Strength and Stiffness Analysis of a Rolled I-beam
1 – stringer
Objective: Check of the Resistance of Sections mode
Task: Check the design section of a rolled I-beam for the stringers with a span of 6 m in a normal stub girder system. The top chord of the stringers is continuously restrained by the floor plate.
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, DBN B.2.6-163:2010.
Initial data file:
4.2.sav;
report — Kristall4.2.doc
Initial data:
| а = 1,125 m | Spacing of stringers; |
| Ry = 23 kN/cm2, | Steel grade C235; |
| M = 125,55 kN | Design bending moment; |
| γc = 1 | Service factor; |
| l = 6 m | Beam span; |
| сx = 1,1 | Coefficient allowing for plastic deformations; |
| Wx = 597 cm3 iy = 13,524cm, iz = 2,791 cm. |
Selected I-beam No.33 GOST 8239-89; |
KRISTALL parameters:
Steel: C235
Group of structures according to the table 50* of SNiP II-23-81* 4
Importance factor γn = 1
Importance factor (serviceability limit state) = 1
Service factor 1
Structure:
Restraints against lateral displacements and rotations:
|
|
Left |
Right |
|---|---|---|
|
Displacement along Y |
Restrained |
Restrained |
|
Displacement along Z |
Restrained |
Restrained |
|
Rotation about Y |
|
|
|
Rotation about Z |
|
|
Continuous restraint of the compressed chord out of the bending plane
Section:
Profile: I-beam with sloped inner flange surfaces GOST 8239-89 33
Manual calculation (SNiP II-23-81*):
1. Necessary beam section modulus:
\[ W_{nes} =\frac{M_{\max } }{R_{y} \gamma_{c} }=\frac{\mbox{125},55\cdot 100}{23}=545,8696 \quad cm^{3}. \]
2. Slenderness of the member in the moment plane:
\[ \lambda_{y} =\frac{\mu l}{i_{y} }=\frac{6\cdot 100}{13,524}=44,3656. \]
3. Slenderness of the member out of the moment plane:
\[ \lambda_{z} =\frac{l_{ef,z} }{i_{z} }=\frac{6\cdot 100}{2,791}=214,9767. \]
Comparison of solutions:
|
Factor |
Source |
Manual calculation |
KRISTALL |
Deviation from the manual calculation, % |
|---|---|---|---|---|
|
Strength under action of bending moment Му |
0,83 |
545,8696/597 = 0,914 |
0,915 |
0,0 |
|
Strength under combined action of longitudinal force and bending moments, no plasticity |
– |
545,8696/597 = 0,914 |
0,915 |
0,0 |
|
Stability of in-plane bending |
– |
545,8696/1/597 = 0,914 |
0,915 |
0,0 |
|
Limit slenderness in XoY plane |
– |
214,9767/250 = 0,86 |
0,86 |
0,0 |
|
Limit slenderness in XoZ plane |
– |
44,3656/250 = 0,177 |
0,177 |
0,0 |
Comments:
1. In the source the check of the beam strength was performed taking into account the development of the limited plastic deformations.
2. 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.