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 in the “Steel” postprocessor of SCAD.

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 16.13330.2011, DBN B.2.6-163:2010.

Initial data file:

4.5 SectionResistance_Example_4.5.spr;
report — 4.5 SectionResistance _Example_4.5.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 = 27153,848см³ i_y = 70,605см, i_z = 11,577 см.	I-section with flanges 1650×12 mm and a web 530×25 mm.

SCAD Results. STEEL Postprocessor:

[Element No. 1] Forces

N
Max. 0 T
Snap 0 m

Max. 0 Т

Snap 0 m

M_y
Max. 0 T*m
Snap 0 m

Max. 636,6 T*m
Snap 18 m

M_z
Max. 0 T*m
Snap 0 m

Max. 0 T*m
Snap 0 m

M_k
Max. 0 T*m
Snap 0 m

Max. 0 T*m|
Snap 0 m

Q_z
Max. 35,37 T
Snap 0 m

Q_y
Max. 0 T
Snap 0 m

Max. 0 T
Snap 0 m

Length of the bar 18 m
Length of the flexible part 18 m
Loading L1

Analysis complies with SNiP II-23-81*
Structural member section

Steel: C255
Member length 18 m
Limit slenderness for members in compression: 250
Limit slenderness for members in tension: 250
Service factor 1
Importance factor 1
Effective length factor XoZ -- 1
Effective length factor XoY -- 1
Length between out-of-plane restraints 1,125 m

Section

Results	Check	Utilization factor
Sec.5.12	Strength under action of bending moment M_y	1
Sec.5.12,5.18	Strength under action of lateral force Q_z	0,14
Sec.5.24,5.25	Strength under combined action of longitudinal force and bending moments, no plasticity	1
Sec.5.15	Stability of in-plane bending	1
Sec.6.15,6.16	Limit slenderness in XoY plane	0,62
Sec.6.15,6.16	Limit slenderness in XoZ plane	0,1

Utilization factor 1 - Strength under action of bending moment M_y

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

1. Necessary beam section modulus:

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

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

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

Comparison of solutions:

Factor	Manual calculation	SCAD
Strength under action of bending moment М_у	27152,174/27153,848 = 1,0	1,0
Strength under combined action of longitudinal force and bending moments, no plasticity	–	1,0
Stability of in-plane bending	–	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:

1. 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.

2. The check for the stability of in-plane bending was performed in the computer-aided calculation according to the codes at φ_b = 1,0 for the effective length l_ef = 1 m.