Issue 38

S. Bennati et alii, Frattura ed Integrità Strutturale, 38 (2016) 377-391; DOI: 10.3221/IGF-ESIS.38.47

2





b G N l ,

b P N l ,

b G M l ,

b P M l ,

( )

( )

( )

( )

g g L Ph 1 2 )  

(

P

1 2

1  

b





  

(15)

A

W

A

W

b

b

b

b

It can be verified that all the computed values are in magnitude less than the design yield stress, f yd .

Stress at upper surface  1  (MPa)

Stress at lower surface  1  (MPa)

Pre-stressing force P (kN)

Width

Thickness t f (mm)

Area

Cross section No. and type of laminates

b f

A f

(mm)

(mm 2 )

IPE 120 IPE 140 IPE 160 IPE 180 IPE 200 IPE 220 IPE 240 IPE 270 IPE 300 IPE 330 IPE 360 IPE 400 IPE 450 IPE 500 IPE 550 IPE 600

1 S613 1 S613 1 S613 1 S613 1 S626 1 S626 1 S626 1 S626 1 S626 1 S626 2 S626 2 S626 2 S626 2 S626 2 S626 2 S626

60 60 60 60 60 60 60 60 60 60

1.3 1.3 1.3 1.3 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6

78 78 78 78

109.9 109.9 109.9 109.9 219.8 219.8 219.8 219.8 219.8 219.8 439.6 439.6 439.6 439.6 439.6 439.6

-25.7 -16.7 -32.4 -45.1 -20.3 -32.2 -44.5 -48.6 -51.3 -53.1 -42.9 -42.9 -47.7 -53.1 -49.7 -55.3

-140.7 -117.1

-77.0 -46.7

156 156 156 156 156 156 312 312 312 312 312 312

-134.0

-99.5 -67.8 -47.1 -30.4 -17.1 -78.0 -61.2 -41.2 -23.0 -15.7

120 120 120 120 120 120

-1.1

Table 3 : Pre-stressing of FRP laminates.

Elastic limit state of the system Now, we turn to evaluate the imposed load for which the strengthened beam abandons the range of linearly elastic behaviour. This load will be the minimum between the loads corresponding to the elastic limit states in the beam, adhesive, and laminate. We start from the elastic limit state of the adhesive, which occurs when the maximum shear stress in the interface reaches the design strength,   . The abscissa, s , where the shear stress is maximum is first determined by differentiating Eq. (11) and setting the derivative to zero:



d

1

  

q q l   

s      s ) 0

l ln( ) 

exp(

(16)



ds

Hence, the maximum shear stress value turns out to be





1







s ( )      q l  

l 1 ln( ) 

(17)

max

By putting max 0  

 , the corresponding imposed load is obtained,

0 1 1 ln( ) 

1 1



(18)

q

a









l 

 

l

Q



where  Q

= 1.5 is the partial factor for variable actions [19, 21].

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