Moment Resistance System

Abstract

In the recent two decades, the number of high intensity earthquake occurrence is incredibly increased which resulted many building damages and human lost. Inappropriate design of structures and construction process are the main reasons of buildings damage and collapse due to seismic load. The main challenge of structure design is determining the imposed earthquake load to the building and also the distribution of seismic load to the different structural components. Therefore, the main focus of this chapter is about calculation of earthquake load and process of seismic load distribution between structural members in various type of buildings such as steel and concrete structures. However, the same procedure can be implemented for distribution of any lateral load effect on structural elements such as wind load. In this chapter, the moment-resistance frame system is considered which is one of the most conventional earthquake resistant systems for buildings. This chapter is divided into 5 main sections: In the first section of this chapter, behavior of the moment-resistance frame system subjected to gravity and the lateral load is demonstrated. The approximate methods are implemented for analysis of the framed structure, and slope-deflection method is explained to calculate the displacement of moment resistant frame subjected to lateral load after determining of lateral stiffness of the frame. In order to clear understanding the highlighted concepts in this book, it is tried to demonstrate the application of explained theories and methods in real buildings in each section and describe all calculations and computations process for real structure details. For this purpose, a 6 story building is considered, and in the second section of this chapter, the all architectural plans and structure detail are presented. The third section of the first chapter is devoted to defining the gravity load and seismic force based on IBC Code and EURO CODE and determining of the center of mass, stiffness, shear rigidity and the eccentricity of each floor level of building by proposing the calculation charts. Furthermore, the distribution of the earthquake force in the structural members using the Portal and Cantilever methods are explained in details. The fourth section illustrates the calculation procedure for determining displacements in the different frames in two perpendicular directions of the moment-resistance structure subjected to earthquake force. Finally, the fifth section of this chapter presents the proposed charts and detail calculation of weight, stiffness, and displacement of the floor levels and frames of the considered structure.

Appendix

• Total weight of each story (Charts 1.22,  1.23, 1.24, 1.25, 1.26, 1.27, 1.28).

• Calculation of stiffness and center of stiffness in each story (Figs. 1.112, 1.114 and 1.116; Charts 1.28, 1.29, 1.30, 1.31, 1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.38, 1.39, 1.40, 1.41, 1.42, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, 1.49, 1.50, 1.51, 1.52, 1.53, 1.54, 1.55, 1.56, 1.57, 1.58, 1.59, 1.60).

• Calculation of Eccentricity in each story (Figs. 1.113, 1.115, 1.117, and 1.118;Charts 1.38, 1.39, 1.60 and 1.61).

• Calculation of Total displacement of frames (Figs. 1.119, 1.120, 1.121, 1.122, 1.123, 1.124, 1.125; Tables 1.76, 1.77, 1.78, 1.79, 1.80, 1.81, 1.82, 1.83, 1.84, 1.85, 1.86, 1.87, 1.88, 1.89, 1.90, 1.91, 1.92, 1.93, 1.94, 1.95 and 1.96; Graphs 1.2, 1.3, 1.4, 1.5, 1.6, 1.7 and 1.8).

  Fig. 1.112

  

  a The shear rigidity in X direction and distance between bents and arbitrary origin. b Shear rigidity in Y direction and distance between bents and arbitrary origin

  Chart 1.36

  

  Calculation of coordinate of stiffness in Y direction

  Chart 1.37

  

  Calculation of coordinate of stiffness in X direction

  Fig. 1.113

  

  Eccentricity in the second floor

  Chart 1.38

  

  Eccentricity in the first floor

  Chart 1.39

  

  Shear rigidity of bent (A) story (3), (4)

  Chart 1.40

  

  Shear rigidity of bent (B), (C) story (3), (4)

  Chart 1.41

  

  Shear rigidity of bent (D) story (3), (4)

  Chart 1.42

  

  Shear rigidity of bent (E) story (3), (4)

  Chart 1.43

  

  Shear rigidity of bent (1) story (3), (4)

  Chart 1.44

  

  Shear rigidity of bent (2) story (3), (4)

  Chart 1.45

  

  Shear rigidity of bent (3) story (3), (4)

  Chart 1.46

  

  Shear rigidity of bent (A) story (2)

  Fig. 1.114

  

  a The shear rigidity in X direction and distance between bents and arbitrary origin. b Shear rigidity in Y direction and distance between bents and arbitrary origin

  Chart 1.47

  

  Calculation of coordinate of stiffness in Y direction

  Chart 1.48

  

  Calculation of coordinate of stiffness in X direction

  Fig. 1.115

  

  Eccentricity In third and fourth floors

  Chart 1.49

  

  Eccentricity in third and fourth floor

  Chart 1.50

  

  Shear rigidity of bent (A) story (5), (6)

  Chart 1.51

  

  Shear rigidity of bent (B), (C) story (5), (6)

  Chart 1.52

  

  Shear rigidity of bent (D) story (5), (6)

  Chart 1.53

  

  Shear rigidity of bent (E) story (5), (6)

  Chart 1.54

  

  Shear rigidity of bent (1) story (5), (6)

  Chart 1.55

  

  Shear rigidity of bent (2) story (5), (6)

  Chart 1.56

  

  Shear rigidity of bent (3) story (5), (6)

  Chart 1.57

  

  Shear rigidity of bent (4) story (5), (6)

  Fig. 1.116

  

  a The shear rigidity in X direction and distance between bents and arbitrary origin. b Shear rigidity in Y direction and distance between bents and arbitrary origin

  Chart 1.58

  

  Calculation of coordinate of stiffness in Y direction

  Chart 1.59

  

  Calculation of coordinate of stiffness in X direction

  Fig. 1.117

  

  Eccentricity in the fifth floor

  Chart 1.60

  

  Eccentricity in the fifth floor

  Fig. 1.118

  

  Eccentricity in sixth floors

  Chart 1.61

  

  Eccentricity in the first floor

  Fig. 1.119

  

  a Shear force in frame (B), b force and moment in frame (B)

  Graph 1.2

  

  Displacement of frame (A)

  Fig. 1.120

  

  a Shear force in frame (C), b force and moment in frame (C)

  Graph 1.3

  

  Displacement of frame (C)

  Fig. 1.121

  

  a Shear force in frame (D), b force and moment in frame (D)

  Graph 1.4

  

  Displacement of frame (D)

  Fig. 1.122

  

  a Shear force in frame (1), b force and moment in frame (1)

  Graph 1.5

  

  Displacement of frame (1)

  Fig. 1.123

  

  a Shear force in frame (2), b force and moment in frame (2)

  Graph 1.6

  

  Displacement of frame (A)

  Fig. 1.124

  

  a Shear force in frame (3), b force and moment in frame (3)

  Graph 1.7

  

  Displacement of frame (3)

  Fig. 1.125

  

  a Shear force in frame (4), b force and moment in frame (4)

  Table 1.76 Overall bending displacement of frame (B)

  Table 1.77 Flexure displacement of frame (B)

  Table 1.78 Total displacement of frame (B)

  Table 1.79 Overall bending displacement of frame (C)

  Table 1.80 Flexure displacement of frame (C)

  Table 1.81 Total displacement of frame (C)

  Table 1.82 Overall bending displacement of frame (D)

  Table 1.83 Flexure displacement of frame (D)

  Table 1.84 Total displacement of frame (D)

  Table 1.85 Overall bending displacement of frame (1)

  Table 1.86 Flexure displacement of frame (1)

  Table 1.87 Total displacement of frame (1)

  Table 1.88 Overall bending displacement of frame (2)

  Table 1.89 Flexure displacement of frame (2)

  Table 1.90 Total displacement of frame (2)

  Table 1.91 Overall bending displacement of frame (3)

  Table 1.92 Flexure displacement of frame (3)

  Table 1.93 Total displacement of frame (B)

  Table 1.94 Overall bending displacement of frame (4)

  Table 1.95 Shear displacement frame (4)

  Table 1.96 Total displacement of frame (4)

  Graph 1.8

  

  Displacement of frame (4)