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IS-800-2007 Example 002 WIDE FLANGE MEMBER UNDER BENDING EXAMPLE DESCRIPTION The frame object axial strengths are tested in this example. A continuous beam is subjected to factored distributed load w = 48.74 kN/m. This example was tested using the Indian IS 800:2007 steel frame design code. The design capacities are compared with independent hand calculated results.
GEOMETRY, PROPERTIES AND LOADING
Section A-A L1
L2
L3
A
w
A L1 = 4.9 m Material Properties E = 200x103 MPa v = 0.3 G = 76923 MPa
L2 = 6 m Loading w = 48.74 kN/m
L3 = 4.9 m Design Properties f y = 250 MPa Section: ISLB 500
IS-800-2007 Example 002 - 1
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TECHNICAL FEATURES TESTED
Section compactness check (beam) Section shear capacity Member bending capacity
RESULTS COMPARISON Independent results are taken from hand calculations based on the CSI steel design documentation contained in the file “SFD-IS-800-2007.pdf,” which is available through the program “Help” menu. The example was taken from Example 10.8 on pp. 897-901 in “Design of Steel Structures” by N. Subramanian.
Output Parameter
ETABS
Independent
Percent Difference
Compactness
Class 1
Class 1
0.00%
157.70
157.93
0.14%
603.59
603.59
0.00%
Section Bending Resistance, M d(LTB) (kN-m) Section Shear Resistance, V d (kN)
COMPUTER FILE: IS-800-2007 EX002 CONCLUSION The results show an acceptable comparison with the independent results.
IS-800-2007 Example 002 - 2
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HAND CALCULATION Properties:
Material: Fe 250 E = 200,000 MPa G = 76,923 MPa f y = 250 MPa
Section: ISLB 500 (Note: In ETABS, the section is not available with original example properties, including fillet properties. A similar cross-section with fillet r = 0 was used, with similar results, shown below.) 2
A = 9550 mm
h = 500 mm , b f = 180 mm , t f = 14.1 mm , t w = 9.2 mm b d
b f 2
180 2
90mm
h 2 t f r 500 2 14.1 0 471.8 mm 4
4
I z = 385,790,000 mm , I y = 10,639,000.2 mm 3
3
Z ez = 1,543,160 mm , Z pz = 1,543,160 mm r y = 33.4 mm Member: Lleft = 4.9 m Lcenter = 6 m (governs) Lright = 4.9 m KL y = KL z = 6,000 mm (unbraced length)
M 0 1.1
IS-800-2007 Example 002 - 3
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Loadings:
N Ed 0 kN
48.75kN/m Section Compactness:
250 f y
250
250
1
r 1 = 0 since there is no axial force
Localized Buckling for Flange:
p 9.4 9.4 1 9.4 e
b t f
90
14.1
6.38
e 6.38 p 9.40 So Flange is Class 1 in pure bending
Localized Buckling for Web:
p e
84 (1 r 1 ) d t w
84 1 (1 0)
471.8 9.2
84
51.28
e 51.28 p 84.00 So Web is Class 1 in pure bending
Since Flange & Web are Class 1, Section is Class 1.
IS-800-2007 Example 002 - 4
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Section Shear Capacity:
Vd
f y
M 0
ht w
3
250 1.1 3
500 9.2
V d 603.59kN
Member Bending Capacity
h t f 500 14.1 485.9
h f
I t
bi ti 3 3
2b f t f 3 3
di tw 3 3
2 180 14.13 3
485.9 9.23 3
4.63 105 mm4
From Roark & Young, 5th Ed., 1975, Table 21, Item 7, pg.302 t1
t2 t f
I w
and b1
b2 b f
h f 2 t1t2b13b23 12 t b
3 1 1
t2b2
3
for symmetric sections
485.92 14.1 14.1 1803 1803 12 14.2 180
3
14.2 180
3
8.089 1011 mm6
C 1 = 1.0 (Assumed in example and specified in ETABS) M cr
C1
M cr 1.0
2 EI y 2 EI w GI t 2 2 KL KL 2 200, 000 10, 639, 000.2 2 200, 000 8.089 1011 76,923 462, 508 2 2 6, 000 6, 000
M cr 215,936,919.3N-mm
LT 0.21 b 1.0 LT
b Z pz f y M cr
1 1, 770, 800 250 215,936,919.3
1.337
IS-800-2007 Example 002 - 5
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LT 0.5 1 LT LT 0.2 LT 2 0.5 1 0.21 1.337 0.2 1.3372 LT 1.5127 LT LT f bd
1
LT LT 2
2 LT
1.0
1 1.5127 1.5127
2
1.337
2
0.450 1.0
LT f y 0.450 250 102.3MPa 1.1 M 0
M d , LTB
Z pz f bd 1770.8 103 102.3 157, 925, 037.7 N-mm
M d , LTB
157.93kN-m
IS-800-2007 Example 002 - 6
