lH1> lH2
VRdl
VRd2 VRd3
Vsd a
Maximum design shear resistance per unit length of the critical perimeter, for a slab with shear reinforcement
Design shear resistance per unit length of the critical perimeter, for a slab with shear reinforcement
Shear force per unit length along critical section Angle between reinforcement and the plane of the slab
Coefficient, taking account of the effects of eccentricity of load (Equation 4.50 and Figure 4.21)
A moment coefficient (Table 4.9) Equivalent longitudinal reinforcement ratio Longitudinal reinforcement ratio in x-direction Longitudinal reinforcement ratio in y-direction
Basic shear strength of members without shear reinforcement (Table 4.8)
n Pl
Plx Ply rRd
P(1) The principles and rules given in this section complement those given in 4.3.2. They are concerned with punching shear in slabs containing flexural reinforcement determined according to 4.3.1; they also cover punching shear in foundations and waffle slabs with a solid section around the "loaded area".
P(2) Punching shear may result from a concentrated load or reaction acting on a relatively small area, called the "loaded area", of a slab or of a foundation.
(3) An appropriate design model for checking punching shear failure at the ultimate limit state is shown in Figure 4.16.
P(4) The shear resistance shall be checked along a defined critical perimeter. Outside the critical perimeter the slab has to satisfy the requirements of section 4.3.2.
(5) In slabs subjected to punching shear an enhancement of shear resistance in accordance with Equation (4.17) should not be carried out. In foundation slabs, the applied shear may be reduced to allow for the soil reaction within the critical perimeter.
P(6) The flexural strength of the slab shall also be checked independently in accordance with 4.3.1.
P(7) If the thickness of a slab or foundation is not sufficient to ensure adequate punching shear resistance, shear reinforcement, column heads or other types of shear connector shall be provided.
(8) The rules in this section also apply to waffle slabs with a solid section around the loaded area provided that the solid area extends at least 1.5d beyond the critical perimeter.
(9) The amount of longitudinal tensile reinforcement in two perpendicular directions, x and y should be greater than 0.5 %, calculated allowing for any differences in effective depth in the two directions.
(10) The force component parallel to Vsd due to inclined prestressed tendons placed inside the critical area may be taken into account according to 4.3.2.4.6.
(1) The provisions of this section are applicable to the following types of loaded area: a) Shape (d denotes the average effective depth of the slab):
— circular, with diameter not exceeding | 3.5 d |
— rectangular, with perimeter not exceeding | 11 d | and the ratio of length to breadth not exceeding |2|
— any shape, the limiting dimensions being fixed by analogy with the shapes mentioned above;
d) The loaded area is not so close to other concentrated forces that their critical perimeters intersect — nor in a zone subjected to significant shear forces of a different origin.
(2) If the conditions in 1) a) above are not satisfied for wall or rectangular column supports, since the shear force in wall-shaped supports are concentrated in the corners, the critical perimeters according to Figure 4.17 only should be taken into account, in the absence of a more detailed analysis
4.3.4.2.2 Critical perimeter
(1) The critical perimeter for circular or rectangular loaded areas located away from unsupported edges is defined as a perimeter surrounding the loaded area and at a defined distance from it. It is assumed to be 1.5d. See Figure 4.18.
(2) For loaded areas situated near openings, if the shortest distance between the perimeter of the loaded area and the edge of the opening does not exceed | 6_d |, that part of the critical perimeter contained between two tangents drawn to the outline of the opening from the centre of area of the loaded area is considered to be ineffective. See Figure 4.19.
(3) For a loaded area situated near an unsupported edge or a corner, the critical perimeter should be taken as shown in Figure 4.20, if this gives a perimeter (excluding the unsupported edges) less than that obtained from (1) and (2) above.
(4) For loaded areas situated near or on an unsupported edge or near or on a corner, i.e. at a distance less than d , special edge reinforcement along the edge is always required, (see 5.4.3.2.4).
4.3.4.2.3 Critical area
(1) The critical area is the area within the critical perimeter.
(1) The critical section is the section which follows the critical perimeter and extends over the effective depth, d. For slabs of constant depth, the critical section is perpendicular to the middle plane of the slab. For slabs of variable depth (e.g. the foundation slab in Figure 4.16), it is assumed to be perpendicular to the tension face.
(1) The method for punching shear design set out in the following sections is based on three values of the design shear resistance at the critical perimeter:
VRdi — the design shear resistance per unit length of the critical perimeter, for a slab without shear reinforcement.
VRd2 — the maximum design shear resistance per unit length of the critical perimeter, for a slab with shear reinforcement.
VRd3 — the design shear resistance per unit length of the critical perimeter, for a slab with shear reinforcement.
(2) No shear reinforcement is required if vSd k vRd1
(3) If vSd exceeds vRd1, shear reinforcement or other forms of shear connector, where their application can be justified, should be provided such that vSd r vRd3
(4) In the case of a concentrated load or support reaction, the applied shear per unit length is
d u where
Vsd is the total design shear force developed. In a slab this is calculated along the perimeter u. For a foundation this is calculated along the perimeter of the base of the truncated punching shear cone, assumed to form at 33.7°, provided this falls within the foundation.
u is the perimeter of the critical section.
" is a coefficient which takes account of the effects of eccentricity of loading. In cases where no eccentricity of loading is possible, " may be taken as 1.0. In other cases, the values given in Figure 4.21 may be adopted. Based on a more rigorous analysis, other values for " may be used, when associated with appropriate methods for ensuring the anchorage of the reinforcement at the edge of the slab.
4.3.4.4 Slabs with variable depth
(1) For slabs with circular column heads for which 1h < 1.5h^ (see Figure 4.22) a check in accordance with 4.3.4.3 is only required on the critical section outside the column head. The distance of this section from the centroid of the column, dcrit, may be taken as:
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