# The Displacement Method of Matrix Analysis

## The Displacement Method of Matrix Analysis

• Submitted By: trust02
• Date Submitted: 10/26/2009 12:46 PM
• Category: Science
• Words: 311
• Page: 2
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ENGINEERING Analysis 5
(MAJOR COURSEWORK)

Author: Ummar Khalid
Matric No: 200405977
Module: Engineering Analysis 5
Programme: BEME5
Lecturer: Dr. David Gordan

The structure shown below is pinned at B and D and Fully fixed at E and G. the members have the relative flexural rigidity shown where EI = 10MNm2. Using the Displacement (stiffness) method of Matrix Analysis and consideration flexural deformation only, Determine, making use of the Datasheet.

i) the stiffness matrix for the structure:
iii) the rotation at C and F and the translation at A;
iv) the reaction at B,D,E and G.
v) the Bending Moment Diagram for the structure.
vi) Conduct a Finite Element Analysis using ANSYS to compare your answer.

[pic]

i) Determine the stiffness matrix for the structure

[pic] and all other [pic]

[pic]
[pic]

k11 = [pic][pic]+[pic]+[pic]

k11 = [pic][pic]+[pic]+[pic]

k11 = [pic]+[pic]+[pic]+[pic]

k11 = [pic]

k21 = [pic]

k21 = [pic]

k21 = [pic]

k21 = [pic]

k21 = [pic]

k31 = [pic]

k31 = [pic]

k31 = [pic]

k31 = [pic]

k31 = 0

[pic] and all other [pic]
[pic]

K12 = [pic][pic]

K12 = [pic][pic]

K12 = [pic][pic]

K12 = [pic]

K12 = [pic]

k22 = [pic][pic][pic]

k22 = [pic][pic][pic]

k22 = [pic][pic][pic]

k22 = [pic]

k22 = [pic]

K32 = [pic]

K32 = [pic]

K32 = [pic]

K32 = [pic]

[pic] and all other [pic]

[pic]

K13 = [pic]

.

k23 = [pic]

k23 = [pic]

k23 = [pic]

k23 = [pic]

k33 = [pic]

k33 = [pic]

k33 = [pic]
k33 = [pic]

k33 = [pic]

[pic]

[pic]

[pic]
-----------------------

30kN

5kN/m

EI

EI

2EI

4EI

4EI

C

2m

2m

2m

4m

4m

2m

30kN

20kN

F

A

B

E

D

G

8m

C

F

A

E

D

C

F

A

E

D

G

C

F

A...