237_Mechanics Homework Mechanics of Materials Solution

# 237_Mechanics Homework Mechanics of Materials Solution -...

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Unformatted text preview: PROBLEM 3 99 3.98 The solid circular shaﬁ show is made of a steel which is assumed to be ' elastoplastic with 1'}, = 21 ksi. Determine the magnitude Tof the applied torque when the plastic mmis (a) 0.6 in. deep, (b) 1 in. deep. 3.99 For the shaﬂ and loading of Prob. 3.98, determine the angle of twist in a 4-ﬂ length of shaft. SOLUTION c: 1.25;”, 21.: 2: k5: = zrxlo‘ pan") eatzuo‘rsl L:- i'-\-F‘I' 1-433“ 1;]; _ (49%?! Ho“; '3 - _—_ = - M C 9 (1.251012 ”(0‘) 7? 00210 .5 pi, = c-tyu mgr-ox. = 0.65 45-“ O 5- - c. " LZS = F252 : 7:52:30” 2 l32.‘l§’/0.\$V‘°J = 193., f I pp c-t, =I.25'—1.o a 0.25‘ q! C? 33% = 72020;"“l0 =' 360 :46st PROBLEM 3 100 3.100 A torque '1‘ is applied to the 20-mm-diameter steel rodAB. Assuming the steel ' to be elastoplastie with G = 77 GPa and 7,, = 145 MPa, determine (a) the torque T when the angle of twist at A is 25 ° , (b) the corresponding diameter of the elastic core of the shaﬂ. SOLUTION Lrl.5m1 G=77¥lo “a. _LTr CPY'GC _ (:.5)(H\$x:o‘) 09" ‘ (77x107)(o.0lo) Ty 1’ \$3.61? = latest; 2 -¥(0.OIO)SCV+S VIO‘) ? 227.77 N-M 282.47 x lo" mt - s .47. 0'3 g) = 25° = 434-33xro‘ mt > cp, gt: M ._. 0.69737 (‘13 T = :3: Ts? ( ' - ﬁ 335%!) = %(227.77)[1- zi-(amsﬂﬂ = 223 Man «a (5) gr 2 0.5q737 ,or = 0.9973? c = (0.64737)(o.om) 6.4737 vzo'sm -.~ 6.14737 m». av: 2p, = 12.75 mm ...
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