A circular shaft AB of length L is fixed against rotation at the ends and loaded by a distributed torque (x) that varies linearly in intensity from zero at end A to to at end B (see figure). The reaction torque at B is known to be toL/3. Find the reaction torque at A, then plot the torsional moment diagram.

A circular shaft AB of length L is fixed against rotation at the ends and loaded by a distributed torque (x) that varies linearly in intensity from zero at end A to to at end B (see figure). The reaction torque at B is known to be toL/3. Find the reaction torque at A, then plot the torsional moment diagram.

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 3.4.18P: A prismatic bar AB of length L and solid circular cross section (diameter d) is loaded by a...

See similar textbooks

Similar questions

Find expressions for shear force V and moment Mat x = 2L/3 of beam (a) in terms of peak load intensity q0and beam length variable L. Repeat for beam (b) but at x = L/2.
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.
Find shear (V) and moment (M) at x = 3L/4 for the beam shown in Fig. a. Let MA= 24 kN m,P = 48 kN, L = 6 m, and q0= 8 kN/m. Repeat for the beam in Fig, b (first solve for the reaction moment at fixed support A).
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).
Find expressions for shear force V and moment M at x = x0of beam AB in terms of peak load intensity q0and beam length variable L. Let x0= 2L/3.
Frame ABCD carries two concentrated loads (2P at T and P at ZX see figure) and also a linearly varying distributed load on AB, Find expressions for shear force Fand moment A/at x = L/3 of beam AB in terms of peak load intensity q0, force P, and beam length variable L. Let q0= P/L.
A stepped shaft consisting of solid circular segments having diameters D1= 2.0 in, and D2= 2.4 in. (see figure) is subjected to torques T. The radius of the fillet is R = 0,1 in. If the allowable shear stress at the stress concentration is 6000 psi, what is the maximum permissible torque Tmax?
A uniformly tapered tube AB with a hollow circular cross section is shown in the figure. The tube has constant wall thickness t and length L, The average diameters at the ends are dAand dB= 2dA. The polar moment of inertia may be represented by the approximate formula Ipttd3t4[see Eq. (3-21)]. Derive a formula for the angle of twist e of the tube when it is subjected to torques T acting at the ends.
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?
Find expressions for shear force V and moment M at mid-span of beam AB in terms of peak load intensity q0and beam length variables a and L Let a = 5L/b.
A prismatic bar AB of length L and solid circular cross section (diameter d) is loaded by a distributed torque of constant intensity t per unit distance (sec figure). Determine the maximum shear stress tmaxin the bar. Determine the angle of twist between t the ends of the bar.
A round bar ABC of length 2L (see figure) rotates about an axis through the midpoint C with constant angular speed w (radians per second). The material of the bar has weight density y. (a) Derive a formula for the tensile stress a’ in the bar as a function of the distance x from the midpoint C. (b) What is the maximum tensile stress a max?