CEE 379 Problem Set 5 Autumn 2007
(Due Oct. 26th , 4:30 PM in 233 More)
Problem 1. Consider the truss shown in the figures below. For each member, the elastic
modulus, E = 29,000 ksi. the cross-sectional area, A = 8 in.2 and the yield stress is 50 ksi.
Use pencil and paper to solve this problem (with the exception that you can use a
spreadsheet or calculator to solve the simultaneous equations).
a) Compute the element stiffness matrix, k, for each of the six truss members.
b) Express the equations of equilibrium at the free kinematic DOF in terms of the
applied external loads, the member properties and the displacements at the free kinematic
DOF. (i.e., Qk = K11Du)
c) For θ = 135 degrees, compute the unknown joint displacements, and sketch the
deflected structure.
d) For θ = 135 degrees, compute the element forces at the end of each truss member.
Then, show the member axial forces on a neat drawing of the structure.
e) Compute the axial stress in each member. (σ = P/A). Compare this value with
the yield stress? Which members have yielded, if any?
Problem 2.
Repeat (c)-(d) from Problem 1, but instead of applying loads P1 and P2 at an angle of
theta, assume that both loads are applied downwards.
YOU CAN COMPARE YOUR RESULTS WITH THOSE OF OTHERS, BUT YOU
SHOULD DEVELOP AND SUBMIT INDIVIDUAL SOLUTIONS.
12 ft
15
ft
15
ft
15
ft
θ
P
2
=5
0k
1
4
2
3
5
6
2
1
4
3
6
5
8
7
DOF
θ
P
1
=2
0k