## Info

Figure 6.36. Combination of truss and strut and tie

Measurements on shear reinforcement showed that the stirrups just adjacent to the load- and support area do not reach the yield stress, (Asin, 2000). Therefore the shear reinforcement is considered to be effective only within the central 0,75 area between load and support.

6.3 Torsion

See example 6.6 and 6.7

6.4 Punching

C6.4. Basic equation for symmetrical punching at interior columns

6.4.1. Punching shear capacity of non-prestressed slabs without punching reinforcement

In ENV 1992-1-1 a nominal shear stress was defined as the load divided by the product the slab's effective depth and the length of the control perimeter, which was defined to located at (1.5d) from the edge of the column. The design punching shear capacity was

VRd1 - VRd1U

Where u is the length of the critical perimeter, taken at a distance 1.5d from the loaded area, the design shear resistance per unit length vRdi followed from vRdi = iRd k (1.2 + 40pl)d (6.31b)

where TRd basic shear strength = 0.25 fctk /yc k size factor = 1.6- d [m] > 1.0 d effective depth of slab = (dx + dy)/2 pl flexural reinforcement ratio = (px + py)/2

It was already shown in 1980 , that in the derivation of this equation an error was committed, which leads to unconservative results for higher concrete strengths. Therefore it was decided adopt the formulation for the punching shear capacity given in Model Code 1990. when the design punching shear capacity is given by

where u = length of the critical perimeter, taken at a 2d distance from the loaded area d = mean effective slab depth = (dx + dy)/2 and where the design punching shear stress for non-prestressed slabs value is vRdc = 0.12 k (100 plfck )1/3

with k = size factor = 1+ V(200/d) < 2.0 d in mm pl = V(plx . ply) < 0.02

fck = characteristic cylinder strength of concrete

In the new definition, according to MC'90, the control perimeter is moved from a distance 1.5d from the column, to a distance of 2d, see Fig. 6.37. There are two reasons to adopt the distance 2d. First it makes the limiting shear stress much more uniform for different column sizes. Second now for punching the same formulation can be used as for normal shear in members without shear reinforcement, where also Eq. 6.32b is applied.

2.0d 2.0d Figure6.37. Basic control perimeters around loaded areas

Often questions are raised with regard to the coefficient 0.12 in Eq. 6.32b. Therefore at first an evaluation is carried out in order to verify this value. Altogether 112 test results have been considered, taken from [2-12]. 78 of those results refer to tests on specimens with cylinder strength ranging from 15 to 60 Mpa, whereas 32 refer to tests on high strength concrete specimens with concrete cylinder strengths ranging from 60 to 120 MPa. This enables a good evaluation of the validity of the punching shear formula (Eq. 6.32a and 6.32b) for higher concrete strengths. The tests cover the interval of individual parameters given in Table 6.9.

Table 6.9. Range of parameters in tests used for evaluation

Compressive strength on cylinders

14- 120 Mpa

Effective slab depth

100- 275 mm

Reinforcement ratio for bending

0.4-2.5%

Column diameter/effective slab thickness