PSI - Issue 2_A

Abdoullah Namdar et al. / Procedia Structural Integrity 2 (2016) 2796–2802 Author name / Structural Integrity Procedia 00 (2016) 000–000

2798

3

Hence, w= f(x, y) Where the w is independents of z . And from (Eqs 2-3), since w is independent of z , these two equations can be integrated to; ( , ) 1 f x y y v z w      (Eq 7) ( , ) 2 f x y x u z w      (Eq 8) Strain at any point in the plate may be calculated from Eqs 9-11.

2

x u y v

   



2 x z w  y z w   2 2

x  

 

(Eq9)

y  

 

(Eq10)

x y z w    2

y u

x v

 

 

2





 



(Eq11)

xy

The stress-strain relations for a thin plate are; ) ( 1 2 y x x v v E       

(Eq12)

E

(   

)

v





x 

(Eq13)

y

y

2

1

v



xy xy G    (Eq14) In terms of curvatures of the middle surface these equations are; ) ( 1 2 y x x X vX v z E       (Eq15) ) ( 1 2 x y y X vX v z E       (Eq16)

xy (Eq17) (Housner and Thad Vreeland 1991). With attention to theoretical concept, the numerical simulation has been performed. 3. Numerical analysis and materials v z E 1  (1 ) 2   xy    v X

Numerically failure analysis of concrete frame has been studied. In this work, the response of a 4-stories concrete frames rested on a rigid raft concrete foundation and subject to forcing frequency excitation were investigated. The aim is to consider nonlinear behavior of a concrete structures. The structure considered is with 13.2 m of height without 1.5 height of foundation, and a square area of 21.8 (m) * 21.8 (m). Therefore, this study focuses on effect of shear wall geometry and location on nonlinear structural response. With attention to developing stress, strain, forcing frequency and displacement at each floor. In order to obtain the reliable results in numerically analysis, the theoretical concept was studied. The displacement at the top floor was main attention, for realize deformation of each floor. Table 1, indicates mechanical property of concrete. Figures 1 and 2 illustrate concrete structure and shear walls have been used in numerical analysis.