Question

The following is the torque versus angle of twist diagram for a 0.75 inch diameter steel bar tested in torsion. The gage length of the bar is 3 inches. The angle of rotation and torque at points Q and P are (0.8 radian, 1500 in-lb) and (11.3 radian, 4000 in-lb) respectively. The power-law curve fitting relation for the data above the yield point is given by T = 329880.21, where T is in in-lb and e is in radian. Torque T-in. Ib. TWIST-O (rad)

Answer 1

. Size of Steel bar es d = 0.75 inch diameter of bar L = 3 en ches Gauge length & torque The values of angle of rotation points Q & are at Q [ 0.8 radian 1500 in-16) P [1.3 radian, 4000 in-86] The torsion formula formula for shear stress of solid bar es given as, T GO J L ㅏ where T= applied torque polar moment of inertia J = JE 4 TT d For solid shaft 32 G = Modulus of rigidity : shear stress from torsion formula es given as Ior T (2) J

Also GO L r IL a shear stress G = (+2) shear strain shear strain (e) (3) L Let us solve asked question 1) Shear stress at point a At point Q , T = 150.0 in- eb in de J = T (0.75) = 0.03106 32 ens 32 From. equation (2), 0.75 T 15 OO X 0.03106 2 J ...?@ Q = 18108. 30 P pse Correct answer o's 18000 pse 2) shear stress at P At point P. T = 4000 in lb

from equation (2) Ir. 4000 0.75 2 J 0.03106 ..^=48293.62 psi The shear stress at point p should be closest to 54ooo psi @ Р correct answer es 54ooo pse 3) shear strain at point a from equation (3), (0-15) x 0.8 shear strain (&) = ro U 3 € - 0.1 at Q e's E = 0.1 shear strain correct answer e's o.1 4) Shear strain at point (5-75) 11.3 . shear strain (E) L 3 E = 1.4125 Shear strain at point p closest to los correct answer is 1.5