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MACHINE DESIGN – An Integrated Approach
ME 322A
Dr. Mark Jakiela
PROBLEM 2-1 (15%)
Statement: Figure P2-1 shows stress-strain curves for three failed tensiletest specimens. All are plotted on the same scale.
(a) Characterize each material as brittle or ductile.
(b) Which is the stiffest?
(c) Which has the highest ultimate strength?
(d) Which has the largest modulus of resilience?
(e) Which has the largest modulus of toughness?
Hints:
(a) (20%) Consider the amount of strain following the onset of
yielding, but before the point of fracture. If this portion of the
stress-strain curve is large relative to the elastic portion of the
curve, it is a ductile material.
(b) (20%) The stiffest material is the one with the greatest slope in the
elastic range. Find the slope (rise over run) for the straight-line
portion of each curve.
(c) (20%) Ultimate strength corresponds to the highest stress that is
achieved by a material under test. Find the material with the
maximum stress plotted on the vertical axis to determine which has
the highest ultimate strength.
(d) (20%) Determine the stress and strain values at the yield points and
use equation (2.7) to find the modulus of resiliency.
1
U R   y   y
2
(e) (20%) The modulus of toughness is the area under the stress-strain
curve up to the point of fracture. This can be determined by
comparison of the three graphs.
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MACHINE DESIGN – An Integrated Approach
ME 322A
Dr. Mark Jakiela
PROBLEM 2-7 (15%)
Statement: A metal has a strength of 41.2kpsi (284 Mpa) at its elastic limit
and the strain at that point is 0.004. What is the modulus of elasticity?
What is the strain energy at the elastic limit? Assume that the test specimen
is 0.505 inch diameter and has a 2 inch gage length. Can you define the type
of metal based on the given data?
Hints:
(a) (25%) The modulus of elasticity is the slope of the stress-strain
curve, which is a straight line, in the elastic region.
(b) (50%) The strain energy per unit volume at the elastic limit is the
area under the stress-strain curve up to the elastic limit. (Perhaps
prove to yourself that using stress and strain does give you a result
with units of energy per unit volume.) Given the volume and gage
length, how much volume is absorbing energy?
(c) (25%) Using a material property that you found in this problem,
what material might this be?
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MACHINE DESIGN – An Integrated Approach
ME 322A
Dr. Mark Jakiela
PROBLEM 3-9 (15%)
Statement: A vise grip plier wrench is drawn to scale in Figure P3-3.
Scale the drawing for dimensions. Find the forces acting on each pin and
member of the assembly for an assumed clamping force P = 4000N in the
position shown. What force F is required to keep it in the clamped position
shown?
Hints:
(a) (30%) The biggest and best hint available is to actually experiment
with some Vise Grips to observe how they work. Your instructor
will do this in class, and this should lead to an important
realization that will facilitate solving the problem. Even if you
don’t observe this, a secondary hint is to recognize that some parts
of the tool are 2-force members and some are 3-force members.
You will get 30% of the problem credit if you correctly exploit
these facts on the free body diagrams that you draw.
(b) (50%) Beyond that, you will get 50% if your free body diagrams
are done correctly (or as correctly as they can be done given what
you did or did not realize).
(c) (20%) Getting the right numerical answers involves using
trigonometry correctly.
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MACHINE DESIGN – An Integrated Approach
ME 322A
Dr. Mark Jakiela
PROBLEM 3-14 (15%)
Statement: Figure P3-5 shows a child’s toy called a pogo stick. The child
stands on the pads, applying half her weight on each side. She jumps off the
ground, holding the pads up against her feet, and bounces along with the
spring cushioning the impact and storing energy to help each rebound. Find
the natural frequency of the system, the static deflection of the spring with
the child standing still, and the dynamic force and deflection when the child
lands after jumping 2 inches off the ground.
Hints:
(a) (40%) Consider the child to be the only “sprung” weight for the
purposes of determining the natural frequency. You must find the
mass of the child. Does this value “feel” right to you?
(b) (15%) This is a very direct computation. 10% off if you use the
wrong mass value.
(c) (15%) This problem is solved like a vertical slide hammer
problem. You will need to compute the mass ratio correction
factor etc.
(d) (15%) Once you have this, you can compute the dynamic force.
(e) (15%) Once you have they dynamic force, you can compute the
spring deflection due to that force. Again, does this “feel” right?
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