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 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, DBN B.2.6-163:2010.

Initial data file:

4.4.sav;
report — Kristall4.4.doc

Initial data:

R_y = 23 kN/cm²,	Steel grade C235;
M = 508,5 kNm	Design bending moment;
γ_c = 1	Service factor;
l = 6 m	Beam span;
с_х = 1,1	Coefficient allowing for plastic deformations;
W_x = 2034,982 cm³ i_y = 21,777 cm, i_z = 3,39 cm.	Selected I-beam No.55 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 55

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	Source	Manual calculation	KRISTALL
Strength under action of bending moment М_у	0,99	2210,8696/2034,982 = 1,086	1,086
Strength under combined action of longitudinal force and bending moments, no plasticity	–	2210,8696/2034,982 = 1,086	1,086
Stability of in-plane bending	–	2210,8696/1/2034,982 = 1,086	1,086
Limit slenderness in XoY plane	–	176,99/250 = 0,708	0,708
Limit slenderness in XoZ plane	–	27,552/250 = 0,110	0,11

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.