Figure 6.46. Reduced perimeters for assumed uniform shear for edge and corner columns
The most important difference between punching of a slab around a column and punching of column base supporting a column is the presence of a significant counter pressure from the soil. A second difference is that the distance from columns to the edges of their bases are commonly much smaller than those to sections of radial contra flexure in suspended slabs .
Due to the influence of the vertical soil pressure, the inclination of the punching cone in column bases may well be steeper than in suspended slabs, which gives rise to uncertainty with regard to the critical perimeter to be checked. This was not regarded in the EC-2 version of 1988. The CE Model Code 1990 gives an alternative, in which the position of the control perimeter is treated as a variable and the unit punching resistance, is taken to vary with the distance from the column to the control perimeter, i.e. with the inclination of the failure surface. For concentric loading the design punching force is
VEd column load
AVEd the upward force within the control perimeter considered i,e. upward pressure from soil minus self weight of base vEd = VEd,red/ud (6.47)
where u is the control perimeter taking a value a < 2d instead of 2d into account (see also fig. 6.37). The nominal ultimate shear stress at the perimeter is vRdc = 0,12 k(100pfck )1/3 2d/a < 0.5vfcd (6.48)
where a distance from the periphery of the control perimeter considered v 0.60 (1 - fck /250) (6.49)
Fig. 6.47 shows a result of a parameter study, carried out with the previous equations. For many combinations of base width to column width l/c and column width to effective slab depth c/d the critical ratio acrit /d has been determined, for which the lowest column load is obtained. The results are shown in Fig. 6.47. It turns out that the ultimate column load is a function of the based to column width l/c but is independent of the ratio c/d. In the lower diagram of fig. 6.47 the design column load VEd can immediately be determined as a function of the ratio l/c. The corresponding value of the critical control perimeter acrit /d is read in the upper diagram. It can be seen that in the utmost number of cases the value of acrit is smaller than 2d, which means indeed that the inclination of the punching cone is much steeper than in suspended slabs.
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