PSI - Issue 33

Anas Ibraheem et al. / Procedia Structural Integrity 33 (2021) 942–953 Anas Ibraheem, Yulia Pronina / Structural Integrity Procedia 00 (2019) 000–000

944

3

are designed to resist the shear force, and the bending moment. Columns are designed generating three-dimensional biaxial interaction surfaces for the column section, and achieving its bearing capacity according to ACI. 3. Spring model (elastic solutions for rigid footing spring constraints) The uncoupled spring model shown in Fig. 1 is used to represent the stiffness of a foundation.

Fig. 1. Uncoupled spring model for rigid footings.

Any of the six degrees of freedom at any of the joints in the structure can have translational or rotational spring support conditions. These springs elastically connect the joint to the ground. The spring forces that act on a joint are related to the displacements of that joint by a 6x6 symmetric matrix of spring stiffness coefficients. These forces tend to oppose the displacements. The program calculates the stiffness of foundation at surface using the following equations (ASCE/SEI 41 (2013)):

GB L

0.65

[3.4( )

1.2]

K





, x sur

2

B





GB L

L B

0.65

[3.4( )

0.4 0.8]

K



 

, y sur

2

B





GB L

0.75

[1.55( )

0.8]

K





, z sur

1

B





3 GB L

[0.4( ) 0.1] 

K



, xx sur

1

B





3

GB

L B

2.4

[0.47( )

0.034]

K





, yy sur

1





L B

3 2.45 , zz sur K GB   Here, is the base level depth (embedment depth); is thickness of the footing; B is the width of the footing; L is the length of the footing; is the shear modulus of the footing material; ν is Poisson ratio of the footing material; � �,��� , �,��� , �,��� � is the stiffness of foundation at surface for translation degree of freedom along x, y and z axis respectively; � ��,��� , ��,��� , ��,��� � is the stiffness of foundation at surface for rotation degree of freedom about x, y and z axis respectively. [0.53( ) 0.51]