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CSA S16-01 Example 001

WIDE FLANGE MEMBER UNDER BENDING

EXAMPLE DESCRIPTION

The frame object moment and shear strength is tested in this example.

In the example a simply supported beam is (a) laterally restrained along its fulllength, (b) laterally restrained along its quarter points, at mid-span and at the

ends (c) laterally restrained along at mid-span and is subjected to a uniformfactored load of DL = 7 kN/m and LL = 15 kN/m. This example was tested using

the CSA S16-01 steel frame design code. The moment and shear strengths arecompared with Handbook of Steel construction (9thEdition) results.

GEOMETRY,PROPERTIES AND LOADING

L = 8.0 m

TECHNICAL FEATURES TESTED

Section Compactness Check (Bending) Member Bending Capacity, Mr (Fully Restrained) Member Bending Capacity, Mr (Buckling) Member Bending Capacity, Mr (LTB)

Material Properties

E = 2x108kN/m2

Fy = 350 kN/m2

Loading

WD = 7 kN/mWL = 15 kN/m

Design Properties

ASTM A992CSA G40.21 350W

W410X46

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RESULT COMPARISON

Independent results are taken from Example 1, 2 and 3 on page 5-84 and 5-85 ofthe Hand Book of Steel Construction to CSA S16-01 published by Canadian

Institute of Steel Construction.

Output Parameter SAP2000 IndependentPercent

Difference

Compactness Class 1 Class 1 0.00%

Design Moment, Mf(kN-m) 250.0 250.0 0.00%

(a) Moment Capacity, Mr33of

W410X46 (kN-m) w/ lb= 0 m

278.775 278.775 0.00%

(b) Moment Capacity, Mr33of

W410X46 (kN-m) w/ lb= 2 m

268.57 268.42 0.06%

(c) Moment Capacity, Mr33ofW410X60 (kN-m) w/ lb= 4 m

287.69 287.64 0.02%

COMPUTER FILE: CSAS16-01EX001

CONCLUSION

The results show an exact match with the independent results.

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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

2 404 2 11.2 381.6fh d t mm

Ag= 5890 mm2

I22= 5,140,000 mm4

Z33= 885,000 mm3

J = 192,000 mm4

11 61.97 10

w

C mm

Section: W410x60

bf= 178 mm, tf= 12.8 mm, d = 408 mm, tw= 7.7 mm

2 408 2 12.8 382.4fh d t mm

Ag= 7580 mm2

I22= 12,000,000 mm4

Z33= 1,190,000 mm3

J = 328,000 mm4

11 64.68 10wC mm

Member:

L = 8 m

= 0.9

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Loadings:

wf= (1.25wd+ 1.5wl)=1.25(7) + 1.5(15) = 31.25 kN/m

2 231.25 8

8 8

f

f

w LM

250fM kN m

Section Compactness:

Localized Buckling for Flange:

.1

145 1457.75

350Cl

yF

W410x46

1406.25

2 2 11.2

f

f

b

t

.1Cl , No localized flange buckling

Flange is Class 1.W410x60

1786.95

2 2 12.8

f

f

b

t

.1Cl , No localized flange buckling

Flange is Class 1.

Localized Buckling for Web:

.1

1100 1100 01 0.39 1 0.39 58.8

5890 350350

f

Cl

yy

C

CF

W410x46

381.654.51

7w

h

t

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.1Cl , No localized web buckling

Web is Class 1.

Section is Class 1

W410x60

382.449.66

7.7w

h

t

.1Cl , No localized web buckling

Web is Class 1.

Section is Class 1

Section Bending Capacity for W410x46:

75.30910/000,885350 6

33 ZFM yp kN-m

775.27875.3099.0 pM kN-m

Member Bending Capacity for L b=0 mm (Ful ly Restrained):

Braced segment center moment is greater than the braced segment end moments, so

2 = 1.000

2

2

22 22 0

u w

EM EI GJ I C as L

L L

33

33 33 331.15 1 0.28

p

r p p

u

MM M M

M

33

0.28 0p

u

u

MasM

M

33 33 331.15r p pleading to M M M

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So

33 33 278.775r pM M kN m

Member Bending Capacity for L b=2000 mm:

Braced segment center moment is greater than the braced segment end moments, so

2 = 1.000

2

2

22 22u w

EM EI GJ I C

L L

5 6 3

25

6 9

2. 10 5.14 10 76923 192 10

1.02. 10

2000 5.14 1 0 197 102000

uM

6532.96 10 532.96uM N mm kN m

0.67 0.67 309.75 208 532.96 ,p uM M kN m so

33

33

3333 28.0115.1

p

u

p

pr M

M

MMM

33

309.751.15 0.9 309.75 1 0.28 268.42 278.775

532.96r

M kN m kN m

33 268.42

rM kN m

Section Bending Capacity for W410x60:

6

33 350 1,190,000 /10 416.5p yM F Z kN m

85.3745.4169.0 pM kN-m

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Member Bending Capacity for L b= 4000 m:

Braced segment center moment is greater than the braced segment end moments, so

2 = 1.000

2

2

22 22u w

EM EI GJ I C

L L

5 6 3

25

6 9

2. 10 12 10 76923 328 10

1.02. 10

4000 12 10 468 104000

uM

6350.47 10 350.47uM N mm kN m

0.67 0.67 309.75 279 350.47 ,p uM M kN m so

33

33

3333 28.0115.1 p

u

p

pr M

M

MMM

33

416.51.15 0.9 416.5 1 0.28 287.64 278.775

350.47r

M kN m kN m

33 287.64

rM kN m