Calculation of a Rib of a TTshaped Floor Slab for Loadbearing Capacity under Lateral Forces
Objective: Check of the calculation of the resistance of reinforced concrete sections.
Task: Verify the correctness of the strength analysis of oblique sections and a concrete strip between the oblique sections.
References: Guide on designing of concrete and reinforced concrete structures made of heavyweight concrete (no prestressing) (to SP 521012003), 2005, p. 5657.
Initial data file:
when the lateral force is Q = 62 kN — Example 12.1.SAV
report – Arbat 12.1.doc.
when the lateral force is Q = 58,4 kN — Example 12.2.SAV
report – Arbat 12.2.doc.
Compliance with the codes: SP 521012003, SP 63.13330.2012.
Initial data:
b×h = 85×350 mm  Slab rib section sizes 
а = 35 mm  Distance from the center of gravity of the longitudinal reinforcement to the fiber of the section under the greatest tension 
d = 8 mm  Diameter of transverse reinforcement 
s_{w} = 100 mm  Spacing of transverse reinforcement 
q = 21,9 kN/m  Load on the rib 
q_{v} = 18 kN/m  Temporary equivalent load 
Q_{max} = 62 kN  Lateral force on the support 
Concrete class В15 
ARBAT initial data when the lateral force is Q = 62 kN:
Importance factor γ_{n} = 1
Importance factor (serviceability limit state) = 1
Member length 1 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 
A400 
1 
Concrete:
Concrete type: Heavyweight
Concrete class: B15
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 = 0 kN
M_{y} = 0 kN*m
Q_{z} = 62 kN
M_{z} = 0 kN*m
Q_{y} = 0 kN
T = 0 kN*m
Factor for sustained load 1
ARBAT initial data when the lateral force is Q = 58,4 kN:
Importance factor γ_{n} = 1
Importance factor (serviceability limit state) = 1
Member length 1 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 
A400 
1 
Concrete:
Concrete type: Heavyweight
Concrete class: B15
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 = 0 kN
M_{y} = 0 kN*m
Q_{z} = 58,4 kN
M_{z} = 0 kN*m
Q_{y} = 0 kN
T = 0 kN*m
Factor for sustained load 1
Comparison of solutions:
Check 
strength in a concrete strip between oblique sections 
strength for an oblique section 
Guide 
62/68,276 = 0,908 
58,4/63,97 = 0,913 
ARBAT 
0,908 
0,912 
Deviation, % 
– 
0,11 
Comments:
 The strength check of oblique sections is performed by comparing a sum of lateral forces resisted by concrete and stirrups in the oblique section (Q_{b} + Q_{sw}), with a lateral force Q in the oblique section which is determined as a projection on the normal to the longitudinal axis of the element of the resultant of all external forces acting on the element on one side of the considered oblique section (Q = Q_{max} – q_{1}c). In order to check the strength of the oblique section the value of the lateral force in the normal section is taken as Q = 58,4 kN according to the Guide.
 The member length has to be specified in ARBAT. Since it is not defined in the problem, it is taken as 1 m.
 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 = 35 – 6/2 = 32 mm.