Strength and Stiffness Analysis of a Rolled I-beam
1 – stringer;
2 – secondary beam
Objective: Check of the Resistance of Sections mode in the “Steel” postprocessor of SCAD.
Task: Check the design section of a rolled I-beam for the secondary beams with a span of 6 m in a complex stub girder system. The top chord of the secondary beams is restrained by the stringers arranged with a spacing of 1 m.
Source: Steel Structures: Student Handbook / [Kudishin U.I., Belenya E.I., Ignatieva V.S and others] - 13-th ed. rev. - M.: Publishing Center "Academy", 2011. p. 183.
Compliance with the codes: SNiP II-23-81*, SP 16.13330.2011, DBN B.2.6-163:2010.
Initial data file:
4.4 SectionResistance_Example_4.4.spr;
report — 4.4 SectionResistance _Example_4.4.doc
Initial data:
| Ry = 23 kN/cm2, | Steel grade C235; |
| M = 508,5 kNm | Design bending moment; |
| γc = 1 | Service factor; |
| l = 6 m | Beam span; |
| сх = 1,1 | Coefficient allowing for plastic deformations; |
| Wx = 2034,982 cm3 iy = 21,777 см, iz = 3,39 cm. |
Selected I-beam No.55 GOST 8239-89 |
SCAD Results. STEEL Postprocessor:
[Element No. 1] Forces
|
N
Max. 0 T |
My
Max. 51,83 T*m |
Mz
Max. 0 T*m |
|
Mk
Max. 0 T*m |
Qz
|
Qy
Max. 0 T |
|
|
Length of the bar 6 m |
|
Analysis complies with SNiP II-23-81*
Structural member section
Steel: C235
Member length 6 m
Limit slenderness for members in compression: 250
Limit slenderness for members in tension: 250
Service factor 1
Importance factor 1
Effective length factor XoZ -- 1
Effective length factor XoY -- 1
Length between out-of-plane restraints 1,125 m
Section
Profile: I-beam with sloped inner flange surfaces GOST 8239-89 55
|
Results |
Check |
Utilization factor |
|---|---|---|
|
Sec.5.12 |
Strength under action of bending moment My |
1,09 |
|
Sec.5.12,5.18 |
Strength under action of lateral force Qz |
0,12 |
|
Sec.5.24,5.25 |
Strength under combined action of longitudinal force and bending moments, no plasticity |
1,09 |
|
Sec.5.15 |
Stability of in-plane bending |
1,09 |
|
Sec.6.15,6.16 |
Limit slenderness in XoY plane |
0,71 |
|
Sec.6.15,6.16 |
Limit slenderness in XoZ plane |
0,11 |
Utilization factor 1,09 - Strength under action of bending moment My
Manual calculation (SNiP II-23-81*):
1. Necessary beam section modulus:
\[ W_{nes} =\frac{M_{\max } }{R_{y} \gamma_{c} }=\frac{\mbox{508},5\cdot 100}{23}=2210,8696 \quad cm^{3}. \]
2. Slenderness of the member in the moment plane and out of the moment plane:
\[ \lambda_{y} =\frac{\mu l}{i_{y} }=\frac{6,0\cdot 100}{21,777}=27,552; \] \[ \lambda_{z} =\frac{\mu l}{i_{z} }=\frac{6,0\cdot 100}{3,39}=176,99. \]
Comparison of solutions:
|
Factor |
Manual calculation |
SCAD |
Deviation, % |
|---|---|---|---|
|
Strength under action of bending moment Му |
2210,8696/2034,982 = 1,086 |
1,086 |
0,0 |
|
Strength under combined action of longitudinal force and bending moments, no plasticity |
– |
1,086 |
0,0 |
|
Stability of in-plane bending |
– |
1,086 |
0,0 |
|
Limit slenderness in XoY plane |
176,99/250 = 0,708 |
0,708 |
0,0 |
|
Limit slenderness in XoZ plane |
27,552/250 = 0,110 |
0,11 |
0,0 |
Comments:
1. The check of the beam strength taking into account the development of the limited plastic deformations was not performed in the manual calculation, because according to the codes this calculation is possible only when the beam web has stiffeners. In the initial data of the example the stringer was specified without any intermediate stiffeners.
2. The check for the stability of in-plane bending was performed in the computer-aided calculation according to the codes at φb = 1,0 for the effective length lef = 1 m.