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.