SUMMARY BEAM SECTION = > W10X54 = > A d GRAVITY DISTRIBUTED LOAD w = 1.15 klf, (17 kN / m) 15.8 10.1 4.38 2.55 LATERAL POINT LOAD AT MID F = 5 kips, (22 kN) l TORSION AT MID SPAN T = 5.1 ft-kips, (7 kN-m) 103 20.6 0.01744 0.37 AXIAL LOAD P = 96 kips, (427 kN) BEAM LENGTH 15 ft, (4.57 m) BEAM YIELD STRESS 50 ksi, (345 MPa) VERTICAL BENDING UNBRACED LENGTH 15 ft, (4.57 m) AXIAL VERTICAL UNBRACED LENGTH 15 ft, (4.57 m) AXIAL HORIZONTAL UNBRACED LENGTH 7.5 ft, (2.29 m) ANALYSIS DETERMINE GOVERNING MOMENTS AT MIDDLE OF SPAN 32.3 ft-kips 18.8 ft-kips 22.7 ft-kips THE BEAM DESIGN IS ADEQUATE. 13.3 ft-kips 0.584 ,(Philip page 101) CHECK TORSIONAL CAPACITY (AISC 360 H3.3 & Philip page 100) 0.73 < 1.00 [Satisfactory] Where 21.93 ksi 29.94 ksi CHECK COMBINED COMPRESSION AND BENDING CAPACITY (AISC 360 H1) 1.08 < 4/3 [Satisfactory] Where 96 kips 109.7 ft-kips, (Sim. from Philip page 100) 18.8 ft-kips 721 / 1.67 = 431.971 kips, (AISC 360 Chapter E) > [Satisfactory] 252.623 / 1.67 = 151.271 ft-kips, (AISC 360 Chapter F) > [Satisfactory] 130.417 / 1.67 = 78.0938 ft-kips, (AISC 360 Chapter F) > [Satisfactory] DETERMINE DEFLECTIONS 0.22127 Where 11200 ksi 29000 ksi rx ry Iy Sy tw L = Fy = Lb = Lx = Ly = Mx = w L 2 / 8 = My = F L / 4 = M0 = T L / (4d) = MT = bM0 = fbx / Fnx = fbx = Mx / Sx + 2MT / Sy = Fnx = Fy / WT = Fy / 1.67 = Pr = Mrx = (Mx / Sx + 2MT / Sy) Sx = Mry = Pc = Pn / Wc = 3/4 Pr Mcx = Mn / Wb = Mrx Mcy = Mn / Wb = 3/4 Mry o , max twist angle at middle (Philip page 1 G = Es = 2 4 sinh 2 sinh L L L l b l l 2sinh 2 sinh 2 2 2 sinh L T L L GJ L l l l l l 8 , 0.2 9 , 0.2 2 ry r rx r c cx cy c ry r rx r c cx cy c M P M P for P M M P M P M P for P M M P
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PROJECT : PAGE :
CLIENT : DESIGN BY : JOB NO. : DATE : REVIEW BY :
WF Simply Supported Beam Design with Torsional Loading Based on AISC 360-10/16
INPUT DATA & DESIGN SUMMARYBEAM SECTION = > W10X54 = > A dGRAVITY DISTRIBUTED LOAD w = 1.15 klf, (17 kN / m) 15.8 10.1 4.38 2.55 303 60
LATERAL POINT LOAD AT MID F = 5 kips, (22 kN) lTORSION AT MID SPAN T = 5.1 ft-kips, (7 kN-m) 103 20.6 0.01744 0.37 10.00 0.62AXIAL LOAD P = 96 kips, (427 kN)BEAM LENGTH 15 ft, (4.57 m)
BEAM YIELD STRESS 50 ksi, (345 MPa)
VERTICAL BENDING UNBRACED LENGTH 15 ft, (4.57 m)
AXIAL VERTICAL UNBRACED LENGTH 15 ft, (4.57 m)
AXIAL HORIZONTAL UNBRACED LENGTH 7.5 ft, (2.29 m)
ANALYSISDETERMINE GOVERNING MOMENTS AT MIDDLE OF SPAN
32.3 ft-kips
18.8 ft-kips
22.7 ft-kips THE BEAM DESIGN IS ADEQUATE.13.3 ft-kips
0.584 ,(Philip page 101)
CHECK TORSIONAL CAPACITY (AISC 360 H3.3 & Philip page 100)
0.73 < 1.00 [Satisfactory]Where 21.93 ksi
29.94 ksi
CHECK COMBINED COMPRESSION AND BENDING CAPACITY (AISC 360 H1)
0.15 in = L / 1207 , vertical deflection at middle
Where 303
0.20 in = L / 885 , horizontal deflection at middle
Where 103
Technical References: 1. AISC: "Steel Construction Manual 14th Edition", American Institute of Steel Construction, 2010. 2. Philip H. Lin: "Simplified Design for Torsional Loading of Rolled Steel Members", Engineering Journal, AISC, 1977.
Plate Girder Design Based on AISC Manual 13th Edition (AISC 360-05)
INPUT DATA & DESIGN SUMMARYSTEEL YIELD STRESS 50 ksiSIMPLY SUPPORTED SPAN 15 ftSUPERIMPOSED UNIFORM DEAD LOAD kips / ftUNIFORM LIVE LOAD kips / ft
POINT DEAD LOAD kips
POINT LIVE LOAD kipsDISTANCE POINT LOAD TO END ft
TOP FLANGE WIDTH 10.00 in
TOP FLANGE THICKNESS 0.62 in
BOTTOM FLANGE WIDTH 10 in
BOTTOM FLANGE THICKNESS 0.615 in
WEB THICKNESS 0.37 inBEAM DEPTH 10.1 in Err:502UNBRACED LENGTH 15 ft FLANGE TO WEB WELDING USE 1/4 in - 24 in @ 2293 in o.c.
THE GIRDER DESIGN IS ADEQUATE.
ANALYSISCHECK LIMITING WIDTH-THICKNESS RATIOS FOR WEB (AISC 365-05 Table B4.1)
23.97 < 137.27
< 90.55Compact Web
where E = 29000 ksi
137.27
87.03
90.55
8.87 in 9.46 in
277.5 ft-kips 250.0 ft-kips
CHECK LIMITING WIDTH-THICKNESS RATIOS FOR FLANGES (AISC 365-05 Table B4.1)
8.13 < 25.09
< 9.15
Compact Flangeswhere 25.09
9.15
0.76
60 60
35 ksi, (AISC 360-05 Table note B4.1 & Eq F4-6)
DETERMINE CRITERIA FOR ALLOWABLE FLEXURAL STRENGTH (AISC 365-05 Table F1.1)
Required ConditionsChapter F Sections
F2 F3 F4 F5Double Symmetric x x
Compact Web x xx
Noncompact Web
Slender Web 151.3 ft-kipsCompact Flanges x ( from following analysis)
Noncompact FlangesSlender Flanges
Applicable Section ok
9.02 ft
33.66 ft
where 2.55 in 60
Fy = S =
DL = LL =
PDL =
PLL = c =
bf,top =
tf,top =
bf,bot =
tf,bot =
tw = d =
Lb =
hc / tw = lr =
lp =
lr = 5.7 (E / Fy)0.5 =
lp = (hc / hp) (E / Fy)0.5 / (0.54 Mp / My -0.09)2 = ,for Af,top ≠ Af,bot
lp = 3.76 (E / Fy)0.5 = ,for Af,top = Af,bot
hc = hp =
Mp = My =
0.5 bf,top / tf,top = lr =
lp =
lr = 1.0 (kc E / FL)0.5 =
lp = 0.38 (E / Fy)0.5 =
kc = Min [0.76 , Max (0.35 , 4 / (h / tw)0.5 )] =
Sxt = in3 Sxc = in3
FL =
Mallowable = Mn / Wb =
DETERMINE ALLOWABLE FLEXURAL STRENGTH , Mn / Wb , BASED ON AISC 365-05 Chapter F2
ry = Sx = in3
1.76p yy
EL r
F
2
0
0.7 01.95 1 1 6.760.7 0.7
r ts tsy x y
FE Jc Ey S hxL r rE JcS h FF
9.49 in 103h0 = Iy = in4
(cont'd)
2316.6 , (AISC 365-05 F2.2)
31.8102(Use J = 1.82
2.85 in
1.0 1.0 , (AISC Manual 13th Table 3-1, page 3-10)
101.524 ksi
252.6 ft-kips
151.3 ft-kips where 1.67 , (AISC 365-05 F1)
<== Not Applicable.
284.1 ft-kips
where 8.13
9.15 25.09
151.3 ft-kips
<== Not Applicable.
6.33 ft
33.85 ft
where 0.53
2.87 in
277.5 ft-kips
250 ft-kips 250 ft-kips
23.97
87.03 137.27
1.11
102.385 0.50 > 0.23, AISC 360-05 F4-5 )
245.2238 ft-kips
Cw = Iy h02 / 4 =
J = [tw d (tw2 + d2)] / 12 = in4, (not applicable if taken web only, EIT Manual page 26)
in4 )rts =[( Iy Cw)0.5/ Sx)]0.5 =
c = Cb =
Mallowable, F2 =Mn / Wb = Wb =
DETERMINE ALLOWABLE FLEXURAL STRENGTH , Mn / Wb , BASED ON AISC 365-05 Chapter F3
l = bf / (2 tf) =
lpf = lp = lrf = lr =
Mallowable, F3 =Min(Mn,F2 , Mn,F3) / Wb =
DETERMINE ALLOWABLE FLEXURAL STRENGTH , Mn / Wb , BASED ON AISC 365-05 Chapter F4
aw =hc tw/ (bfc tfc) =
Mp = Min [Zx Fy , 1.6Sxc Fy ] =
Myc = Sxc Fy = Myt = Sxt Fy =
l = hc / tw =
lpw = lp = lrw = lr =
ksi, (for Iyc / Iy =
22
20
1 0.078b bcr
tsxb
ts
E JcC LFrS hL
r
, 2
,
0.7 , ,
, ,
p b p
b pp p y p p b rb xn F
r p
cr p r bx
forM L L
L LMin forC SM M F M L L LM L L
Min forSF M L L
, 3
2
0.7 ,
0.9 ,
pfp p y x
rf pfn F
c x
for Noncompact FlangesSM M FM
Ek S for Slender Flanges
l ll l
l
1.1p ty
EL r
F
2
0
01.95 1 1 6.76 Lr t
L xc
E J S hF xcL r E JS hF
, 4.2
,
, ,
, ,
pc yc b p
b ppc yc pc yc L pc yc p b rb xcn F
r p
cr pc yc r bxc
forR M L L
L LMin forC SR M R M F R M L L LM L L
Min forSF R M L L
20
0
1126
fct
w
br
h had dh
, /
1 , , /
pc w pw
ycpc
p p pw pc w pw
yc yc ycrw pw
M for h tM
RM M MMin for h tM M M
l
l ll
l l
22
20
1 0.078b bcr
txcb
t
E JC LFrS hL
r
(cont'd)
277.5 ft-kips
1.11
146.8 ft-kips
<== Not Applicable.
21.62 ft
41.4981 ksi
50 ksi
1
124.2 ft-kips
9 24 , 3.7414.7 ft
5.00 1.000
112.11 kips
67.1317 kips 1.67 , (AISC 365-05 G1)
TOTAL SUPERIMPOSED GRAVITY LOAD
w = DL + LL = 0.000 kips / ft , 0.00 kips
CHECK EACH SECTION CAPACITIES
Section Left 0.00 S 0.00 S 0.00 S 0.00 S 0.00 S Point 0.17 S 0.33 S 0.50 S 0.67 S 0.83 S RightDistance 0 0.00 0.00 0.00 0.00 0.00 0.00 2.50 5.00 7.50 10.00 12.50 15.00
0.15 in = L / 1207 , vertical deflection at middle
Where 303
0.20 in = L / 885 , horizontal deflection at middle
Where 103
Technical References: 1. AISC: "Manual of Steel construction 9th", American Institute of Steel Construction, 1990. 2. Philip H. Lin: "Simplified Design for Torsional Loading of Rolled Steel Members", Engineering Journal, AISC, 1977.
fa / Fa =
fa = P / A =
Es =Fa = {
(1-F2/2)Fy / (5/3+3F/8-F3/8) = ksi, for Cc > (Kl/r)Cc = (22Es/Fy)0.5 = 122Es/[23(KL/r)2] = ksi, for Cc < (Kl/r)KL/r = MAX(KLx/rx, KLy/ry) =