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UNIVERSITY OF CALIFORNIA, BERKELEY
Dept. of Civil and Environmental Engineering
Spring Semester 2008
Instructor: Filip C. Filippou
CE 121 – Advanced Structural Analysis
Homework Set #13 (due May 2, 2008)
1.
Problem (7 points)
The two span continuous beam in the figure is subjected to a concentrated force of 100 units at
midspan of the right span, as shown. The flexural section stiffness of all members is EI =
300,000. It is obvious from the absence of axial forces, that axial deformations are irrelevant for
the solution.
1.
Use the displacement method to solve for the basic element forces.
2.
Draw the bending moment diagram.
3.
Determine the support reactions and check global equilibrium.
4.
Draw the deformed shape under the given loading.
100
20
20
1
2
3
4
40
5.
Use the displacement method of analysis to solve for the case of a uniform distributed load of
5 units of force per unit of length acting over the right span of the beam.
40
40
5
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View Full Document CE121  Advanced Structural Analysis
Homework 13
Filip C. Filippou
Problem 1
100
20
1
2
3
4
40
L
a
40
:=
L
b
20
:=
L
c
20
:=
EI
300000
:=
There are 3 free dofs, and 5 basic forces, as shown in the following figure.
1
2
3
Q
1
Q
2
Q
3
Q
4
Q
5
the equilibrium equations are
P
1
Q
2
Q
3
+
=
P
2
Q
3
Q
4
+
20
−
Q
5
20
+
=
P
3
Q
4
Q
5
+
=
Page 131
CE121  Advanced Structural Analysis
Homework 13
Filip C. Filippou
for the displacement method of analysis we need to set up the stiffness matrix at the free dofs
4
b
EI
L
2
b
EI
L
4
b
EI
L
2
b
EI
L
3
c
EI
L
4
a
EI
L
2
a
EI
L
2
6
b
EI
L
2
6
b
EI
L
2
6
b
EI
L
2
6
b
EI
L
2
3
c
EI
L
2
3
c
EI
L
3
12
b
EI
L
3
12
b
EI
L
2
6
b
EI
L
2
6
b
EI
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This note was uploaded on 01/04/2010 for the course CE 121 taught by Professor Filippou during the Fall '09 term at University of California, Berkeley.
 Fall '09
 filippou
 Environmental Engineering

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