exam091710 - Clarkson University

ME 341 Mechanics of Machine Elements
Clarkson University, Fall 10', Prof. Yurgartis
First Hour Exam 9/ 1711 0 (Exam 112)
Open textbook, closed notes. Good luck!
Short answer questions (8 pts each)
1. Why are factors of safety used in design, and where do the values come from
2. Do the stress elements shown below have the same state of stress Explain your
answer.
3. Give three distinct conditions when the equation Me/I may fail to give a COlTect
estimate of the bending stress in a beam.
4. If minimum weight is an important criteria in a design, explain how the equation
for shear stress in a round beam subjected to torsion, Tr/J, suggests that a hollow
round shaft will be more efficient at transmitting torque than a solid round shaft.
5. Draw a stress element oriented in the principle axes direction, and show the
principle stresses associated with a general case ofplane stress.
Problem 1. (35 pts.) A chain-driven transmission shaft is shown in Figure 1. Previous
analysis has estimated at a steady speed the chain force is about 360 lbs. The end of the
shaft drives a belted pulley. The belt return tension is about 10% of the drive side
tension. You may assume the bearings act as simple supports. Given the dimensions
shown,
I. Draw a shear and moment diagram for the shaft.
2. Identify where along the length of the shaft the stresses are greatest and draw a
stress element to show the direction and magnitude of all the non-zero stress
components.
Problem 2. (25 pts.) A thin-walled pressurized cylinder has an internal gage pressure of
125 psi., as shown in Figure 2. An engineer is contemplating putting an inspection port
(a "hole") in about the center of the cylinder.
1. Without the hole, estimate the current maximum shear stress in the wall.
2. Discuss briefly the stress implications of putting a hole in the wall.

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Exam 112, Problem 1 solution
From a FBD of the sprocket it is determined that the torque transmitted by the shaft is 750
in-lb.
T := 360· 1.5 T = 540
From a FBD of the pulley is is determined that.
0 := I T = 540+ (.18)( 3)-8·3•
2.00
S-'tO
8 := 200 so Rd := 220
From the FBD of the shaft it can be determined that,
Rc := 380 and Ra := 200 M
So the bending moment at bearing Cis:
And the bending moment at the gear B is Mb := 360· 1
Therefore the largest bending stress will be at the bearing C.
The cross section properties of the shaft are,
4
.6 1 : = _TI-,(_c·_2'--)
c := - I = 0.006362 J := J·2 J = 0.0 13
2 64
The stresses at bearing C caused by the bending moment and the torque are ,
T· c
T xy := -J­
T xy = 12732
CT = 20749
X
12. -r~z..

Problem 2, exam 112
Th is is a thin walled pressure cyl inder
t := .15
p := 125
3
(Jt = 5.063 x 10
The longitudinal stress is tensile, but smaller than the tangential stress (about half), so
3
T max = 2 .53 1 x 10
Putting a hole in the wall will cause a stress concentration, on the order of 3.