Calculation of Critical Area And Critical Circumference
The shape of the critical area depends on the support geometry or support head, inclination angle of the surface subjected to shearing, as well as the position with respect to slab edges and corners. Shape and size of the critical area are stricly determined in the code, but for every code calculations consist in determining the area subjected to action of a punching force. In calculation of this, zone edges of slab and of openings are considered. The table displays the length of the u critical circumference. Note that the effect of openings on the length of the critical circumference is considered in the program.
A = u * d
where:
A - Critical area
u - Length of the critical circumference
d - Usable height of the slab section.
Calculation of Limit Punching Forces or Limit Stresses
This stage of calculations includes determining maximal values of puching force allowed by the code or maximal stresses that can be carried by a concrete section. The limit (maximal) force is a product of the critical area and stresses allowed by the code.
Qadm = τ * A
where:
Qadm - Admissible punching force
τ - Admissible stress
A - Critical area.
Calculation of Punching Forces or Stresses Resulting from External Impact
Each of the codes determines the manner how a force or stress caused by external impact should be received on the punching area. In the simplest case, calculations involve multiplication of a punching force by an appropriate factor, whereas in the most complicated ones, calculations of stresses considering acting moments are required. The table displays a value of the Q calculation designing force, obtained from the formula.
Q = τ * A
τ = V / A
τ = V * b / u (for EC2 code)
(for ACI code)
where:
Q - Calculation designing force
τ - Stress on the critical area
V - Maximum punching force
β - The parameter determines position of the critical circumference with respect to the slab edge (for EC2)
Mx, My, V - Bending moments and the force at the gravity center of the critical area
Jx, Jy - Inertia moments of the critical area with respect to axes passing through its gravity center
γ x , γ y, c x , c y - Parameters depending on the geometry of the critical area [ACI 318 11.12.2.2].
Check of the Load Capacity Condition
This consists in comparing stresses or forces caused by external impact with limit values. There are three states possible.
- If calculated stresses are smaller than admissible for a concrete section, reinforcement is not required
- If stresses are greater than admissible for a concrete section and simultaneously smaller than admissible, reinforcement is required
- If stresses are greater than admissible stresses, then the slab section is too small.
When reinforcement is not required or when a slab section is too small, results are presented in a form of the maximal punching force (for calculations based on stresses, the force is calculated from stresses multiplied by the punching area) and the ratio of admissible force to equivalent acting force. If reinforcement is required, then calculations of the reinforcement needed are carried out by the program.
Calculation of Required Reinforcement
If stresses are greater than those admissible for a concrete section and simultaneously smaller than those admissible, then calculated punching reinforcement is necessary. Calculations are carried out according to the code guidelines concerning bar reinforcement. Required reinforcement area and range of a zone within which reinforcement is required are shown in the table on the Punching tab. Also available are punching force (for calculations based on stresses, the force is calculated from stresses multiplied by the punching area) and ratio of the load capacity with reinforcement considered to the equivalent acting force. The range of reinforcement zone is additionally presented in drawings. The table shows the following parameters.
L1, L2 - Reinforcement range from the member center in both perpendicular directions.
u - Length of reinforcement zone circumference according to code recommendations.
A - Total reinforcement area that should be distributed evenly around the column within the reinforcement zone determined by the lengths L1 and L2.
n x ϕ - Number and diameter of bars calculated on the basis of the total area and settings in the options for punching.