A single torque of T = 50 N-m is applied to a compound torsion member. Segment (1) is a 32-mm diameter solid brass (G = 37 GPa) rod. Segment (2) is a solid aluminum (G = 26 GPa) rod. %3D Determine the minimum diameter of the aluminum segment if the rotation angle at C relative to support A must not exceed 3°.

A single torque of T = 50 N-m is applied to a compound torsion member. Segment (1) is a 32-mm diameter solid brass (G = 37 GPa) rod. Segment (2) is a solid aluminum (G = 26 GPa) rod. %3D Determine the minimum diameter of the aluminum segment if the rotation angle at C relative to support A must not exceed 3°.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.3.17P: A stepped shaft ABC consisting of two solid, circular segments is subjected to torques T}and...

See similar textbooks

Related questions

Q: A solid bar of circular cross section has a diameter of 40mm and length of 1300mm. G=80GPa and…

A: Given T = 340Nm. , d = 40mm = 0.04m.

Q: (A,) See the figure below. There are two torques applied at B and D. Segment CD is a tube, while AB…

A: In the given problem, the dimensions and Modulus of rigidity have been converted to feet. Radius,…

Q: A hollow aluminium shaft of 80 mm outer diameter & 60 mm inner diameter is rotating @ 5 Hz when…

Q: A single torque of T = 60 N.m is applied to a compound torsion member. Segment (1) is a 32-mm…

Q: The figure below shows a shaft of three segments. It is restrained (fixed support) at both sides and…

A: Bronze: Length, Lbronze= 2 mDiameter, Dbronze= 25 mm= 25×10-3 mGbronze= 35 GPa= 35×109 Pa Aluminum:…

Q: The torsional assembly consists of solid 1.6 in. diameter aluminum [G = 4,000 ksi] segments (1) and…

Q: The assembly shown consists of the solid steel shaft (1) with a diameter of D₁ = 14 in and a copper…

A: According to the given dataThe outer diameter of the BC=D2=7.5 int2=0.35 inThe diameter of the…

Q: A shaft consisting of an aluminum segment and a steel segment is acted upon by two torques. The…

A: The diameter of the aluminum section is The diameter of steel section is The shear modulus of…

Q: The diameter of and LCD = 240 mm. 1. The lengths LAB = LBC = 200 mm parts AB and CD of the bar is 25…

A: Find the angle of twist and torque .

Q: The solid-circular member AC, having a diameter D and a shear modulus of 69 GPa, is subjected to the…

Q: A constant torque of 75 lb-in. is applied to the circular rod below, with a radius of 2 in. The…

A: We have:- Twisting momentT=75lb-in=8473.86N-mmRadius of shaftR=2in=50.8mm⇒Polar Moment of Inertia of…

Q: 3. A cylindrical rod is composed of two pieces of different diameters. Both pieces are made of the…

A: As per given Question TB=4000 in-lb TD=3000 in-lb JAC=4 in4 JCD=2 in4 L=10 in G=10×106 We have…

Q: An aluminium bar is in the form of an equilateral triangle 30 mm on a side. What torque is required…

A: We know that an aluminium bar has 30 mm on each side and is in the shape of an equilateral…

Q: A steel cable is supporting a load of F = 9800 lb and is wrapped around a drum attached to gear A as…

Q: The copper pipe has an outer diameter of 2.5 in. and an inner diameter of 2.25 in. It is tightly…

A: Given data is

Q: 1. The rotating solid steel shaft is simply supported by bearings at points B and C and is driven by…

A: given data D=150mmSy=420Mpaθ=20°SUT=560MpaTA=340NmFOS=2.5(A) Consider the equation of torque acting…

Q: 2. A shaft is designed to carry torque as shown below. The shaft consists of a steel rod which is…

Q: The 60 mm diameter solid shaft is subjected to the distributed and concentrated torsional loadings…

Q: The steel shaft is made from two segments: AC has a diameter of 50 mm, and CB has a diameter of 100…

Q: 2. A steel shaft rotating at 600 rpm is supported by two bearings as shown. E=30 Mşi, d=1.0" (inch),…

A: Assume the shaft is static initially and evaluate the reaction forces at bearing supports.Consider…

Q: 7. You are applying torque of 50Nm to a rectangular bar, with a width (b) of 5cm and a height (h) of…

A: Since we only answer only 1 question. We’ll answer the first question since the exact one wasn’t…

Q: A steel shaft with a length of 3.00 m. One meter of the steel is contained in a brass tube and…

Q: A single torque of T = 60 N.m is applied to a compound torsion member. Segment (1) is a 32-mm…

A: The angle of rotation: The angle at which the fixed end rotates with respect to the free end is…

Q: A brass rod 8mm diameter and 400mm long fits centrally inside aluminum tube of the same length…

Q: Torsional T is applied to the hollow axis (G=80 GPa). Ewha Womans University, the maximum shear…

Q: 1. A solid cylindrical rod is made of brass (G = 39 GPa); the rod has a diameter of 42 mm and is 750…

Q: A steel shaft BCD (G=80 GPa) of total length 3 m is encased for 1/3 of its length by a bronze sleeve…

A: given data; ⇒stifness of steel shaft (G)=80GPa⇒diameter of steel shaft (D1)=60mm⇒stiffness of bronze…

Q: Question 4 fixed. The shear modulus G and the polar moment of inertia I, of the bar's cross-section…

Q: 4-Determine the rotation angle between A and C, if the torque is T=0.9 N.m in point C, if G=80 GPa…

A: The torque at point C is given as, T=0.9 N.m The modulus of rigidity is given as, G=80 GPa The…

Q: Question 3 The 80-mm diameter shaft, having an ultimate tensile and compressive strength of 80 MPa…

A: Given Data The diamater of the shaft is:d=80 mm The tensile strength is:St=80MPa The conmpressive…

Q: The compound shaft is attached to a rigid wall at each end and is subjected to the torque T = 10…

Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

Problem (4):
(1)
T= 50 N-m
B
1,800 mm
800 mm
A single torque of T = 50 N-m is applied to a
compound torsion member. Segment (1) is a 32-mm
diameter solid brass (G = 37 GPa) rod. Segment (2)
is a solid aluminum (G = 26 GPa) rod.
%3D
%3D
Determine the minimum diameter of the aluminum
segment if the rotation angle at C relative to
support A must not exceed 3°.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

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?
Two sections of steel drill pipe, joined by bolted flange plates at Ä are being tested to assess the adequacy of both the pipes. In the test, the pipe structure is fixed at A, a concentrated torque of 500 kN - m is applied at x = 0.5 m, and uniformly distributed torque intensity t1= 250 kN m/m is applied on pipe BC. Both pipes have the same inner diameter = 200 mm. Pipe AB has thickness tAB=15 mm, while pipe BC has thickness TBC= 12 mm. Find the maximum shear stress and maximum twist of the pipe and their locations along the pipe. Assume G = 75 GPa.
A solid circulai' aluminum bar AB is fixed at both ends and loaded by a uniformly distributed torque 150N·n/m. The bar has diameter d = 30 mm. Calculate the reactive torques at the supports and the angle of twist at midspan. Assume that G = 28 GPa.
A tubular shaft being designed for use on a construction site must transmit 120 kW at 1,75 Hz, The inside diameter of the shaft is to be one-half of the outside diameter. If the allowable shear stress in the shaft is 45 MPa, what is the minimum required outside diameter d?
A stepped shaft ABC consisting of two solid, circular segments is subjected to torques T}and T2acting in opposite directions, as shown in the figure. The larger segment of the shaft has a diameter of dv- 2.25 in. and a length Lt= 30 in.; the smaller segment has a diameter d2— 1.75 in. and a length L, = 20 in. The torques are T, = 21,000 lb-in. and fz=10.000 lb-in. (a) Find reaction torque TAat support A. (b) Find the internal torque T(x) at two locations: x = L1/2 and x = L1+ L2/2. Show these internal torques on properly drawn free-body diagrams (FBDs).
A magnesium-alloy wire of diameter d = 4mm and length L rotates inside a flexible tube in order to open or close a switch from a remote location (see figure). A torque Tis applied manually (either clockwise or counterclockwise) at end 5, thus twisting the wire inside the tube. At the other end A, the rotation of the wire operates a handle that opens or closes the switch. A torque T0 = 0.2 N · m is required to operate the switch. The torsional stiffness of the tube, combined with friction between the tube and the wire, induces a distributed torque of constant intensity t = 0.04N m/m (torque per unit distance) acting along the entire length of the wire. (a) If the allowable shear stress in the wire is T allow = 30 MPa, what is the longest permissible length Lmaxof the wire?
Three round, copper alloy bars having the same length L but different shapes are shown, in the figure. The first bar has a diameter d over its entire length, the second has a diameter d over one-fifth of its length, and the third has a diameter d over one-fifteenth of its length. Elsewhere, the second and third bars have a diameter Id. All three bars are subjected to the same axial load P. Use the following numerical data: P = 1400 kN, L = 5m,d= 80 mm, E= 110 GPa. and v = 0.33. (a) Find the change in length of each bar. (b) Find the change in volume of each bar.
Repeat Problem 2.3-4, but now include the weight of the bar. Sec Table 1.1 in Appendix I for the weight density of steel.
Repeat Problem 11.2-3 assuming that R= 10 kN · m/rad and L = 2 m.
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 small lab scale has a rigid L-shaped frame ABC consisting of a horizontal arm AB (length b = 10 in.) and a vertical arm BC (length c = 7 in.) pivoted al point B. The pivot is attached to the outer frame BCD that stands on a laboratory bench. The position of the pointer al C is controlled by a spring, Jt = 5 lb/in., that is attached to a threaded rod. The pitch of the threads is p = 1/16 in. Under application of load W, 12 revolutions of the nut are required to bring the pointer back to the mark. Calculate the weight W.
Repeat Problem 11.3-9. Use two C 150 × 12.2 steel shapes and assume that E = 205 GPa and L = 6 m.