Issue 54

A. Boulebd et alii, Frattura ed Integrità Strutturale, 54 (2020) 21-35; DOI: 10.3221/IGF-ESIS.54.02

The behaviour of a reinforced concrete beam subjected to bending can be schematized as shown in Fig. 12, [26]. Where the deformation force curve can be divided into three parts:

Figure 12: Typical force deformation curve of a reinforced concrete beam subjected to bending.

A- N ON - CRACKED SECTION 0< M< M CR : The Force and the deformation ( P cr , ∆ cr ) representing this phase were calculated from the neutral axis y cr according to the balance of the static moments of the section. The moments M cr and the inertia of the section I cr were calculated according to the transformed section method [26]:







b h y 

3 cr





by





2

2





2











cr

'

'

 

 

  

1 n A y d n 



A d y 

I

1 n A d y

1

(6)

cr

s

s

f

cr

cr

f

f

cr

3

3

with, A s , A’ s and A f the sections of the tensioned and compressed steels and the strengthening respectively, and d f is the ultimate height of the strengthening. Whose values in the equation change from one strengthening techniques to another according to the strengthening position.

I cr tr y cr 



M cr

(7)

with σ tr is the tensile stresses of the concert.

2 M cr



P cr

(8)

L a



 

24 P L cr

2



2 3 4 a L L 

2

 

(9)

cu

a

E Ic cr

E c is the concrete elasticity modulus; L a is the distance between the support and the applied force point and L the span between supports.

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