16.20 Handed Out: Lecture 12
Due: Lecture 16
HOME ASSIGNMENT #3
Warm-Up Exercises
Let’s explore the use of Mohr’s circle for strains in the case of plane stress. Use
geometrical arguments/considerations to:
1. Show that the transformation of an arbitrary state of in-plane strain (ε11, ε22,
~ ~
ε12) to another in-plane system (ε
~
11, ε22, ε12) yields the three equations
represented by:
~
εαβ = l~ βλ εσλ
ασ l~
2. Look at the circle diameter. The circle diameter is some combination of the
strains that is invariant. Determine what this is (in terms of ε αβ and the
transformation angle θ).
3. Does the combination of strains that coincides to the circle diameter have any
physical significance? If so, what is it; if not, is there another geometric item
with physical significance?
Practice Problems
4. A 2-meter long aluminum bar has a
square cross-section (35 cm to a side) and
is subjected to uniform side pressures of
p1 and p2. The modulus of aluminum is
70.8 GPa and the Poisson’s ratio is 0.3.
Determine the stress and strain states
using both the plane stress and plane
strain assumptions for various ratios and
values of the two pressures. What is the
applicability of the two models?
y2
p2
p1
y1
CROSS-
SECTION
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