Machine Design – An Integrated ApproachME 322A
Dr. Mark Jakiela
PROBLEM 2-7 (15%)
Statement: Figure P2-1 shows stress-strain curves for three failed tensile-test 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.
(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 ApproachME 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 ApproachME 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 ApproachME 322A
Dr. Mark Jakiela
PROBLEM 3-9 (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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