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CSA S16-14 Example 001 WIDE FLANGE MEMBER UNDER COMPRESSION & BENDING EXAMPLE DESCRIPTION The frame object moment and shear strength is tested in this example. A simply supported beam is (a) laterally restrained along its full length, (b) laterally restrained along its quarter points, at mid-span, and at the ends (c) laterally restrained along mid-span, and is subjected to a uniform factored load of DL = 7 kN/m and LL = 15 kN/m. This example was tested using the CSA S1614 steel frame design code. The moment and shear strengths are compared with Handbook of Steel construction (9th Edition) results. GEOMETRY, PROPERTIES AND LOADING
L = 8.0 m Material Properties E= Fy =
2x108 kN/m2 350 kN/m2
Design Properties
Loading WD = WL =
7 kN/m 15 kN/m
ASTM A992 CSA G40.21 350W W410X46 W410X60
TECHNICAL FEATURES TESTED Section compactness check (bending) Member bending capacity, Mr (fully restrained) Member bending capacity, Mr (buckling) Member bending capacity, Mr (LTB)
CSA S16-14 Example 001 - 1
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RESULT COMPARISON Independent results are taken from Examples 1, 2 and 3 on pages 5-84 and 5-85 of the Hand Book of Steel Construction to CSA S16-01 published by Canadian Institute of Steel Construction.
SAP2000
Independent
Percent Difference
Class 1
Class 1
0.00%
250.0
250.0
0.00%
(a) Moment Capacity, Mr33 of W410X46 (kN-m) w/ lb = 0 m
278.775
278.775
0.00%
(b) Moment Capacity, Mr33 of W410X46 (kN-m) w/ lb = 2 m
268.97
268.83
0.05%
(c) Moment Capacity, Mr33 of W410X60 (kN-m) w/ lb = 4 m
292.10
292.05
0.02%
Output Parameter Compactness Design Moment, Mf (kN-m)
COMPUTER FILE: CSA S16-14 EX001 CONCLUSION The results show an acceptable comparison with the independent results.
CSA S16-14 Example 001 - 2
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HAND CALCULATION Properties: Material: CSA G40.21 Grade 350W fy = 350 MPa E = 200,000 MPa G = 76923 MPa Section: W410x46 bf = 140 mm, tf = 11.2 mm, d = 404 mm, tw = 7 mm
h d 2t f 404 2 11.2 381.6mm Ag = 5890 mm2 I22 = 5,140,000 mm4 Z33 = 885,000 mm3 J
= 192,000 mm4
Cw 1.976 1011 mm6 Section: W410x60 bf = 178 mm, tf = 12.8 mm, d = 408 mm, tw = 7.7 mm
h d 2t f 408 2 12.8 382.4mm Ag = 7580 mm2 I22 = 12,000,000 mm4 Z33= 1,190,000 mm3 J
= 328,000 mm4
Cw 4.698 1011 mm6 Member: L=8m Ф = 0.9
CSA S16-14 Example 001 - 3
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Loadings: wf = (1.25wd + 1.5wl) = 1.25(7) + 1.5(15) = 31.25 kN/m Mf
w f L2 8
31.25 82 8
M f 250 kN-m Section Compactness: Localized Buckling for Flange: 145 145 7.75 Fy 350
Cl .1
W410x46
bf 2t f
140 6.25 2 11.2
Cl .1 , No localized flange buckling Flange is Class 1. W410x60
bf 2t f
178 6.95 2 12.8
Cl .1 , No localized flange buckling Flange is Class 1. Localized Buckling for Web:
Cl .1
Cf 1100 1 0.39 Cy Fy
1100 0 1 0.39 58.8 5890 350 350
W410x46
h 381.6 54.51 tw 7
CSA S16-14 Example 001 - 4
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Cl .1 , No localized web buckling Web is Class 1. Section is Class 1
W410x60
h 382.4 49.66 tw 7.7
Cl .1 , No localized web buckling Web is Class 1. Section is Class 1 Calculation of ω2: ω2 is calculated from the moment profile so is independent of cross section and is calculated as:
2
4 M max M max 2 4M a 2 7 M b 2 4M c 2
where: Mmax = maximum moment Ma = moment at ¼ unrestrained span Mb = moment at ½ unrestrained span Mc = moment at ¾ unrestrained span Section Bending Capacity for W410x46: M p Fy Z 33 350 885,000 / 10 6 309.75 kN-m
M p 0.9 309.75 278.775 kN-m
Member Bending Capacity for Lb = 0 mm (Fully Restrained): Lb = 0, so Mmax = Ma = Mb = Mc = Mu = 250 kN-m and ω2 = 1.000
CSA S16-14 Example 001 - 5
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E Mu 2 EI 22GJ I 22Cw as L 0 L L 2
M p 33 M r 33 1.15M p 33 1 0.28 M p 33 Mu 0.28
M p 33 Mu
0 as M u
leading to M r 33 1.15 M p33 M p33 So
M r 33 M p33 278.775kN-m
Member Bending Capacity for Lb = 2000 mm: M a @ xa
Ma
L Lb Lb 8 2 2 3.5 m 2 4 2 4
f Lxa 2
f xa 2 2
31.25 8 3.5 31.25 3.52 246.094 kN-m 2 2
Ma = Mc = 246.094 kN-m @ 3500 mm and 4500 mm Mmax = Mb = 250 kN-m @ 4000 mm
2
4 250 250 4 246.0942 7 2502 4 246.0942 2
1.008
ω2 = 1.008
2 E EI 22GJ I 22Cw L L 2
Mu
CSA S16-14 Example 001 - 6
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2 10 5.14 10 76923 192 10 2 10 5.14 10 197.6 10 2000 5
Mu
1.008 2000
SAP2000 0
6
3
2
5
6
9
M u 537.82 106 N-mm = 537.82 kN-m
0.67 M p 0.67 309.75 208 M u 537.82kN-m, so
M p 33 M r 33 1.15M p 33 1 0.28 M p 33 Mu 309.75 M r 33 1.15 0.9 309.75 1 0.28 268.89 kN-m 278.775 kN-m 537.82
M r 33 268.89kN-m
Section Capacity for W410x60: M p Fy Z 33 350 1190,000 / 10 6 416.5 kN-m
M p 0.9 416.5 374.85 kN-m
Member Bending Capacity for Lb = 4000 m: M a @ xa
Ma
L Lb Lb 8 4 4 3m 2 4 2 4
f Lxa 2
f xa 2 2
31.25 8 3 31.25 32 234.375 kN-m 2 2
Ma = Mc = 234.375 kN-m @ 3500 mm and 4500 mm Mmax = Mb = 250 kN-m @ 4000 mm
2
4 250 250 4 234.3752 7 2502 4 234.3752 2
1.032
ω2 = 1.032
CSA S16-14 Example 001 - 7
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E M u 2 EI 22GJ I 22Cw Ly L 2
2 10 12 10 76923 328 10 2 10 12 10 469.8 10 4000 5
Mu
1.032 4000
6
3
2
5
6
9
M u 362.06 106 N-mm = 362.06 kN-m 0.67 M p 0.67 309.75 279 M u 362.06kN-m, so
M p 33 M r 33 1.15M p 33 1 0.28 M p 33 Mu 416.5 M r 33 1.15 0.9 416.5 1 0.28 362.06
M r 33 292.23kN-m
CSA S16-14 Example 001 - 8