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Unformatted text preview: MAE 101
_ Midterm Examination #2 November 25, 2009 Instructor: Professor Gupta
TA: Jason Citron; J aedal Jung DO ALL WORK ON THE EXAM
ATTTACH ADDITIONAL SHEETS AS NEEDED
WRITE YOUR NAME ON EVERY SHEET YOU USE
BOX YOUR FINAL ANSWERS NOTE: ALL EQUATIONS OF EQUILIBRIUM MUST HAVE
ASSOCIATED FREE BODY DIAGRAMS Problem 2 29
Problem 3 30 Problem 4 2.3
TOTAL (100) :00 l Problem 1 25 NAME: SOLUTIONS ID: Problem I: For the beam shown below, draw the bending moment and shear force
diagrams along the centerline of the beam. The beam is subjected to a vertical and a
horizontal force of magnitude F. The horizontal force acts at point “a” of the cross
section as shown in the ﬁgure. stem: {2anwa as ex Eff‘0 = RANKWO 23’ PHEE? 1‘ QEMACD 1"%+LRE +h§1:0 «=7 Q23“: M Mbﬂ
K”... ANAL; ,th a ea: sass m9; Problem 2: A ﬂat triangular slab of weight W and uniform thickness (t) is to be mounted
on three identical vertical springs, each with spring constant K, that rest on a ﬂat,
horizontal floor. Each of the springs will support one corner of the slab (A, B, and C).
Determine the force in each spring when the slab is mounted on the springs. The
geometrical dimensions of the slab are given in the figure. f!
‘ i
t 
'9 iMa ’30 WEED“ Q51 On Big)
Lea «w tc.(%5b‘> i W (sari) Problem 3: A rigid, uniform bar, AB, of negligible weight, is 5 feet long, and is
supported by a steel rod, CD. Directly under point B is a wooden block, and a
measurement shows that there is a clearance of 0.005 inches between the bar and the top
of the block. After this measurement, a load P is applied to the rigid bar at point B.
a) What is the load P necessary to cause the bar to first touch the top of the
wooden block?
b) What is the axial stress in rod CD when the bar first touches the top of the
block?
c) If the load P is twice the value as in (a), what is the axial stress in the wooden
block? Assume pin connections at A, C and D. The properties of the wooden block and the steel
rod are: — CrossSectional Area Modulus of Elasticit Wooden Block 15*10 si
Steel Red CD 30*10 psi Parliament*5: {3
Fees. 57’
lac” D .. '3 § .QOS"? lnt‘i‘iﬁﬂ 3; r g ‘ etaaeeﬁﬁﬁi‘ Problem 4: A clutch is a device used to connect and disconnect two coaxial rotating
shafts. The type shown below consists of disks of radius r attached to the ends of the
shafts. When the disks are separated (Figure a), the clutch is disengaged, and the shafts
can rotate freely relative to each other. When the clutch is engaged by pressing the disks
together with axial forces F (Figure b), the shafts can support a couple M due to the
friction forces between the disks. If the couple M becomes too large, the clutch slips. Derive the equation for the maximum couple M that the clutch can support without
relative slipping between the discs. Assume that the pressure is uniformly distributed
over the face of each disk (that is, it is independent of the radius), and that the coefficient of static friction between the two disks is pg. (l3)
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 Fall '09
 Chatterjee

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