Building Frames | Structural Analysis - Civil Engineering (CE) PDF Download

 Page 1


Instructional Objectives: 
After reading this chapter the student will be able to 
1. Analyse building frames by approximate methods for vertical loads. 
2. Analyse building frames by the cantilever method for horizontal loads. 
3. Analyse building frame by the portal method for horizontal loads. 
 
 
36.1 Introduction 
The building frames are the most common structural form, an analyst/engineer 
encounters in practice. Usually the building frames are designed such that the 
beam column joints are rigid. A typical example of building frame is the reinforced 
concrete multistory frames. A two-bay, three-storey building plan and sectional 
elevation are shown in Fig. 36.1. In principle this is a three dimensional frame. 
However, analysis may be carried out by considering planar frame in two 
perpendicular directions separately for both vertical and horizontal loads as 
shown in Fig. 36.2 and finally superimposing moments appropriately. In the case 
of building frames, the beam column joints are monolithic and can resist bending 
moment, shear force and axial force. The frame has 12 joints , 15 beam 
members( , and 9 reaction components
() j
) b ( ) r . Thus this frame is statically 
indeterminate to degree() ( 18 3 12 9 15 3 ) = × - + × = (Please see lesson 1, module 1 
for more details). Any exact method, such as slope-deflection method, moment 
distribution method or direct stiffness method may be used to analyse this rigid 
frame. However, in order to estimate the preliminary size of different members, 
approximate methods are used to obtain approximate design values of moments, 
shear and axial forces in various members. Before applying approximate 
methods, it is necessary to reduce the given indeterminate structure to a 
determinate structure by suitable assumptions. These will be discussed in this 
lesson. In lesson 36.2, analysis of building frames to vertical loads is discussed 
and in section 36.3, analysis of building frame to horizontal loads will be 
discussed. 
 
                                                                             
                                                         
Page 2


Instructional Objectives: 
After reading this chapter the student will be able to 
1. Analyse building frames by approximate methods for vertical loads. 
2. Analyse building frames by the cantilever method for horizontal loads. 
3. Analyse building frame by the portal method for horizontal loads. 
 
 
36.1 Introduction 
The building frames are the most common structural form, an analyst/engineer 
encounters in practice. Usually the building frames are designed such that the 
beam column joints are rigid. A typical example of building frame is the reinforced 
concrete multistory frames. A two-bay, three-storey building plan and sectional 
elevation are shown in Fig. 36.1. In principle this is a three dimensional frame. 
However, analysis may be carried out by considering planar frame in two 
perpendicular directions separately for both vertical and horizontal loads as 
shown in Fig. 36.2 and finally superimposing moments appropriately. In the case 
of building frames, the beam column joints are monolithic and can resist bending 
moment, shear force and axial force. The frame has 12 joints , 15 beam 
members( , and 9 reaction components
() j
) b ( ) r . Thus this frame is statically 
indeterminate to degree() ( 18 3 12 9 15 3 ) = × - + × = (Please see lesson 1, module 1 
for more details). Any exact method, such as slope-deflection method, moment 
distribution method or direct stiffness method may be used to analyse this rigid 
frame. However, in order to estimate the preliminary size of different members, 
approximate methods are used to obtain approximate design values of moments, 
shear and axial forces in various members. Before applying approximate 
methods, it is necessary to reduce the given indeterminate structure to a 
determinate structure by suitable assumptions. These will be discussed in this 
lesson. In lesson 36.2, analysis of building frames to vertical loads is discussed 
and in section 36.3, analysis of building frame to horizontal loads will be 
discussed. 
 
                                                                             
                                                         
 
                                                                             
                                                         
Page 3


Instructional Objectives: 
After reading this chapter the student will be able to 
1. Analyse building frames by approximate methods for vertical loads. 
2. Analyse building frames by the cantilever method for horizontal loads. 
3. Analyse building frame by the portal method for horizontal loads. 
 
 
36.1 Introduction 
The building frames are the most common structural form, an analyst/engineer 
encounters in practice. Usually the building frames are designed such that the 
beam column joints are rigid. A typical example of building frame is the reinforced 
concrete multistory frames. A two-bay, three-storey building plan and sectional 
elevation are shown in Fig. 36.1. In principle this is a three dimensional frame. 
However, analysis may be carried out by considering planar frame in two 
perpendicular directions separately for both vertical and horizontal loads as 
shown in Fig. 36.2 and finally superimposing moments appropriately. In the case 
of building frames, the beam column joints are monolithic and can resist bending 
moment, shear force and axial force. The frame has 12 joints , 15 beam 
members( , and 9 reaction components
() j
) b ( ) r . Thus this frame is statically 
indeterminate to degree() ( 18 3 12 9 15 3 ) = × - + × = (Please see lesson 1, module 1 
for more details). Any exact method, such as slope-deflection method, moment 
distribution method or direct stiffness method may be used to analyse this rigid 
frame. However, in order to estimate the preliminary size of different members, 
approximate methods are used to obtain approximate design values of moments, 
shear and axial forces in various members. Before applying approximate 
methods, it is necessary to reduce the given indeterminate structure to a 
determinate structure by suitable assumptions. These will be discussed in this 
lesson. In lesson 36.2, analysis of building frames to vertical loads is discussed 
and in section 36.3, analysis of building frame to horizontal loads will be 
discussed. 
 
                                                                             
                                                         
 
                                                                             
                                                         
 
                                                                             
                                                         
Page 4


Instructional Objectives: 
After reading this chapter the student will be able to 
1. Analyse building frames by approximate methods for vertical loads. 
2. Analyse building frames by the cantilever method for horizontal loads. 
3. Analyse building frame by the portal method for horizontal loads. 
 
 
36.1 Introduction 
The building frames are the most common structural form, an analyst/engineer 
encounters in practice. Usually the building frames are designed such that the 
beam column joints are rigid. A typical example of building frame is the reinforced 
concrete multistory frames. A two-bay, three-storey building plan and sectional 
elevation are shown in Fig. 36.1. In principle this is a three dimensional frame. 
However, analysis may be carried out by considering planar frame in two 
perpendicular directions separately for both vertical and horizontal loads as 
shown in Fig. 36.2 and finally superimposing moments appropriately. In the case 
of building frames, the beam column joints are monolithic and can resist bending 
moment, shear force and axial force. The frame has 12 joints , 15 beam 
members( , and 9 reaction components
() j
) b ( ) r . Thus this frame is statically 
indeterminate to degree() ( 18 3 12 9 15 3 ) = × - + × = (Please see lesson 1, module 1 
for more details). Any exact method, such as slope-deflection method, moment 
distribution method or direct stiffness method may be used to analyse this rigid 
frame. However, in order to estimate the preliminary size of different members, 
approximate methods are used to obtain approximate design values of moments, 
shear and axial forces in various members. Before applying approximate 
methods, it is necessary to reduce the given indeterminate structure to a 
determinate structure by suitable assumptions. These will be discussed in this 
lesson. In lesson 36.2, analysis of building frames to vertical loads is discussed 
and in section 36.3, analysis of building frame to horizontal loads will be 
discussed. 
 
                                                                             
                                                         
 
                                                                             
                                                         
 
                                                                             
                                                         
36. 2 Analysis of Building Frames to Vertical Loads  
Consider a building frame subjected to vertical loads as shown in Fig.36.3. Any 
typical beam, in this building frame is subjected to axial force, bending moment 
and shear force. Hence each beam is statically indeterminate to third degree and 
hence 3 assumptions are required to reduce this beam to determinate beam. 
 
Before we discuss the required three assumptions consider a simply supported 
beam. In this case zero moment (or point of inflexion) occurs at the supports as 
shown in Fig.36.4a. Next consider a fixed-fixed beam, subjected to vertical loads 
as shown in Fig. 36.4b. In this case, the point of inflexion or point of zero moment 
occurs at from both ends of the support. L 21 . 0
 
 
 
                                                                             
                                                         
Page 5


Instructional Objectives: 
After reading this chapter the student will be able to 
1. Analyse building frames by approximate methods for vertical loads. 
2. Analyse building frames by the cantilever method for horizontal loads. 
3. Analyse building frame by the portal method for horizontal loads. 
 
 
36.1 Introduction 
The building frames are the most common structural form, an analyst/engineer 
encounters in practice. Usually the building frames are designed such that the 
beam column joints are rigid. A typical example of building frame is the reinforced 
concrete multistory frames. A two-bay, three-storey building plan and sectional 
elevation are shown in Fig. 36.1. In principle this is a three dimensional frame. 
However, analysis may be carried out by considering planar frame in two 
perpendicular directions separately for both vertical and horizontal loads as 
shown in Fig. 36.2 and finally superimposing moments appropriately. In the case 
of building frames, the beam column joints are monolithic and can resist bending 
moment, shear force and axial force. The frame has 12 joints , 15 beam 
members( , and 9 reaction components
() j
) b ( ) r . Thus this frame is statically 
indeterminate to degree() ( 18 3 12 9 15 3 ) = × - + × = (Please see lesson 1, module 1 
for more details). Any exact method, such as slope-deflection method, moment 
distribution method or direct stiffness method may be used to analyse this rigid 
frame. However, in order to estimate the preliminary size of different members, 
approximate methods are used to obtain approximate design values of moments, 
shear and axial forces in various members. Before applying approximate 
methods, it is necessary to reduce the given indeterminate structure to a 
determinate structure by suitable assumptions. These will be discussed in this 
lesson. In lesson 36.2, analysis of building frames to vertical loads is discussed 
and in section 36.3, analysis of building frame to horizontal loads will be 
discussed. 
 
                                                                             
                                                         
 
                                                                             
                                                         
 
                                                                             
                                                         
36. 2 Analysis of Building Frames to Vertical Loads  
Consider a building frame subjected to vertical loads as shown in Fig.36.3. Any 
typical beam, in this building frame is subjected to axial force, bending moment 
and shear force. Hence each beam is statically indeterminate to third degree and 
hence 3 assumptions are required to reduce this beam to determinate beam. 
 
Before we discuss the required three assumptions consider a simply supported 
beam. In this case zero moment (or point of inflexion) occurs at the supports as 
shown in Fig.36.4a. Next consider a fixed-fixed beam, subjected to vertical loads 
as shown in Fig. 36.4b. In this case, the point of inflexion or point of zero moment 
occurs at from both ends of the support. L 21 . 0
 
 
 
                                                                             
                                                         
 
 
Now consider a typical beam of a building frame as shown in Fig.36.4c. In this 
case, the support provided by the columns is neither fixed nor simply supported. 
For the purpose of approximate analysis the inflexion point or point of zero 
moment is assumed to occur at L
L
1 . 0
2
21 . 0 0
˜
?
?
?
?
?
? +
 from the supports. In reality 
the point of zero moment varies depending on the actual rigidity provided by the 
columns. Thus the beam is approximated for the analysis as shown in Fig.36.4d.