A shaft with a cylindrical cross - section is subjected at the same time to a torsional torque T = 30 x 10º N mm and bending moment M = 15. x 106 N mm . A circular groove is made in the shaft with the following dimensions ( t = 0.6 cm , p = 0.22 cm , and b = 6 cm ) , as shown in Figure D , Table 1 , lecture 5 . By Neuber’s nomograph ( Figure 9 ) , determine the value of Scc , and then find the following stress quantities that produce in the shaft at the root of the groove : a . the maximum principal stress b . the maximum shear stress

A shaft with a cylindrical cross - section is subjected at the same time to a torsional torque T = 30 x 10º N mm and bending moment M = 15. x 106 N mm . A circular groove is made in the shaft with the following dimensions ( t = 0.6 cm , p = 0.22 cm , and b = 6 cm ) , as shown in Figure D , Table 1 , lecture 5 . By Neuber’s nomograph ( Figure 9 ) , determine the value of Scc , and then find the following stress quantities that produce in the shaft at the root of the groove : a . the maximum principal stress b . the maximum shear stress

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter3: Torsion

Section: Chapter Questions

Problem 3.4.5P: A hollow tube ABCDE constructed of monel metal is subjected to five torques acting in the directions...

See similar textbooks

Similar questions

A nonprismatic bar ABC with a solid circular cross section is loaded by distributed torques (sec figure). The intensity of the torques, that is, the torque per unit distance, is denoted t(x) and varies linearly from zero at A to a maximum value T0/L at B. Segment BC has linearly distributed torque of intensity r(x) = T0/3L of opposite sign to that applied along AB. Also, the polar moment of inertia of AB is twice that of BC and the shear modulus of elasticity of the material is G. Find the reaction torque RA. Find internal torsional moments T(x) in segments AB and BC. Find the rotation t0 Find the maximum shear stress tmaxand its location along the bar, Draw the torsional moment diagram (TMD:T(x),0 < x < L).
What is the maximum power that can be delivered by a hollow propeller shaft (outside diameter 50 mm, inside diameter 40 mm, and shear modulus of elasticity 80 GPa) turning at 600 rpm if the allowable shear stress is 100 MPa and the allowable rate of twist is 3.0°/m?
A stepped shaft ABC consisting of two solid, circular segments is subjected to uniformly distributed torque t1acting aver segment 1 and concentrated torque t2applied at C, as shown in the figure. Segment 1 of the shaft has a diameter of d1= 57 mm and length of L1= 0.75 m; segment 2 has a diameter d2— 44 mm and length L2= 0.5 m. Torque intensity /,"= 3100 N . m/m and T2= 1100 N. m. (a) Find reaction torque TAat support A. (b) Find the internal torque T(x) at two locations: .x = L1/2 and at .x = L1+ L2/2. Show these internal torques on properly drawn free-body diagrams.
A long, thin-walled tapered tube AB with a circular cross section (see figure) is subjected to a torque T. The tube has length L and constant wall thickness t. The diameter to the median lines of the cross sections at the ends A and B are dAand dB, respectively. Derive the following formula for the angle of twist of the tube: Hint: If the angle of taper is small, you may obtain approximate results by applying the formulas for a thin-walled prismatic tube to a differential element of the tapered tube and then integrating along the axis of the tube.
A hollow tube ABCDE constructed of monel metal is subjected to five torques acting in the directions shown in the figure. The magnitudes of the torques are T1= 1000 lb-in., T2= T4= 500 lb-in., and T3= T5= 800 lb-in. The tube has an outside diameter of d2= 1.0 in. The allowable shear stress is 12,000 psi and the allowable rate of twist is 2.0°/ft. Determine the maximum permissible inside diameter d1, of the tube.
A motor driving a solid circular steel shaft with diameter d = 1.5 in, transmits 50 hp to a gear at B, The allowable shear stress in the steel is 6000 psi. Calculate the required speed of rotation (number of revolutions per minute) so that the shear stress in the shaft does not exceed the allowable limit.
A solid circular shaft AB of diameter d is fixed against rotation at both ends (sec figure), A circular disk is attached to the shaft at the location shown. What is the largest permissible angle of rotation 0max of the disk if the allowable shear stress in the shaft is Tallow? [Assume that a >b. Also, use Eqs. (3-50a and b) of Example 3-9 to obtain the reactive torques.]
A propeller shaft of solid circular cross section and diameter d is spliced by a collar of the same material (see figure). The collar is securely bonded to both parts of the shaft. What should be the minimum outer diameter dyof the collar in order that the splice can transmit the same power as the solid shaft?
Compare the angle of twist 1 for a thin-walled circular tube (see figure) calculated from the approximate theory for thin-walled bars with the angle of twist 2 calculated from the exact theory of torsion for circular bars, Express the ratio 12terms of the non-dimensional ratio ß = r/t. Calculate the ratio of angles of twist for ß = 5, 10, and 20. What conclusion about the accuracy of the approximate theory do you draw from these results?
A full quarter-circular fillet is used at the shoulder of a stepped shaft having diameter D2= 1.0 in. (see figure), A torque T = 500 lb-in. acts on the shaft. Determine the shear stress at the stress concentration for values as follows: D1= 0.7,0.8, and 0.9 in. Plot a graph showing versus D?
A solid circular bar A BCD with fixed supports at ends A and D is acted upon by two equal and oppositely directed torques T0, as shown in the figure. The torques arc applied at points B and C each of which is located at distance x from one end of the bar. (The distance x may vary from zero to L/2.) For what distance x will the angle of twist at points B and C be a maximum? What is the corresponding angle of twist 0max?
A stepped shaft ACE is held against rotation at ends A and B and subjected to a torque T0acting at section C(see figure). The two segments of the shaft (AC and CB) have diameters dAand dg, respectively, and polar moments of inertia IpAand IpBrespectively. The shaft has length L and segment AC has length a. For what ratio a/L will the maximum shear stresses be the same in both segments of the shaft? For what ratio a/L will the internal torques be the same in both segments of the shaft?