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:

Ry = 23 kN/cm2,
Rs = 0,58*23=13,3 kN/cm2
Steel grade C255 with thickness t>20 mm;
M = 6245 kNm Design bending moment;
γc = 1 Service factor;
l = 18 m Beam span;
Iy = 2308077,083 cm4 Geometric properties for a welded
Wy = 27153,848см3
iy = 70,605см,
iz = 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

My
Max. 0 T*m
Snap 0 m

Max. 636,6 T*m
Snap 18 m

Mz
Max. 0 T*m
Snap 0 m

Max. 0 T*m
Snap 0 m

Mk
Max. 0 T*m
Snap 0 m

Max. 0 T*m|
Snap 0 m

Qz
Max. 35,37 T
Snap 0 m

 

 

 

Qy
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 My

1

Sec.5.12,5.18

Strength under action of lateral force Qz

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 My

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

Deviation, %

Strength under action of bending moment Му

27152,174/27153,848 = 1,0

1,0

0,0

Strength under combined action of longitudinal force and bending moments, no plasticity

1,0

0,0

Stability of in-plane bending

1,0

0,0

Limit slenderness in XoZ plane

25,4939/250 = 0,102

0,102

0,0

Limit slenderness in XoY plane

155,481/250 = 0,622

0,622

0,0

 

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 φb = 1,0 for the effective length lef = 1 m.