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-prEN 1092-1

Compensate Traction Block

---Direct Calculation

Adimensional Axial Force

Figure 7.4. Comparison of different approximate expressions for the calculation of the minimum reinforcement

It can be seen that the 2 last methods give almost the same results. It can also be seen that the formula of prEN is mostly on the safe side.

7.3.3 Control of cracking C7.3.3. Formula for maximum bar diameter without direct calculation In this paragraph the formula for the maximum bar diameter is deduced for three crack width formulations: MC-90 [3], EC2 [4] and prEN. This deduction, as will be seen, requires the introduction of simplifications and the assumption that the steel ratio, for which a certain stress as is achieved corresponds to the minimum steel ratio given by prEN equation 7.1. This assumption is on the safe side. A more exact formulation could be obtained if pe/f were to remain a variable.

C7.3.3.1 Deduction of formula

Using the MC-90 formulation, the crack width is given by:

3,6Peff E:

asr is the stress calculated for the fully cracked cross section for the cracking moment. asr may be calculated by:

g _ fct,effActkck _ fct,effkck hcr (711)

In the above expression, k' is a factor which is equal to 1 for bending and equal to 2 for tension. Introducing the expression of asr into equation (7.10), and rearranging:

1-k fct,effkc h

Ps,effCTs 2,5k'(h-dI

In order to obtain numerical values from this expression, it is necessary to assume values for those coefficients which are not considered as variables in table 7.1. The following values have been assumed to derive table 7.1: k = 1,0 ^ h < 0,3 (assumption on safe side) kc = 0,4; k' = 1 (pure bending) kt = 0,38

Wk = 0,3 mm the above values equation (7.12) can be written as: , 720000 • wkpeff 1

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