Punching Analysis of a Reinforced Concrete Floor Slab
Figure 1. To the example of the calculation 40
1  1st design section, 2  2nd design section
Objective: Check the Punching mode.
Task: Verify the correctness of the punching strength analysis of a concrete element with transverse reinforcement under a concentrated force and bending moments and punching strength analysis beyond the boundary of transverse reinforcement.
References: Guide on designing of concrete and reinforced concrete structures made of heavyweight concrete (no prestressing) (to SP 521012003), 2005, p. 137140.
Initial data file:
Пример 40.SAV
report – Arbat 40.doc
Compliance with the codes: SP 521012003, SP 63.13330.2012.
Initial data from the source:
The same in the direction of the Y axis
h = 220 mm  Slab thickness 
a×b = 500×800 mm  Column section sizes 
N = 800 kN  Load transferred from the floor slab to the column 
M_{x,sup} = 70 kN∙m  Moment in the column section on the upper face of the slab in
the direction of the X axis 
M_{y,sup} = 30 kN∙m  
M_{x,inf} = 60 kN∙m  Moment in the column section on the lower face of the slab in
the direction of the X axis 
M_{y,inf} = 27 kN∙m  The same in the direction of the Y axis 
d = 6 mm  Diameter of transverse reinforcement 
Concrete class Class of reinforcement 
В30 А240 
ARBAT initial data:
Importance factor γ_{n} = 1
Load application area is inside the element
a = 500 mm 
Concrete:
Concrete type: Heavyweight
Concrete class: B30
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 
Loads:

P 
M_{x} 
M_{y} 

kN 
kN*m 
kN*m 

1 
800 
57 
130 
Uniform reinforcement:
Class of reinforcement: A240
Diameter 6 mm
Distance to the load application area 75 mm
Spacing of rebars in a row 60 mm
Number of rebars in a row 20
Spacing of rows 60 mm
Number of rows of rebars 25
Forces:
P = 800 kN
M_{x} = 57 kN*m
M_{y} = 130 kN*m
Comparison of solutions:
Check 
punching strength of a concrete element with transverse reinforcement under a concentrated force and bending moments with their vectors along X and Y axes 
punching strength of a concrete element with transverse reinforcement under a concentrated force beyond the boundary of transverse reinforcement 
Guide 
343,5/347,7 = 0,988 
146,5/218,5 = 0,67 
ARBAT 
0,973 
0,75 
Deviation, % 
1,518% 
10,667% 
Comments:
 The average effective height of the slab is taken as h_{0} = 190 mm in the calculation of the problem in the Guide. This value is used in ARBAT.
 In the Guide moments M_{x} and M_{y} are moments in the directions of X and Y axes respectively. In ARBAT moments M_{x} and M_{y} are moments about Х and Y axes respectively, therefore moments M_{x} and M_{y} in the example of the Guide correspond to the moments M_{y} and M_{x} in ARBAT. The values of the sum of moments M_{sup} and M_{inf} on the upper and lower faces of the slab are used in ARBAT. Thus, M_{x} = 30 + 27 = 57 kN∙m, M_{y} = 70 + 60 = 130 kN∙m.
 The number of rebars in a row 20 and the number of rows of rebars 25 are taken in accordance with the sizes given in the drawing in the Guide.
 The difference between the second factor and the solution from the Guide is due to the following reasons:
 in the problem the boundaries of the second design contour are considered at the distance of 0,5h_{0} from the boundary of the specified transverse reinforcement. Moreover, in the calculation of the geometric properties in the Guide the sizes of the contour were incorrectly taken as greater by 0,5h_{0} than the sizes of the considered contour. In ARBAT the boundaries of the second design contour were taken at the distance of 0,5h_{0} from the boundary of the transverse reinforcement considered in the calculation;
 in the Guide this strength check is performed taking into account the bending moments. In ARBAT the check is performed according to Sec.6.2.48 of SP 521012003 by the formula for the punching analysis under the action of a concentrated force.