Issue 57

K. Benyahi et alii, Frattura ed Integrità Strutturale, 57 (2021) 195-222; DOI: 10.3221/IGF-ESIS.57.16

k V , by writing that the moment of the forces

The equilibrium of the section makes it possible to calculate the shear value

is zero at point P:

 ( G G ) h k-1 k k

(25)



V

k

2

d

The average value of the shear stress on the layer k is then given by:

 ( G G ) k-1 k

k V b h

(26)







k

2 d b

k k

k

The mean shear strain of the section  moy is calculated from the theorem of virtual work expressing the equality of the external forces work  e W and that of the internal forces  i W :     m i 1 w e W From where:

 m



 i



 i

 b h V i

i

   moy

(27)

1

For the resolution of the problem, we explain some quantities from the previous general equations. We take from Eqn. 10:        2 1 2 2 sin x tg (28) We also rewrite the Eqn. 4, Eqn. 5 and Eqn. 6 between the concrete stresses in the following form (taking into account Eqn. 7):        2 1 bx b b by (29)

      2 ' b



1

1/2

bx





tg

(

)

(30)

b

by

2



(31)

  2 by

 

b



tg

The study of the equilibrium of a reinforced concrete layer, where x  and  are known uses a system of equation. To solve it, we call on an iterative method. For a given distribution of the longitudinal strains, we assume known the main strain 2  and we look for the value of the angle  which makes it possible to satisfy the conditions of compatibility and equilibrium of the layer. The tangential stresses  ( ) y are calculated by the equilibrium of two neighboring sections (Eqn. 26). The complete resolution at the section level is described by the flowchart in Fig. 7. R ELIABILITY CALCULATION PROCEDURE he concept of safety based on the concept of allowable stress was recognized insufficient because of the uncertainty of the loading parameters and the uncertainty of the structures mechanical properties. However, in recent years, a so-called semi-probabilistic theory ensures safety by introducing various partial coefficients taking T

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