Calculation of a Column of a Multistorey Frame for Loadbearing Capacity under a Lateral Force
Objective: Check of the calculation of the resistance of reinforced concrete sections.
Task: Verify the correctness of the strength analysis of oblique sections.
References: Guide on designing of concrete and reinforced concrete structures made of heavyweight concrete (no prestressing) (to SNiP 521012003), 2005, p. 104105.
Initial data file:
Example 34.SAV;
report:
when the analysis is performed according to SNiP 52012003 – Arbat 34.1.doc,
when the analysis is performed according to SP 63.13330.2012 – Arbat 34.2.doc.
Compliance with the codes: SNiP 521012003, SP 63.13330.2012.
Initial data from the source:
b×h = 400×600 mm  Column section sizes 
l = 3,3 m  Column length (distance between support sections) 
а = а' = 50 mm  Distance from the center of gravity of the longitudinal reinforcement to the fiber of the section under the greatest tension 
d = 12 mm  Diameter of transverse reinforcement 
s_{w} = 400 mm  Spacing of transverse reinforcement 
M_{sup} = 350 kN∙m  Bending moment in the upper support section 
M_{inf} = 250 kN∙m  Bending moment in the lower support section 
N = 572 kN  Longitudinal force 
Concrete class  В25 
Class of transverse reinforcement  А240 
ARBAT initial data:
Importance factor γ_{n} = 1
Importance factor (serviceability limit state) = 1
Member length 3,3 m
Effective length factor in the XoY plane 1
Effective length factor in the XoZ plane 1
Random eccentricity along Z according to SNiP 52012003 (Russia)
Random eccentricity along Y according to SNiP 52012003 (Russia)
Structure is statically indeterminate
Limit slenderness  200
Section


Reinforcement 
Class 
Service factor 
Longitudinal 
A400 
1 
Transverse 
A240 
1 
Concrete
Concrete type: Heavyweight
Concrete class: B25
Service factor for concrete 


γ_{b1} 
allowance for the sustained loads 
1 
γ_{b2} 
allowance for the failure behavior 
1 
γ_{b3} 
allowance for the vertical position during concreting 
1 
γ_{b4} 
allowance for the freezing/thawing and negative temperatures 
1 
Humidity of environmental air  4075%
Crack resistance:
No cracks
Forces

N 
My 
Qz 
Mz 
Qy 
T 
Safety factor for load 
Factor for sustained load 
Shortterm 
Seismic 

kN 
kN*m 
kN 
kN*m 
kN 
kN*m 

1 
572 
600 
181,8 
0 
0 
0 
1 
1 


Comparison of solutions (according to SNiP 521012003):
File 
Example 34.SAV 
Report file 
Arbat 34.1.doc 
Check 
strength for an oblique section 
Guide 
181,8/184,8 = 0,984 
ARBAT 
0,982 
Deviation, % 
0,17 % 
Comparison of solutions (according to SP 63.13330.2012):
File 
Example 34.SAV 
Report file 
Arbat 34.2.doc 
Check 
strength for an oblique section 
Guide 
181,8/184,8 = 0,984 
ARBAT 
0,898 
Deviation, % 
8,7% 
Comments:
 Bending moment My is determined as a sum of moments in the upper and lower support sections M_{y} = M_{sup} + M_{inf} = 350 + 250 = 600 kN.
 The lateral force in the column is determined as: Q_{z} = M_{y}/l = 600/3,3 = 181,8 kN.
 The data on the longitudinal reinforcement has to be specified in ARBAT. Since it is not defined in the problem, the following reinforcement is used: class А400, rebars 2Ø6. Respectively, the value of the concrete cover is а_{1} = а_{2} = а – d/2 = 50 – 6/2 = 47 mm.
 The difference between the utilization factors of 14,3% in the results of the solution in the Guide and in ARBAT according to SP 63.13330.2012 is due to the fact that compressive stresses are taken into account in different ways according to the given codes (Sec. 8.1.34) and according to SNiP 521012003.