PSI - Issue 44

Francesca Barbagallo et al. / Procedia Structural Integrity 44 (2023) 363–370 Francesca Barbagallo et al. / Structural Integrity Procedia 00 (2022) 000 – 000

367

5

Fig. 4 compares the design shear resistance of the joints listed in Table 1 evaluated according to the authors’ proposal (i.e., with the assumption  sh =  sv = f yd ) and those obtained by Fardis capacity model. The maximum difference has been an over-estimation of 6.8% while the mean difference was only 0.7%. Although not exhaustive, the comparison shows that the difference is really negligible and that the assumption of fully yielded joint reinforcement may be used for verification and design purposes.

1200

Authors' proposal

1000

800

600

400

200

Fardis

0

0 200 400 600 800 1000 1200

Fig. 4. Comparison between design shear resistance obtained by the authors’ proposal and Fardis formulation

4. Proposed design procedure 4.1. Evaluation of the shear resistance of a joint In order to propose a closed form procedure for the determination of the shear resistance of a joint, it is important to examine the trend of the functions V Rdj ( eq.h ) and V Rdj(eq.v) governed by their first derivatives. V Rdj ( eq.h ) , shear resistance given by horizontal equilibrium:

dV

f



2

cot

2 cot cot  −   − 1

( . )

Rdj eq h

if

cd

A

  

=

, j ef

1.6

d

2 + 



1 cot

(4)

dV

A f

(

)

( . )

Rdj eq h

sh yd

2 + 

if

1 cot

  

= −

cot

d





When    the first derivative of V Rdj ( eq.h ) is less than 0 and the function is always decreasing. The maximum will be reached when    at a value  h,max given by

(5)

2 1 h  =  +  + ,max cot cot

cot

that depends only on  . V Rdj ( eq.v ) , shear resistance given by vertical equilibrium: ( ) 2 ( . ) 1 cot if Rdj eq v sv yd dV N A f   +     = +  

d

2



cot cot cot 





(6)

dV

f



2 2 cot   +  −  cot

( . )

Rdj eq v

if

cd

A

  

=

(

)

, j ef

1.6

d



2  + 

cot 1 cot

When    the first derivative of V Rdj ( eq.v ) is greater than 0 and the function is always increasing. The maximum will be achieved for    at a value  v,max given by