Issue 53

M. C. Oliveira et alii, Frattura ed Integrità Strutturale, 53 (2020) 13-25; DOI: 10.3221/IGF-ESIS.53.02

presented with the purpose of quantify the behaviour of RC beams under impact loads. Thus, the energy dissipated ( E p ) during the impact is given by [17]:

2

 m m mm vm  1 2 2 1

 max 2

 

 

2 dwwP E

(20)

    2 2

 

gw m m v

p

1

2

being m 1 and m 2 the beam and hammer masses respectively, g the acceleration of gravity, w max the maximum displacement (mid-span), and v the impact velocity, given by :

2 

v

gh

(21)

where h is the drop height. It is worthy noted that the analytical Eqn. (20), presented by Fujikake et al. [17], has been successfully applied on shear impact problems in the technical literature [18-21]. Therewith, by equalling both energy dissipation equations, i.e. (19) and (20), for a simply supported beam as the one depicted in Fig. 2 and assuming, for the sake of simplicity, that shear damage and plastic distortion after impact are characterised by their final values ( d s and   p ), then:

2

j M M gw mm v   p

2

 mm mm vm 1 2 2 1  



2



 



d

(22)





 s 2

j

2

max

2 2

d 1 2 

LGA

1

2

s

being the bending moment M j calculated with the mean impact force P m (Fig. 3):

     d T

T I

p

(23)

P

dt tP I

m

p

d

0

where I p is the impulse and T d is the impact duration.

Figure 2: Simply supported beam under impact load and its mathematical model in the aftermath.

18