EBK MECHANICS OF MATERIALS
10th Edition
ISBN: 8220102744110
Author: HIBBELER
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 9.3, Problem 9.1P
Prove that the sum of the normal stresses σx + σy = σx′ + σy′ is constant. See Figs.9-2a and 9-2b.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Two blocks joined by a single pin are subjected to a pulling force of P = 250 Ib. The pin has a diameter of 0.25 in and the
dimensions of the blocks with respect to the figure below are listed below.
a = 2.42 in
b = 1.52 in
C = 1.5 in
ti = 0.89 in
t2 = 1.2 in
Note that the dimensions b and c represent the distance from the edge of the block to the middle of the pin
t, 1
a
Vinter201920-Engr220-001/images/9de8f780-b478-3fb6-91f7-bd1015381538_fafc4bb4-e5d
Image is not drawn to scale.
Calculate the normal stresses at points A and B of the bracket caused by the 30-kN force.
A machine component is fabricated from a bent tube as shown below. One part of the tube lies along the z-
axis, and the other part is parallel to the y-axis. The outside diameter of the tube is do 122 mm and its
inside diameter is dį = 108 mm. A force F = 8.5 kN acts along a line from point to point D. Determine
the principal stresses and the absolute maximum shear stresses at points A and B. Note that point A lies
along the y-axis and point Blies along the x-axis.
Given:
• L₁ 258 mm
L₂ = 118 mm
• L -281 mm
LA-602 mm
4
P
(α₂₁)A-
(₁2) A
(Tmax) A
L2
Z
²1
00
B
L₁7
number (rtol=0,01, atol=1e-05)
number (rtol-0.01, atol-1e-05)
number (rtol-0.01 atol-le-057
F
0
MPA
LA
D
L3
y
0
0
Chapter 9 Solutions
EBK MECHANICS OF MATERIALS
Ch. 9.3 - In each case, the state of stress x, y, xy...Ch. 9.3 - Given the state of stress shown on the element,...Ch. 9.3 - Determine the normal stress and shear stress...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - Also, find the corresponding orientation of the...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - Determine the maximum principal stress at point B.Ch. 9.3 - Determine the principal stress at point C.Ch. 9.3 - Prove that the sum of the normal stresses x + y =...Ch. 9.3 - Determine the stress components acting on the...
Ch. 9.3 - Determine the stress components acting on the...Ch. 9.3 - Determine the normal stress and shear stress...Ch. 9.3 - Determine the normal stress and shear stress...Ch. 9.3 - Determine the stress components acting on the...Ch. 9.3 - Determine the stress components acting on the...Ch. 9.3 - Solve Prob.97 using the stress transformation...Ch. 9.3 - Determine the stress components acting on the...Ch. 9.3 - Solve Prob.99 using the stress transformation...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - Determine the equivalent slate of stress on an...Ch. 9.3 - Determine the stress components acting on the...Ch. 9.3 - Determine (a) the principal stresses and (b) the...Ch. 9.3 - The state of stress at a point is shown on the...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - A point on a thin plate is subjected to the two...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - The stress along two planes at a point is...Ch. 9.3 - The stress acting on two planes at a point is...Ch. 9.3 - The state of stress at a point in a member is...Ch. 9.3 - The grains of wood in the board make an angle of...Ch. 9.3 - The wood beam is subjected to a load of 12 kN. If...Ch. 9.3 - The internal loadings at a section of the beam are...Ch. 9.3 - Solve Prob.925 for point B. 925. The internal...Ch. 9.3 - Solve Prob.925 for point C. 925. The internal...Ch. 9.3 - It is subjected to a torque of 12 kip in. and a...Ch. 9.3 - The bell crank is pinned at A and supported by a...Ch. 9.3 - The beam has a rectangular cross section and is...Ch. 9.3 - A paper tube is formed by rolling a cardboard...Ch. 9.3 - Solve Prob.931 for the normal stress acting...Ch. 9.3 - The 2-in.-diameter drive shaft AB on the...Ch. 9.3 - Determine the principal stresses in the...Ch. 9.3 - The internal loadings at a cross section through...Ch. 9.3 - The internal loadings at a cross section through...Ch. 9.3 - The shaft has a diameter d and is subjected to the...Ch. 9.3 - The steel pipe has an inner diameter of 2.75 in....Ch. 9.3 - Solve Prob.938 for point B, w1ich is located on...Ch. 9.3 - The wide-flange beam is subjected to the 50-kN...Ch. 9.3 - Solve Pro b. 9-40 for point B located on the web...Ch. 9.3 - The box beam is subjected to the 26-kN force that...Ch. 9.3 - Solve Prob.942 for point B. 942. The box beam is...Ch. 9.4 - Use Mohrs circle to determine the normal stress...Ch. 9.4 - Also, find the corresponding orientation of the...Ch. 9.4 - Draw Mohrs circle and determine the principal...Ch. 9.4 - Determine the principal stresses at a point on the...Ch. 9.4 - Determine the principal stresses at point A on the...Ch. 9.4 - Point A is just below the flange.Ch. 9.4 - Solve Prob.9-2 using Mohrs circle. 92. Determine...Ch. 9.4 - Solve Prob.93 using Mohrs circle. 93. Determine...Ch. 9.4 - Solve Prob.96 using Mohrs circle. 96. Determine...Ch. 9.4 - Solve Prob.911 using Mohrs circle. 911. Determine...Ch. 9.4 - Solve Prob.915 using Mohrs circle. 915. The state...Ch. 9.4 - Solve Prob.916 using Mohrs circle. 916. Determine...Ch. 9.4 - Mohrs circle for the state of stress is shown in...Ch. 9.4 - Determine (a) the principal stresses and (b) the...Ch. 9.4 - Determine (a) the principal stresses and (b) the...Ch. 9.4 - Determine the equivalent state of stress if an...Ch. 9.4 - Draw Mohrs circle that describes each of the...Ch. 9.4 - Draw Mohrs circle trial describes each of the...Ch. 9.4 - Determine (a) the principal stresses and (b) the...Ch. 9.4 - Determine (a) the principal stresses and (b) the...Ch. 9.4 - Determine (a) the principal stresses and (b) the...Ch. 9.4 - Determine (a) the principal stresses and (b) the...Ch. 9.4 - Determine (a) the principal stresses and (b) the...Ch. 9.4 - Draw Mohrs circle that describes each of the...Ch. 9.4 - The grains of wood in the board make an angle of...Ch. 9.4 - The post is fixed supported at its base and a...Ch. 9.4 - Determine the principal stresses, the maximum...Ch. 9.4 - The thin-walled pipe has an inner diameter of 0.5...Ch. 9.4 - The frame supports the triangular distributed load...Ch. 9.4 - The frame supports the triangular distributed load...Ch. 9.4 - The rotor shaft of the helicopter is subjected to...Ch. 9.4 - The pedal crank for a bicycle has the cross...Ch. 9.4 - A spherical pressure vessel has an inner radius of...Ch. 9.4 - The cylindrical pressure vessel has an inner...Ch. 9.4 - Determine the normal and shear stresses at point D...Ch. 9.4 - Determine the principal stress at point D, Which...Ch. 9.4 - If the box wrench is subjected to the 50 lb force,...Ch. 9.4 - If the box wrench is subjected to the 50-lb force,...Ch. 9.4 - The post is fixed supported at its base and the...Ch. 9.5 - Draw the three Mohrs circles that describe each of...Ch. 9.5 - Draw the three Mohrs circles that describe the...Ch. 9.5 - Draw the three Mohrs circles that describe the...Ch. 9.5 - Determine the principal stresses and the absolute...Ch. 9.5 - Determine the principal stresses and the absolute...Ch. 9.5 - Determine the principal stresses and the absolute...Ch. 9.5 - Determine the principal stresses and the absolute...Ch. 9.5 - The solid shaft is subjected to a torque, bending...Ch. 9.5 - The frame is subjected to a horizontal force and...Ch. 9.5 - The bolt is fixed to its support at C. If a force...Ch. 9.5 - The bolt is fixed to its support at C. If a force...Ch. 9 - Prob. 9.1RPCh. 9 - The steel pipe has an inner diameter of 2.75 in....Ch. 9 - Determine the equivalent state of stress If an...Ch. 9 - The crane is used to support the 350-lb load....Ch. 9 - Determine the equivalent state of stress on an...Ch. 9 - The propeller shaft of the tugboat is subjected to...Ch. 9 - Determine the principal stresses in the box beam...Ch. 9 - Determine (a) the principal stresses and (b) the...Ch. 9 - Determine the stress components acting on the...
Additional Engineering Textbook Solutions
Find more solutions based on key concepts
Repeat Problem 4-6 except solve by the vector loop method.
DESIGN OF MACHINERY
List several uses of the arbor press.
Machine Tool Practices (10th Edition)
The spring of k and unstretched length 1.5R is attached to the disk at a radial distance of 0.75R from the cent...
Engineering Mechanics: Statics
Assume the following vectors are already defined: V1=[302]V2=[214]V3=[5131]V4=[0.50.10.20.2] For each of the fo...
Thinking Like an Engineer: An Active Learning Approach (4th Edition)
Select a mechanical component from Part 3 of this book (roller bearings, springs, etc.), go to the Internet, an...
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
23.23 A highly oxidized and uneven round bar is being turned on a lathe. Would you recommend a small or a large...
Manufacturing Engineering & Technology
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
- Determine the principal stresses at points A and B of the cylinder. Consider: L = 70 mm; d = 20 mm; F = 12 kN; P = 15 kN; T = 800 Nm.arrow_forwardProblem 2: For the shaft shown below, determine the normal and shear stresses acting on the element located at point A, including stress concentrations. Then draw the stress element at A with the applied stresses and determine the three principal stress (0₁, 02 and, 03) using Mohr's circle. r= 0.0042 m, d = 0.03 m, D = 0.033 m, T= 250 Nm P = 1500 N, M = 300 Nm, A M T J.C₁ P r M T Di darrow_forwardFor the plane-stress condition given below: σx = 400 MPa σy = 500 MPa τxy = - 30 MPa Construct a Mohr’s circle of stress, find: (a) the principal stresses and the orientation of the principal axes relative to the x,y axes (b) determine the stresses on an element, rotated in the x-y plane 60° counter?clockwise from its original position ; Show these stresses on a sketch of an element oriented at this angle (c) Also, using the matrix transformation law to compare the solutions with Mohr’s circlearrow_forward
- Given sigma x=100 MPa, tau xy=50 MPa, determine stresses at an angle 30 degrees CW from x-axis.arrow_forwardSuppose that σ = 330 psi and Try = 150 psi in (Figure 1). Figure Part D Specify the orientation of the principal stress. Take the positive direction of rotation counterclockwise. Express your answer in degrees to three significant figures. Op₁= Part E OF 0₂ = ΑΣΦΙΚΗ vec Specify the orientation of the maximum in-plane shear stress. Take the positive direction of rotation counterclockwise. Express your answer in degrees to three significant figures. 0/ —| ΑΣΦ 11 | vec ? ? oarrow_forwardFill in the blanks. Draw and label the Mohr’s circle. For sigma-yp = 30 kSf. does this fail? Find the stresses on the plane shown. Find the plane on which sigma-1 acts relative to the horizontal. Draw them on the figure. Draw the Tresca plot.arrow_forward
- answer this ; The von Mises equivalent stresses at point H can be calculated as MPaarrow_forwardCalculate non-zero stress components (normal and shear) at points A, B and C. Point C is located at the center of the cross section attached to the wall. Calculate non-zero strain components at point B. Neglect shear stress due to shear force. Given: loading F = 400 N, P-2000 N, and T = 75 N·m, Young's modulus E = 70 GPa, Poisson's ratio v = 0.25 15-mm D. -100 mmarrow_forwardThe internal loadings at a cross section through the 160-mm-diameter drive shaft of a turbine consist of an Part A axial force of 12.5 kN, a bending moment of 1.2 kN m, and a torsional moment of 2.25 kN · m. (Figure 1). Determine the principal stresses at point B. Express your answers using three significant figures separated by a comma. vec ? 01, 02 = 3.112,2.50 MPa Submit Previous Answers Request Answer Figure < 1 of 1 X Incorrect; Try Again; 5 attempts remaining Part B Determine the magnitude of the maximum in-plane shear stress at point B. Express your answer to three significant figures and include the appropriate units. 12.5 kN Tmax = 2.81 MPa 1.2 kN-m Submit Previous Answers 2.25 kN-m v Correctarrow_forward
- 7. Determine the stress developed in the Tensional Cord given that the cable's diameter is 0.6 inches and the bar weigh 6kips. Figure P-106 3 m 5 m 5 m Earrow_forwardConstruct a Mohr's circle for the following point stresses: ox = 60MPa, oy = 10MPa and Txy = +20MPa, and hence determine the stress components and planes in which the shear stress is a maximum.arrow_forwardThe principal strains at a point on the aluminum surface of a tank are P1 = 630(10-6) and P2 = 350(10-6). If this is a case of plane stress, determine the associated principal stresses at the point in the same plane. Eal = 10(103) ksi,nal = 0.33.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Understanding Stress Transformation and Mohr's Circle; Author: The Efficient Engineer;https://www.youtube.com/watch?v=_DH3546mSCM;License: Standard youtube license