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**Unformatted text preview: ** ESM (MSE) 3054
Test No. I
October 1, 2007 Aids Allowed‘ Items Needed Name Signature
(I have neither given nor received unauthorized
assistance on this test.) Open book (textbook for this course). One page, front and back, of formulas, deﬁnitions, diagrams,
etc. Bring paper, full 8.5 X 11 inch size, calculator, and straightedge. Instructions {Points may be deducted for failure to follow instructions.)
- Work on one side ofpaper only. Paper must be full 8.5 X ll inch size.
- When you hand in your work, staple together the question page followed by your work in order by problem number. Keep your formula page. - Clariﬁcations or additional information may be written on the blackboard -- check it before handing in your paper. - Logic and calculations leading to all answers must be given, and any points or lines used from graphs must be marked and labeled. - For discussion or explanation type questions, answers need to be in complete sentences and in
reasonably good English, and the logic must be clear.
- Numerical answers should have neither insufﬁcient nor excessive numbers of signiﬁcant ﬁgures, and correct units are required for full credit. 1. A composite material is to be made from unidirectional glass ﬁbers (Type E) embedded in
a matrix of ABS plastic, with all ﬁbers to be aligned in the same direction. For the composite, the elastic modulus parallel to the reinforcement must be at least 48 GPa, and the elastic
modulus perpendicular to the reinforcement must be at least 5.0 GPa. (a) What is the minimum volume fraction of fibers that will satisfy both requirements?
(b) What value of shear modulus results from the volume fraction chosen from (a)? 2. A block of a titanium alloy is
conﬁned by a rigid die as shown, so
that it cannot deform in either the x- or y—directions. A compressive
stress is applied in the z—direction‘.
Assume that there is no friction along
the walls and that no yielding occurs
in the metal. What is the largest value of the compressive stress oz that can
be applied without the strain in the
z—direction exceeding 0.1% = 0.001
in compression? / X 3. A thin-walled tube with closed ends has an inside radius r1 : 80 mm and a wall thickness 2‘ = 6 mm. It is subjected to an internal pressure of 20 MPa, a torque of 60 kN-m, and an axial
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