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CISC 95 Example 001 - 1

CISC 95 Example 001

WIDE F LANGE MEMBER UNDER B ENDING

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 usingthe CSA S16-94 (CISC 95) steel frame design code. The moment and shearstrengths are compared with Handbook of Steel construction (6 th Edition) results.

G EOMETRY , P ROPERTIES AND LOADING

L=8.0 m

TECHNICAL F EATURES TESTED Section Compactness Check (Bending) Member Bending Capacity, M r (Fully Restrained) Member Bending Capacity, M r (Buckling) Member Bending Capacity, M r (LTB)

Material PropertiesE = 2x108 kN/m2Fy = 300 kN/m2

Loading

WD = 7 kN/mWL = 15 kN/m

Design PropertiesASTM A992CSA G40.21 300W

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CISC 95 Example 001 - 2

R ESULTS C OMPARISON

Independent results are taken from Example 1, 2 and 3 on page 5-91 and 5-92 ofthe Hand Book of Steel Construction to CSA S16-94 published by CanadianInstitute of Steel Construction.

Output Parameter SAP2000 IndependentPercent

Difference

Compactness Class 1 Class 1 0.00%

Design Moment, M f (kN-m) 250.0 250.0 0.00%

(a) Moment Capacity, M r33 ofW410X54 (kN-m) w/ l b = 0 m

283.5 283.5 0.00%

(b) Moment Capacity, M r33 ofW410X54 (kN-m) w/ l b = 2 m

283.5 283.5 0.00%

(c) Moment Capacity, M r33 ofW410X60 (kN-m) w/ l b = 4 m

264.2 264.1 0.04%

C OMPUTER F ILE: CISC 95 EX001

C ONCLUSION The results show an exact match with the independent results.

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CISC 95 Example 001 - 3

HAND C ALCULATION

Properties:

Material: CSA G40.21 Grade 300W

f y = 300 MPa

E = 200,000 MPa

G = 76923 MPa

Section: W410x54b f = 177 mm, t f = 10.9 mm, d = 404 mm, t w = 7.5 mm

2 404 2 10.9 382.2 f h d t mm

A g = 6810 mm 2

I 22 = 10,100,000 mm 4

Z 33 = 1,050,000 mm 3

J = 226,000 mm 4 11 63.92 10

w

C mm

Section: W410x60

b f = 178 mm, t f = 12.8 mm, d = 408 mm, t w = 7.7 mm

2 408 2 12.8 382.4 f h d t mm

A g = 7580 mm 2

I 22 = 12,000,000 mm 4

Z 33 = 1,190,000 mm 3

J = 328,000 mm 4 11 64.68 10wC mm

Member:

L = 8 m

= 0.9

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CISC 95 Example 001 - 4

Loadings:

w f = (1.25 wd + 1.5wl ) = 1.25(7) + 1.5(15) = 31.25 kN/m2 231.25 8

8 8

f f

w L M

250 f M kN m

Section Compactness:

Localized Buckling for Flange:

.1

145 1458.37

300Cl

y F

W410x54

1778.12

2 2 10.9

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 63.51

6810 300300

f Cl

y y

C

C F

W410x54

381.650.96

7w

h

t

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CISC 95 Example 001 - 7

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

2 = 1.000

2

222 22u w

E M 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

u M

6350.47 10 350.47u M N mm kN m

0.67 0.67 321.3 239 350.47 , p u M M kN m so

33

33

3333 28.0115.1

pu

p pr M

M

M M M

33

3571.15 0.9 357 1 0.28 264.1 283.5350.47

r M kN m kN m

33 264.1

r M kN m