Strength and Stiffness Analysis of a Welded I-beam

a – cross-section variation along the beam length; b – beam section and stress diagrams

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 the stringers arranged with a spacing of 1,125 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 195.

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

Initial data file:

4.1.sav;
report — Kristall4.1.doc

Initial data:

M₁ = 3469,28 kNm	Design bending moment;
Q₁ = 925 kN	Design shear force;
R_y = 23 kN/cm², R_s = 0,58*23=13,3 kN/cm²	Steel grade C255 with thickness t>20 mm;
l = 18 m	Beam span;
W_y = 15187,794 cm³	Geometric properties for a welded
I_y = 1290962,5 cm⁴ S_y = 9108,75 cm³ i_y = 63,715 cm, i_z = 4,265 cm	I-section with flanges 240×25 mm and a web 1650×12 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: 220
Limit slenderness for members in tension: 300

Section:

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

1. Necessary beam section modulus:

\[ W_{nes} =\frac{M_{\max } }{R_{y} \gamma_{c} }=\frac{\mbox{3469},\mbox{28}\cdot 100}{23}=15083,826 \quad cm^{3}. \]

2. Maximum tangential stresses in support sections of the beam:

\[ \tau_{\max } =\frac{Q_{\max } S_{y} }{I_{y} t_{w} }=\frac{925\cdot 9108,75}{1290962,5\cdot 1,2}=5,4388 \quad kN/cm^{2}. \]

3. Reduced stresses in the considered beam section:

\[ \sigma_{y} =\frac{M_{y} }{I_{y} }\frac{h_{w} }{2}=\frac{3469,28\cdot 100\cdot 165}{1290962,5\cdot 2}=22,1707 \quad kN/cm^{2} \] \[ \tau_{yz} =\frac{Q_{z} S_{yf} }{I_{y} t_{w} }=\frac{925\cdot \left( {24\cdot 2,5\cdot \left( {0,5\cdot 165+0,5\cdot 2,5} \right)} \right)}{1290962,5\cdot 1,2}=3,00 \quad kN/cm^{2} \] \[\sigma_{red} =\sqrt {\sigma_{y}^{2} +3\tau_{yz}^{2} } =\sqrt {22,1707^{2}+3\cdot 3,00^{2}} =22,7715 \quad kN/cm^{2} \]

4. Slenderness of the member in the moment plane:

\[ \lambda_{y} =\frac{\mu l}{i_{y} }=\frac{18\cdot 100}{63,715}=28,2508. \]

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

\[ \lambda_{y} =\frac{\mu l}{i_{y} }=\frac{1,125\cdot 100}{4,265}=26,3775. \]

Comparison of solutions:

Factor	Source	Manual calculation	KRISTALL
Strength under action of bending moment М_у	0,99	15083,826/15187,794 = = 0,993	0,993
Strength under action of lateral force Q_z	–	5,4388/13,3 = 0,4089	0,408
Strength for reduced stresses	–	22,7715/1,15/23 = 0,861	0,861
Strength under combined action of longitudinal force and bending moments, no plasticity	–	15083,826/15187,794 = = 0,993	0,993
Stability of in-plane bending	–	15083,826/1/15187,794 = = 0,993	0,993
Limit slenderness in XoY plane	–	26,3775/300 = 0,088	0,088
Limit slenderness in XoZ plane	–	28,2508/300 = 0,094	0,094