Various design concepts mentioned above may be illustrated considering a simple example of a reinforced concrete slab in an office building. The example shows how different design methods (permissible stresses, global safety factor, partial factor method) treat uncertainties of basic variables by choosing different input (design) values. The example also indicates significance of the reliability theory in structural design and advantages of the reliability based partial factor method compared to the other design formats.
Some basic terms (e.g. characteristic strength) and calculation procedures used in this Section will be properly defined in various Chapters of this Handbook 2. Nevertheless the following text can be understood at least intuitively.
A simply supported slab having the span of 6 m is exposed to a permanent load (self-weight of the slab and other fixed parts of the building), which is estimated by the characteristic value (equal to the mean value) gk=7 kN/m2. In accordance with the EN 1991-11 [8] the characteristic value of the imposed load in an office area qk=3 kN/m may be assumed. It is, however, well known that the mean value of this load is considerably lower, about 0,8 kN/m2.
Further, the concrete C20/25 having the characteristic strength /ck=20 MPa (the mean 30 MPa) and reinforcement bars S 500 having the characteristic strength fk=500 MPa (the mean 560 MPa) are to be used. Using previous experience, the total height of the slab 0,25 m (effective depth about 0,25 - 0,03 = 0,22 m) was specified in advance. Given the above data verification of the preliminary specifications and estimation of the necessary reinforcement area of the slab should be done.
Consider first a simple drawing of the slab cross-section including simplified stress distribution diagrams in the compressive concrete zone (rectangular and triangular) as indicated in Figure 8.
When the rectangular stress diagram is assumed the following equilibrium conditions can be written (see Figure 8):
The basic variables used in equations (30) and (31) are evident from Figure 8: d denotes the effective depth, x the depth of the neutral axis, b the width of the slab (considered as 1 m), As the area of the reinforcement, fc the concrete strength and fy the reinforcement strength (yield point). The bending moment in equations (31) is given as
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