Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
bartleby

Videos

Textbook Question
Book Icon
Chapter 3, Problem 3.4.22P

-22 Two tubes (AB, BC) of the same material arc connected by three pins (pin diameter = d ) just left of B as shown in the figure. Properties and dimensions for each tube are given in the figure. Torque 2ris applied at x = 2L/5 and uniformly distributed torque intensity tQ= 37/L is applied on tube BC. (a)

Find the maximum value of load variable T(N m) based on allowable shear (tx) and bearing(cha ) stresses in the three pins which connect the two tubes at B.

Use the following numerical properties:

L = 1.5m, E = 74GPa, v = 0.33, dp= 18mm, ta=45MPa, =90 MPa, di=85 mm, di = T$ mm, and d360 mm.

(b)

What is the maximum shear stress in the tubes

for the applied torque in part (a)?

  Chapter 3, Problem 3.4.22P, -22 Two tubes (AB, BC) of the same material arc connected by three pins (pin diameter = d ) just

(a)

Expert Solution
Check Mark
To determine

The maximum value of load variable for the given parameters.

Answer to Problem 3.4.22P

The maximum value of load variable for the given parameters is = 875306Nmm.

Explanation of Solution

Given information:

The total length of the tube is 1.5m, young’s modulus of elasticity is 74GPa, poison ratio is 0.33, diameter of the pin is 18mm, shear stress at point (A) is τaand the bending stress is 90MPa, the outer diameter of the first tube is 85mm, the outer diameter of the second tube is 73mmand the inner diameter of the second tube is 60mm.

       Figure (1) shows the segment from point (A) to x2L5.

  Mechanics of Materials (MindTap Course List), Chapter 3, Problem 3.4.22P , additional homework tip  1

       Figure-(1)

Write the expression for moment about xaxis for the system.

  RA+2Toto(2L5)=0...... (I)

Here, the reaction force at point (A) is RA, the length of the beam tube is Land the uniform distributed torque intensity is to.

Substitute 3To5for toin Equation (I)

  RA+2To3To5(2L5)=0RA=4To5...... (II)

Here, T(x)=RA.

Substitute T(x)for RAin Equation (II).

  T(x)=4To5

       Figure-(2) shows the segment from point Ato point between 2L5<x3L5.

  Mechanics of Materials (MindTap Course List), Chapter 3, Problem 3.4.22P , additional homework tip  2

       Figure-(2)

Write the expression for moment about xaxis for the system.

  T2(x)=45To2ToT2(x)=65To...... (III)

Write the expression for the moment about xaxis for the element 35LxL.

  T3(x)=45To2To+to(x35L)...... (IV)

Substitute 3L5for xin Equation (IV)

  T3(x)=45To2To+to(3L535L)=65To

Substitute Lfor xin Equation (IV)

  T3(x)=45To2To+3ToL(L35L)=0

Maximum torsional moment in both ABand BCis same

  Tmax=6T5...... (V)

Write the expression for torque.

  T=F×r...... (VI)

Here, torque is T, force on the pin is Fand the radius is r.

Write the expression for force on the pin.

  F=6T53(d12t12)...... (VII)

Here, the force on the pin is F, the diameter of the tube ABis d1and the thickness of the tube is t1.

Write the expression for bearing stress on the pin due to the torque.

  σb1=Fdpt1...... (VIII)

Here, the bearing stress on the pin is σb1and the diameter of the pin is dp.

Substitute 6T53(d12t12)for Fin Equation (VIII).

  σb1=6T53(d12t12)×(1dpt1)T=(σb1×dpt1)32(d1t1)56...... (IX)

Calculation:

Substitute 90MPafor σb1, 18mmfor dp, 6mmfor t1and 85mmfor d1in Equation (IX).

  T=((90MPa)×(18mm)(6mm))32((85mm)6mm)56=((90MPa(106Pa1MPa))×(18mm)(6mm))32((85mm)6mm)56=972×107×32((85mm)6mm)56=959850Nmm

Substitute 90MPafor σb1, 18mmfor dp, 6.5mmfor t1and 73mmfor d1in Equation (IX).

  T=((90MPa)×(18mm)(6.5mm))32((73mm)6.5mm)56=((90MPa(106Pa1MPa))×(18mm)(6.5mm))32((73mm)6.5mm)56=1.053×1010×32((73mm)6.5mm)56=875306Nmm

Conclusion:

The maximum value of load variable for the given parameters is = 875306Nmm.

(b)

Expert Solution
Check Mark
To determine

The maximum shear stress in the tubes.

Answer to Problem 3.4.22P

The maximum shear stress in the tubes is = 25.28MPa.

Explanation of Solution

Write the expression for maximum shear stress for the applied torque

  τmax=Tmax×(d2)Ip...... (X)

Here, the maximum shear stress is τmaxand the polar moment of inertia is Ip

Write the expression for maximum torque.

  Tmax=65T...... (XI)

Write the expression for the polar moment of inertia of section AB

  Ip1=π32(d14d24)..... (XII)

Here, the polar moment of inertia is Ip1.

Write the expression for the polar moment of inertia of section BC.

  Ip2=π32(d24d34)..... (XII)

Here, the polar moment of inertia is Ip2.

Calculation:

Substitute 85mmfor d1and 73mmfor d2in Equation (XII)

  Ip1=π32((85mm)4(73mm)4)=0.098((85mm(1m1000mm))4(73mm(1m1000mm))4)=2.3368×106m4

Substitute 73mmfor d1and 60mmfor d2in Equation (XII).

  Ip2=π32((73mm)4(60mm)4)=0.098((73mm(1m1000mm))4(60mm(1m1000mm))4)=1.516×106m4

Substitute 875306Nmmfor Tin Equation ()

  Tmax=65(875306Nmm)=1050367.2Nmm(1m1000mm)=1050Nm

Substitute 1050Nmfor Tmax

  2.3368×106m4for Ipand 85mmfor din Equation (X).

  τmax=1050Nm×(85mm2)2.3368×106m4=1050Nm×(85mm(1m1000mm)2)2.3368×106m4=19.1MPa

Substitute 1050Nmfor Tmax

  1.516×106m4for Ip2and 73mmfor din Equation (X).

  τmax=1050Nm×(73mm2)1.516×106m4=1050Nm×(73mm(1m1000mm)2)1.516×106m4=25.28MPa

Conclusion:

The maximum shear stress in the tubes is 25.28MPa.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 3 Solutions

Mechanics of Materials (MindTap Course List)

Ch. 3 - A prospector uses a hand-powered winch (see...Ch. 3 - When drilling a hole in a table leg, a furniture...Ch. 3 - While removing a wheel to change a tire, a driver...Ch. 3 - -8 An aluminum bar of solid circular cross section...Ch. 3 - A high-strength steel drill rod used for boring a...Ch. 3 - The steel shaft of a socket wrench has a diameter...Ch. 3 - A circular tube of aluminum is subjected to...Ch. 3 - A propeller shaft for a small yacht is made of a...Ch. 3 - Three identical circular disks A, B, and Care...Ch. 3 - The steel axle of a large winch on an ocean liner...Ch. 3 - A hollow steel shaft used in a construction auger...Ch. 3 - Solve the preceding problem if the shaft has an...Ch. 3 - A vertical pole of solid, circular cross section...Ch. 3 - A vertical pole of solid, circular cross section...Ch. 3 - A solid brass bar of diameter d = 1.25 in. is...Ch. 3 - A hollow aluminum tube used in a roof structure...Ch. 3 - A circular tube of inner radius r1and outer radius...Ch. 3 - .1 A stepped shaft ABC consisting of two solid...Ch. 3 - A circular tube of outer diameter d3= 70 mm and...Ch. 3 - A stepped shaft ABCD consisting of solid circular...Ch. 3 - A solid, circular bar ABC consists of two...Ch. 3 - A hollow tube ABCDE constructed of monel metal is...Ch. 3 - A shaft with a solid, circular cross section...Ch. 3 - Prob. 3.4.7PCh. 3 - Two sections of steel drill pipe, joined by bolted...Ch. 3 - Prob. 3.4.9PCh. 3 - -10. A tapered bar AB with a solid circular cross...Ch. 3 - A tapered bar AB with a solid circular cross...Ch. 3 - The bar shown in the figure is tapered linearly...Ch. 3 - The non prismatic, cantilever circular bar shown...Ch. 3 - A uniformly tapered tube AB with a hollow circular...Ch. 3 - A uniformly tapered aluminum-alloy tube AB with a...Ch. 3 - For the thin nonprismatic steel pipe of constant...Ch. 3 - .17 A mountain-bike rider going uphill applies...Ch. 3 - A prismatic bar AB of length L and solid circular...Ch. 3 - A prismatic bar AB with a solid circular cross...Ch. 3 - A magnesium-alloy wire of diameter d = 4mm and...Ch. 3 - A nonprismatic bar ABC with a solid circular cross...Ch. 3 - -22 Two tubes (AB, BC) of the same material arc...Ch. 3 - A circular copper bar with diameter d = 3 in. is...Ch. 3 - A circular steel tube with an outer diameter of 75...Ch. 3 - A hollow aluminum shaft (see figure) has an...Ch. 3 - A hollow steel bar (G = 80 GPa ) is twisted by...Ch. 3 - A tubular bar with outside diameterd2= 4.0 in, is...Ch. 3 - A solid circular bar of diameter d = 50 mm (see...Ch. 3 - -7 A steel tube (G = 11.5 x 106 psi) has an outer...Ch. 3 - A solid circular bar of steel (G = 78 GPa)...Ch. 3 - The normal strain in the 45n direction on the...Ch. 3 - An aluminum tube has inside diameter dx= 50 mm,...Ch. 3 - -11 A solid steel bar (G = 11.8 X 106 psi ) of...Ch. 3 - A solid aluminum bar (G = 27 GPa ) of diameter d =...Ch. 3 - Two circular aluminum pipes of equal length L = 24...Ch. 3 - A generator shaft in a small hydroelectric plant...Ch. 3 - A motor drives a shaft at 12 Hz and delivers 20 kW...Ch. 3 - A motor driving a solid circular steel shaft with...Ch. 3 - Prob. 3.7.4PCh. 3 - The propeller shaft of a large ship has an outside...Ch. 3 - The drive shaft for a truck (outer diameter 60 mm...Ch. 3 - A hollow circular shaft for use in a pumping...Ch. 3 - A tubular shaft being designed for use on a...Ch. 3 - A propeller shaft of solid circular cross section...Ch. 3 - What is the maximum power that can be delivered by...Ch. 3 - A motor delivers 275 hp at 1000 rpm to the end of...Ch. 3 - Prob. 3.7.12PCh. 3 - A solid circular bar ABCD with fixed supports is...Ch. 3 - A solid circular bar A BCD with fixed supports at...Ch. 3 - A solid circular shaft AB of diameter d is fixed...Ch. 3 - A ho 1 low st e el shaft ACB of outside diameter...Ch. 3 - A stepped shaft ACB having solid circular cross...Ch. 3 - A stepped shaft ACB having solid circular cross...Ch. 3 - A stepped shaft ACE is held against rotation at...Ch. 3 - A solid circulai' aluminum bar AB is fixed at both...Ch. 3 - Two sections of steel drill pipe, joined by bolted...Ch. 3 - A circular bar AB of length L is fixed against...Ch. 3 - A circular bar AB with ends fixed against rotation...Ch. 3 - A solid steel bar of diameter d1= 25.0 mm is...Ch. 3 - A solid steel bar of diameter d1= 1.50 in. is...Ch. 3 - The composite shaft shown in the figure is...Ch. 3 - The composite shaft shown in the figure is...Ch. 3 - A steel shaft (Gs= 80 GPa) of total length L = 3.0...Ch. 3 - A uniformly tapered aluminum-ally tube AB of...Ch. 3 - Two pipes {L, = 2.5 m and L, = 1.5 m) are joined...Ch. 3 - A solid circular bar of steel (G = 1L4 × 106 psi)...Ch. 3 - A solid circular bar of copper (G = 45 GPa) with...Ch. 3 - A stepped shaft of solid circular cross sections...Ch. 3 - A stepped shaft of solid circular cross sections...Ch. 3 - A circular tube AB is fixed at one end and free at...Ch. 3 - A cantilever bar of circular cross section and...Ch. 3 - Obtain a formula for the strain energy U of the...Ch. 3 - A statically indeterminate stepped shaft ACE is...Ch. 3 - Derive a formula for the strain energy U of the...Ch. 3 - A thin-walled hollow tube AB of conical shape has...Ch. 3 - A hollow circular tube A fits over the end of a...Ch. 3 - A heavy flywheel rotating at n revolutions per...Ch. 3 - A hollow circular tube having an inside diameter...Ch. 3 - A solid circular bar having diameter d is to be...Ch. 3 - A thin-walled aluminum tube of rectangular cross...Ch. 3 - A thin-walled steel tube of rectangular cross...Ch. 3 - A square tube section has side dimension of 20 in....Ch. 3 - A thin-walled circular tube and a solid circular...Ch. 3 - A thin-walled steel tube having an elliptical...Ch. 3 - Calculate the shear stress and the angle of twist...Ch. 3 - A torque T is applied to a thin-walled tube having...Ch. 3 - Compare the angle of twist 1 for a thin-walled...Ch. 3 - A tubular aluminum bar (G = 4 × 106 psi) of square...Ch. 3 - A thin tubular shaft with a circular cross section...Ch. 3 - A thin-walled rectangular tube has uniform...Ch. 3 - A long, thin-walled tapered tube AB with a...Ch. 3 - A stepped shaft consisting of solid circular...Ch. 3 - A stepped shaft with diameters D1= 40 mm and D2=...Ch. 3 - A full quarter-circular fillet is used at the...Ch. 3 - The stepped shaft shown in the figure is required...Ch. 3 - A stepped shaft (see figure) has diameter D2= 1.5...
Knowledge Booster
Background pattern image
Mechanical Engineering
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
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
BEARINGS BASICS and Bearing Life for Mechanical Design in 10 Minutes!; Author: Less Boring Lectures;https://www.youtube.com/watch?v=aU4CVZo3wgk;License: Standard Youtube License