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Unformatted text preview: Instructor: T,A. Morgan CE 130
University of California, Berkeley Mechanics of Materials I Spring 2008 Midterm #1 Name Scoring Instructions This exam is closed book. For reference, a formula sheet is attached. You must submit
this formula sheet along with your exam. Please write your name at the top of all sheets
submitted. Clearly state any assumptions you make beyond what is described in the
problem. You may assume small angle approximations are valid. Partial credit may be
awarded based on understanding of principles embedded in each problem. Therefore
extraneous or irrelevant computations will decrease your overall score Where the final
answer is incorrect. If you need more space to write, use the back of the page. The duration of the examination is 50 minutes. Good Luck 10f5 Name: Warns!»—
Midterm #1
Problem 1 Consider the ber shown below, having length L and crossSectional area. A. The material
has elastic modulus E, yield stress or”, and coefﬁcient of thermal expansion cu. a.) If this bar is subjected to a uniform increase in temperature AT, What is the gap size
U such that the bar just reaches its yield stress? [0 . b) Given the gap size U computed above, What is the reaction at the right support due
to AT? 5" :: a: oLQT_3 L U ' dimw J0»
a) AT :AT’ *— 5T1?— Shrt—Ss up—loyielcl 19) FewC gyms” q>=O—.A 1
5‘1“” haw Jks‘l' yjelclgj 0.56;? a 8203A S” l.
2 of5 I'
I Name: duo raw...
Midtem #1 f Problem 2 A spherical balloon having radius 'r and thickness t is subjected to an increase in internal pressure Ap. You may assume r > t. The balloon is made of material having elastic
modulus E andPossion’s ratio :1. a.) At any point on the surface of the balloon, what are the three components of axial
strain, emegg, 55050 , due to the pressure change Ap? l 0 b) What is the change in stored energy due to the pressure change Ap? (hint: in
spherical Coordinates, dV = r2td9d<p for small thickness t.) ‘0 ~ 3of5 Name: " . M...
Midterm #1 Problem 3 Consider the circular composite shaft shown below, having length L, and cross—section as .
indicated. The core of the shaft is mild steel having radius R. This mild steel shaft is
ﬁtted with a. titanium encasement of small thickness 33 (that is, R > t.) Mild steel has
shear modulus G, and yield‘shear stress Tm. Titanium has shear modulus G, and yield
shear stress 13,. You may assume elssticperfectlyplastic material response. a) Under the applied. torque T, What is the twist at the end of the shaft (in radians)
assuming elastic behavior?  b) What is the ultimate torque, Tu, that the shaft can carry? Remember, this is greater
than the yield torque, T, (which you are not asked to solve.) ...
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 Spring '09
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