PSI - Issue 70

Oberoi Kabrambam et al. / Procedia Structural Integrity 70 (2025) 74–81

78

The second segment from 0.5 cc f to cc f can be obtained from Eq. (4) proposed by Saenz (1964).

E



f

=

cc

(4)

2

3

cc        

cc        

cc        

(

)

(

)

1

2

2 1 R

R R + + −

R

− −

+

E

Where,

E



(5)

R

=

cc cc

E

f (

cc

)

1 1

E R R

−



(6)

R

=

−

(

) 2

R

1

R

−





R  and R  are taken as 4 as proposed by Hu and Schnobrich (1989). For the third segment from cc f to 3 cc rk f . Reduction factor ( ) 3 k can be calculated from the empirical equation given by Hu et al. (2003). The experimental investigation carried out by Giakoumelis and Lam (2004) showed that the value of 3 k proposed by Hu et al. (2003) is workable for only concrete cube strength up to 30 MPa, because of this reduction factor ( ) r is introduced. The value of reduction factor r is based on the experimental investigation carried out by Giakoumelis and Lam (2004). For cube strength ( ) cu f equal to 30 MPa, r is taken as 1 and r as 0.5 for cube strength of greater than or equal to 100 MPa, as recommended by TOMII (1991) and Mursi and Uy (2003). For the cube strength between 30 and 100 MPa, linear interpolation is used for finding the value of r . For plasticity DRUCKER PRAGER and DRUCKER PRAGER HARDENING are used, angle of friction is taken as 20 and flowstress ratio as 0.8 as recommended by Hu et al. (2003) and dilation angle as 31. 4. Element types, meshing and boundary conditions For the steel tube, shell elements are utilized in the modeling process. Specifically, 4-node doubly curved quadrilateral elements with reduced integration (S4R) are employed for the steel tube's mesh. In contrast, 8-node hexahedral elements with reduced integration (C3D8R) are used for the concrete. The supports and load application points are represented as three-dimensional rigid bodies, using 4-node bilinear rigid quadrilateral elements (R3D4) for meshing. A mesh size of 30 mm was selected based on a convergence study to ensure optimal mesh size for precise results while minimizing computational time. The contact interactions between the concrete and steel tube were modeled in both tangential and normal directions. The penalty method was applied to formulate the tangential friction behavior with finite sliding, while hard contact was implemented for normal contact. The friction coefficient was set at 0.6.