Strength and Stiffness Analysis of a Welded I-beam

a – floor plan; b – design model of the main beam; c – beam section;
1 – load area

Objective: Check of the Resistance of Sections mode

Task: Check the design section of a welded I-beam for the main beams with a span of 18 m in a normal stub girder system. The top chord of the main beams is restrained by secondary beams arranged with a spacing of 1,0 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. 192.

Compliance with the codes: SNiP II-23-81*, SP 16.13330, DBN B.2.6-163:2010.

Initial data file:

4.5.sav; report — Kristall4.5.doc

Initial data:

R_y = 23 kN/cm², R_s = 0,58*23=13,3 kN/cm²	Steel grade C255 with thickness t>20 mm;
M = 6245 kNm	Design bending moment;
γ_c = 1	Service factor;
l = 18 m	Beam span;
I_y = 2308077,083 cm⁴	Geometric properties for a welded
W_y = 27153,848 cm³ i_y = 70,605см, i_z = 11,577 cm.	I-section with flanges 1650×12 mm and a web 530×25 mm;

KRISTALL parameters:

Steel: C255
Group of structures according to the table 50* of SNiP II-23-81* 3
Importance factor 1
Service factor 1
Limit slenderness for members in compression: 180 - 60α
Limit slenderness for members in tension: 250

Section:

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

1. Necessary beam section modulus:

\[ W_{nes} =\frac{M_{\max } }{R_{y} \gamma_{c} }=\frac{\mbox{6245}\cdot 100}{23}=27152,174 \quad см^{3}. \]

2. Slenderness of the member in the moment plane and out of the moment plane:

\[ \lambda_{y} =\frac{\mu l}{i_{y} }=\frac{18,0\cdot 100}{70,605}=25,4939; \] \[ \lambda_{z} =\frac{\mu l}{i_{z} }=\frac{18,0\cdot 100}{11,577}=155,481. \]

Comparison of solutions:

Factor	Source	Manual calculation	KRISTALL
Strength under action of bending moment М_у	1,0	27152,174/27153,848 = 1,0	1,0
Strength under combined action of longitudinal force and bending moments, no plasticity	–	27152,174/27153,848 = 1,0	1,0
Stability of in-plane bending	–	27152,174/1/27153,848 = 1,0	1,0
Limit slenderness in XoZ plane	–	25,4939/250 = 0,102	0,102
Limit slenderness in XoY plane	–	155,481/250 = 0,622	0,622

Comments:

The check of the beam strength taking into account the development of the limited plastic deformations was not performed, 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.