PSI - Issue 71

A. Kumar et al. / Procedia Structural Integrity 71 (2025) 453–460

456

G = Material shear modulus

By applying the Castigliano's second theorem, the shear deformation

13 4 sin F w ltG

U



13  = =

(10)

2

F





13

Shear strain

13 2 4 sin F

13 w ltG 

(11)

= =



13



(12)

4 sin (

cos ) 

s A l =

h l  −

In the direction- 1 ,

 

G

13

=

(13)

13

13

sin

t G G   =  



13

s

(14)

h

l  





cos  −    l 

Out-of-Plane Shear modulus (G 23 )

2.3.

The shear force 23 F is loaded in direction- 2 (Fig. 4(a)). As a consequence of this shear force 23 F , shear stress 23  is transmitted to both inclined and straight walls of the RCE.

Fig. 4. (a) Shear force 23 F acting on the whole structure in direction- 2 ; (b) Shear force 23 F on the RCE

If the shear force in wall AE is EA F , then

EA 2 h   =   l

AB F F

(15)

EA 4 F F =

  , BG

The total force 23 F acting on the RCE

(16)

4 4 cos F F F = +

F  +

23

EA

AB

BG

The total strain energy developed as a result of applied shear force 23 F . 2 2 2 BG EA AB w w w F F F

0 

0 

0 

4

d 4 z +

d

d

(17)

U

z

z

=

+

2( )

2( )

2( ) A G A G

EA A G

AB

BG

According to Castigliano's second theorem, the shear deformation

( 1.5 ) h +

23 F w l

U



23  = =

(18)

2

4 (

cos ) 

F

tG h l −



23