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Unformatted text preview: 547. The A36 steel axle is made from tubes AB and CD
and a solid section BC. It is supported on smooth bearing
that allow it to rotate freely. If the gears. fixed to its ends. are
subjected to 85N  m torques. determine the angle of twist
of gear A relative to gear D. The tubes have an outer
diameter of 30 mm and an inner diameter of 20 mm. 'Ihe
solid section has a diameter of 40 mm. 01'“ 1;. . ~85u.m H‘Pf Tu . 854“, 85Nan :2 16 Mo mac. 4) (ssxo.25)
gmms‘ 0.01‘x75xio') ;(o.02‘)(75)(to') = 0.01534M3 0.879 Ala 563. When drilling a well. the deep end of the drill pipe is
assumed to encounter a torsional resistance TA. Furthermore.
soil friction along the sides of the pipe creates a linear
distribution of torque per unit length. varying from zero at the
surface B to to at A. Determine the necessary torque TB that
must be supplied by the drive unit to turn the pipe. Also. what
is the relative angle of twist of one end of the pipe with
respect to the other end at the instant the pipe is about to turn? The pipe has an outer radius to and an inner radius ri.
The shear modulus is G. gammao n_~l.+21:. _i_ L§L+213__r£
1610‘ 2 ugh“ I ~L+2n ”1‘1" 3 2 6L 0 . uh am.
310 Bowen“! I go;  n.) 2L“! + 313) . . 38(r.‘  r.‘)G *5—80. The two 3ftlong shafts are made of 2014T6
aluminum. Each has a diameter of 1.5 in. and they are
connected using the gears fixed to their ends. Their other
ends are attached to fixed supports at A and B. They are also supported by bearings at C and D, which allow free
rotation of the shafts along their axes. If a torque of 600 lb ° ft is applied to the top gear as shown, determine the
maximum shear stress in each shaft. 4
r F   600 = o 1
A + (12) ( )
T ~ Hi) = 0 (2)
' 12
From Eqs.(l)and(2) 1"” 73
1% + 21'.  600 a 0 (3)
F
4(¢£) = 2(‘10: O; = 05¢:
151. 131.
—=0.5—; T=0.5T 4
JG (JG) A a () Solving Eqs. (swam yields :
1; = 240nm; n =1201bft (1.0).“ = if = W = 435m A... 1 £0.15“) (1m)..‘ = E—c = w = 2.17 hi A” I {(0.75‘) 65. A reinforced concrete pier is used to support the
stringers for a bridge deck. Draw the shear and moment diagrams for the pier when it is subjected to the stringer loads shown. Assume the columns at A and B exert only
vertical reactions on the pier. 617. The ISOlb man sits in the center of the boat. which
has a uniform width and a weight per linear foot of 3 lb/ft.
Determine the maximum bending moment exerted on the
boat. Assume that the water exerts a uniform distributed
load upward on the bottom of the boat. 3 "ll‘ IIIIIIIIIIIIIIII ,
'3 Wk to t 0
van q‘
’ 75
'7:
Mat[u 2.
38! '
1' ~un'2..b'h A. *6—36. Draw the shear and moment diagrams for the
beam. 3 kip /ft 1500lb ft I.
"A2 .
B
12 ft—+—6ft ...
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 Winter '07
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