MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
2.001 Mechanics and Materials I
Fall 2006
Problem Set 8
Distributed:
Wednesday, November 8, 2006
Due:
Monday, November 13, 2006
Problem 1:
Hibbeler 9-70
Problem 2:
Hibbeler 9-78
B
D
C
A
θ
L
L
θ
Problem 3:
A structure is composed of three bars pinned
together as shown in the adjoining diagram.
Each bar has a
cross-sectional area of A, a Young’s modulus of E, and a
coefficient of thermal expansion of
α
.
The bars fit together
perfectly when they are first assembled (that is, there are no
stresses in the bars when the structure is first assembled).
What are the forces in the bars and what is the displacement
of point D when the temperature of bar DC is increased by
∆
T?
Problem 4:
An empty cylindrical pressure vessel is placed between two fixed walls so that it
just fits.
It is free to expand radially.
It has a radius R and wall thickness t << R, and its
Young’s modulus, Poisson ratio, and coefficient of thermal expansion are E,
ν
, and
α
respectively.
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- Spring '09
- Prof
- Shear Stress, wA
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