Strength and Stiffness Analysis of a Rolled I-beam

1 – stringer; 2 – secondary beam

Objective: Check of the Resistance of Sections mode in the “Steel” postprocessor of SCAD.

Task: Check the design section of a rolled I-beam for the stringers with a span of 4,5 m in a normal stub girder system. The top chord of the stringers is continuously restrained by the floor plate.

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 16.13330.2011, DBN B.2.6-163:2010.

Initial data file:

4.3 SectionResistance_Example_4.3.spr;
report — 4.3 SectionResistance _Example_4.3.doc

Initial data:

R_y = 23 kN/cm²,	Steel grade C235;
M = 62,78 кНм	Design bending moment;
γ_c = 1	Service factor;
l = 4,5 м	Beam span;
с_х= 1,1	Coefficient allowing for plastic deformations;
W_x = 288,33 см³ i_y = 9,971 см, i_z = 2,385 см.	Selected I-beam No.24 GOST 8239-89.

SCAD Parameters. STEEL Postprocessor:

[Element No. 1] Forces

N
Max. 0 T
Snap 0 m

Max. 0 T
Snap 0 m

M_y
Max. 0 T*m
Snap 0 m

Max. 6,4 T*m
Snap 4,5 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. 1,42 T
Snap 0 m

Q_y
Max. 0 T
Snap 0 m

Max. 0 T
Snap 0 m

Length of the bar 4,5 m
Length of the flexible part 4,5 m
Loading L1

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

Steel: C235

Member length 4,5 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

Profile: I-beam with sloped inner flange surfaces GOST 8239-89 24

Results	Check	Utilization factor
Sec.5.12	Strength under action of bending moment M_y	0,95
Sec.5.12,5.18	Strength under action of lateral force Q_z	0,09
Sec.5.24,5.25	Strength under combined action of longitudinal force and bending moments, no plasticity	0,95
Sec.5.15	Stability of in-plane bending	0,95
Sec.6.15,6.16	Limit slenderness in XoY plane	0,75
Sec.6.15,6.16	Limit slenderness in XoZ plane	0,18

Utilization factor 0,95 - Strength under action of bending moment M_y

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

1. Necessary beam section modulus:

\[ W_{nes} =\frac{M_{\max } }{R_{y} \gamma_{c} }=\frac{\mbox{62},78\cdot 100}{23}=272,9565 \quad cm^{3}. \]

2. Slenderness of the member in the moment plane:

\[ \lambda_{y} =\frac{\mu l}{i_{y} }=\frac{4,5\cdot 100}{9,971}=45,131. \]

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

\[ \lambda_{z} =\frac{\mu l}{i_{z} }=\frac{4,5\cdot 100}{2,385}=188,679. \]

Comparison of solutions:

Factor	Manual calculation	SCAD
Strength under action of bending moment М_у	272,9565/288,33 = 0,9467	0,947
Strength under combined action of longitudinal force and bending moments, no plasticity	–	0,947
Stability of in-plane bending	–	0,947
Limit slenderness in XoY plane	188,679/250 = 0,755	0,755
Limit slenderness in XoZ plane	45,131/250 = 0,1805	0,181

Comments:

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.
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.