A stepped shaft ABCDE consisting of solid and hollow circular segments is subjec
ID: 1824842 • Letter: A
Question
A stepped shaft ABCDE consisting of solid and hollow circular segments is subjected to two torques, as shown in the figure. The torques have magnitudes TB = 150 N?m, TD = 1000 N?m. The length of each segment are LAB = 250 mm, LBC = 200 mm, LCD = 300 mm, LDE = 500 mm, respectively. And the outer diameters of the segments AC and CD are 25 mm, 50 mm, inner diameter of segment DE is 25 mm. The material is steel with shear modulus of elasticity G = 80 GPa. Compute the angle of twist ?A at end A.
A stepped shaft ABCDE consisting of solid and hollow circular segments is subjected to two torques, as shown in the figure. The torques have magnitudes TB = 150 N?m, TD = 1000 N?m. The length of each segment are LAB = 250 mm, LBC = 200 mm, LCD = 300 mm, LDE = 500 mm, respectively. And the outer diameters of the segments AC and CD are 25 mm, 50 mm, inner diameter of segment DE is 25 mm. The material is steel with shear modulus of elasticity G = 80 GPa. Compute the angle of twist ?A at end A.Explanation / Answer
= TL/(JG)
A = TDLDE/(JDEG)+TDLCD/(JCDG)+TDLBC/(JBCG)+(TD+TB)LAB/(JABG)
J = r4/2 for solid
and J = (r14-r24)/2 for hollow
therefore,
A =1000*0.5/(((0.0254-0.01254)/2)*80*109)+1000*0.3/(((0.0254)/2)*80*109)+1000*0.2/(((0.01254)/2)*80*109)+(1000+150)*0.25/(((0.01254)/2)*80*109) = 0.010865+0.0061115+0.006519+0.09371=0.125 radians
therefore, A = 0.125 radians or 7.160
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