Vibrational Analysis of Multi Storeyed Frames

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Generally the stress and deformation analysis of any structure is done by constructing and analyzing a mathematical model of a structure. One such technique is Finite element method (FEM). A frame is subjected to both static and dynamic loading with dead load comprising the static load and the all other time varying loads making up the dynamic load. This project titled “ Vibrational Analysis of Frames “ aims at analyzing the frame both statically and dynamically using the matrix approach of

FEM by developing

generalized codes in MATLAB. The analysis comprises of the static analysis of frame and the variation of various parameters such as displacement, moment etc with increasing number of storey’s as well as dynamic analysis wherein a code is developed to find the natural frequency of the structure along with the various other parameters. A structure is always vibrating under dynamic loading such as wind etc and if the vibrating frequency equals the natural frequency of the structure, resonance might take place. It is thus necessary to analyze all these aspects of a structure first which we aim with our study.

CONTENTS

Chapter
Chapter 1

Title
Introduction

Page Number
1-2

1.1
Chapter 2

General Introduction
Literature Review

2
3-5

Chapter 3
3.1
3.2

Theoretical and finite
Finite element methods and
Static Analysis

6-25
7-9
9-14

3.3
Chapter 4
4.1
4.2

Dynamic Analysis
Results and Discussions
Static Analysis
Dynamic Analysis

14-25
26-41
27-37
37-41

Chapter 5
Chapter 6

Conclusion
References

42-43
44-46

List of Figures
Figure
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19

Title
Plane frame Element
SDOF system in free vibration with damping
Figure showing local and global co-ordinates of a
beam member
Problem figure for a single storey frame.
Problem figure for single storey frame with
intermediate node=1
Problem figure for single storey frame with
intermediate node=2
Problem figure for analysis of 10 storey frame
subject to constant wind force or lateral loading
Graph for x-displacement at node 2 with variation in
number of storeys
Graph for y-displacement at node 2 with variation in
number of storeys
Graph for x-displacement at node 3 with variation in
number of storeys
Graph for y-displacement at node 3 with variation in
number of storeys
Graph for x-displacement at node 4 with variation in
number of storeys
Graph for y-displacement at node 4 with variation in
number of storeys
Graph for x-displacement at node 5 with variation in
number of storeys
Graph for y-displacement at node 5 with variation in
number of storeys
Graph for x-displacement at node 6 with variation in
number of storeys
Graph for y-displacement at node 6 with variation in
number of storeys
Problem figure for analysis of 2-D frame from Mario
Paz book
Problem figure to find natural frequency variation in
n storey frame

Page Number
9
17
21
27
28
29
30
31
31
32
33
34
34
35
35
36
36
37
40

List of Tables
Table

Table 1

Title

Nodal Connectivity Table for problem 1 with 0

Page Number

27

intermediate nodes
Table 2

Displacements at all the nodes in x, y and rotation in

27

z-direction
Table 3

Nodal Connectivity Table for problem 1 with 1

28

intermediate nodes
Table 4

Displacements at all the nodes in x, y and rotation in

28

z-direction
Table 5

Nodal Connectivity Table for problem 1 with 2

29

intermediate nodes
Table 6

Displacements at all the nodes in x, y and rotation in

29

z-direction
Table 7

Displacement in x and y-direction at node 2 with

30

increase in number of stories
Table 8

Displacement in x and y-direction at node 3 with

32

increase in number of stories
Table 9

Displacement in x...
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