Strength and Stiffness Analysis of a Rolled I-beam

1 – stringer; 2 – secondary beam

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 4,5 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:

4.3.sav;
report — Kristall4.3.doc

Initial data:

R_y = 23 kN/cm²,	Steel grade C235;
M = 62,78 kNm	Design bending moment;
γ_c = 1	Service factor;
l = 4,5 m	Beam span;
с_х= 1,1	Coefficient allowing for plastic deformations;
W_x = 288,33 cm³ i_y = 9,971 см, i_z = 2,385 cm.	Selected I-beam No.24 GOST 8239-89;

KRISTALL parameters:

Steel: C235
Group of structures according to the table 50* of SNiP II-23-81* 4
Importance factor 1
Service factor 1
Limit slenderness for members in compression: 180 - 60α
Limit slenderness for members in tension: 250

Section:

Profile: I-beam with sloped inner flange surfaces GOST 8239-89 24

Manual calculation (SNiP II-23-81*):

1. Necessary beam section modulus:

\[ W_{nes} =\frac{M_{\max } }{R_{y} \gamma_{c} }=\frac{\mbox{62},78\cdot 100}{23}=272,9565 \quad cm^{3}. \]

2. Slenderness of the member in the moment plane:

\[ \lambda_{y} =\frac{\mu l}{i_{y} }=\frac{4,5\cdot 100}{9,971}=45,131. \]

3. Slenderness of the member out of the moment plane:

\[ \lambda_{z} =\frac{\mu l}{i_{z} }=\frac{4,5\cdot 100}{2,385}=188,679. \]

Comparison of solutions:

Factor	Source	Manual calculation	KRISTALL
Strength under action of bending moment М_у	0,86	272,9565/288,33 = 0,947	0,947
Strength under combined action of longitudinal force and bending moments, no plasticity	–	272,9565/288,33 = 0,947	0,947
Stability of in-plane bending	–	272,9565/1/288,33 = 0,947	0,947
Limit slenderness in XoY plane	–	188,679/250 = 0,755	0,755
Limit slenderness in XoZ plane	–	45,131/250 = 0,1805	0,181

Comments:

1. In the source the check of the beam strength was performed taking into account 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.