EBK MECHANICS OF MATERIALS
7th Edition
ISBN: 8220100257063
Author: BEER
Publisher: YUZU
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 7.2, Problem 64P
The Mohr's circle shown corresponds to the state of stress given in Fig. 7.5a and b. Noting that σx’ = OC + (CX') cos (2θp – 2θ) and that τx’y’ = (CX') sin (2θp – 2θ), derive the expressions for σx’ and τx’y’ given in Eqs. (7.5) and (7.6), respectively. [Hint: Use sin (A + B) = sin A cos B + cos A sin B and cos (A + B) = cos A cos B – sin A sin B.]
Fig. P7.64
Fig. 7.5 (repeated) State of plane stress: (a) referred to {xyz}, (b) referred to {x’y’z’}.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
2.2. The stress at a point is defined by the components Ox=7 ksi, Oyy=10 ksi, ơxy
-20 ksi. Sketch the corresponding Mohr's circle and hence find the maximum
Oyx
in-plane shear stress and the orientation of the planes on which it acts. Illustrate your
answer with a sketch of an appropriately rotated rectangular element, taking care to
indicate the correct direction for the shear stress on these planes.
Problem 2: A state of plane stress at a point on the surface of a structure consists of the
following stress components: Ox = 18 ksi, oy = 24 ksi, and Txy = 15 ksi. Note that the stress
components act in the directions shown on the element below.
Ox
Txy
24 ksi
бу
18 ksi
15 ksi
(a) Draw a complete Mohr's circle for this stress state.
Clearly label the X and Y faces, the center C, and
the radius R.
(b) Using Mohr's circle, determine the stress
components Ox, Oy, and Txy on an element rotated
25° counter-clockwise from the original element
shown. Label all of these quantities on the circle.
(c) Show all stresses from part (b) on a properly
oriented stress element. Be sure to include all
stress components acting on the element.
Problem 1: A state of plane stress at a point on the surface of a structure consists of the
following stress components: Ox = 25 ksi, oy = 12 ksi, and Txy = 10 ksi. Note that the stress
components act in the directions shown on the element below.
Ox
Txy
12 ksi
5
25 ksi
10 ksi
(a) Draw a complete Mohr's circle for this stress state.
Clearly label the X and Y faces, the center C, and
the radius R.
(b) Using Mohr's circle, determine the principal
stresses, the maximum in-plane shear stress, and the
normal stress that acts on the maximum shear stress
plane. Label all of these quantities on the circle.
(c) Calculate the orientation of the principal planes and
the planes of maximum shear stress. Label all of
these quantities on the circle.
(d) Show all stresses from part (b) on properly oriented
stress element(s). Be sure to include all stress
components acting on the elements(s).
Chapter 7 Solutions
EBK MECHANICS OF MATERIALS
Ch. 7.1 - 7.1 through 7.4 For the given state of stress,...Ch. 7.1 - 7.1 through 7.4 For the given state of stress,...Ch. 7.1 - 7.1 through 7.4 For the given state of stress,...Ch. 7.1 - 7.1 through 7.4 For the given state of stress,...Ch. 7.1 - 7.5 through 7.8 For the given state of stress,...Ch. 7.1 - 7.5 through 7.8 For the given state of stress,...Ch. 7.1 - 7.5 through 7.8 For the given state of stress,...Ch. 7.1 - 7.5 through 7.8 For the given state of stress,...Ch. 7.1 - 7.9 through 7.12 For the given state of stress,...Ch. 7.1 - 7.9 through 7.12 For the given state of stress,...
Ch. 7.1 - 7.9 through 7.12 For the given state of stress,...Ch. 7.1 - 7.9 through 7.12 For the given state of stress,...Ch. 7.1 - 7.13 through 7.16 For the given state of stress,...Ch. 7.1 - 7.13 through 7.16 For the given state of stress,...Ch. 7.1 - 7.13 through 7.16 For the given state of stress,...Ch. 7.1 - 7.13 through 7.16 For the given state of stress,...Ch. 7.1 - 7.17 and 7.18 The grain of a wooden member forms...Ch. 7.1 - 7.17 and 7.18 The grain of a wooden member forms...Ch. 7.1 - Two wooden members of 80 120-mm uniform...Ch. 7.1 - Two wooden members of 80 120-mm uniform...Ch. 7.1 - The centric force P is applied to a short post as...Ch. 7.1 - Two members of uniform cross section 50 80 mm are...Ch. 7.1 - The axle of an automobile is acted upon by the...Ch. 7.1 - A 400-lb vertical force is applied at D to a gear...Ch. 7.1 - A mechanic uses a crowfoot wrench to loosen a bolt...Ch. 7.1 - The steel pipe AB has a 102-mm outer diameter and...Ch. 7.1 - For the state of plane stress shown, determine the...Ch. 7.1 - For the state of plane stress shown, determine (a)...Ch. 7.1 - For the state of plane stress shown, determine (a)...Ch. 7.1 - Determine the range of values of x for which the...Ch. 7.2 - Solve Probs. 7.5 and 7.9, using Mohr's circle. 7.5...Ch. 7.2 - Solve Probs. 7.7 and 7.11, using Mohrs circle. 7.5...Ch. 7.2 - Solve Prob. 7.10, using Mohrs circle. 7.9 through...Ch. 7.2 - Solve Prob. 7.12, using Mohr's circle. 7.9 through...Ch. 7.2 - Solve Prob. 7.13, using Mohr's circle. 7.13...Ch. 7.2 - Solve Prob. 7.14, using Mohr's circle. 7.13...Ch. 7.2 - Solve Prob. 7.15, using Mohr's circle. 7.13...Ch. 7.2 - Solve Prob. 7.16, using Mohr's circle. 7.13...Ch. 7.2 - Solve Prob. 7.17, using Mohr's circle. 7.17 and...Ch. 7.2 - Solve Prob. 7.18, using Mohr's circle. 7.17 and...Ch. 7.2 - Solve Prob. 7.19, using Mohr's circle. 7.19 Two...Ch. 7.2 - Solve Prob. 7.20, using Mohr's circle. 7.20 Two...Ch. 7.2 - Solve Prob. 7.21, using Mohrs circle. 7.21 The...Ch. 7.2 - Solve Prob. 7.22, using Mohrs circle. 7.22 Two...Ch. 7.2 - Solve Prob. 7.23, using Mohr's circle. 7.23 The...Ch. 7.2 - Solve Prob. 7.24, using Mohr's circle 7.24 A...Ch. 7.2 - Solve Prob. 7.25, using Mohrs circle. 7.25 A...Ch. 7.2 - Solve Prob. 7.26, using Mohrs circle. 7.26 The...Ch. 7.2 - Solve Prob. 7.27, using Mohr's circle. 7.27 For...Ch. 7.2 - Solve Prob. 7.28, using Mohrs circle. 7.28 For the...Ch. 7.2 - Solve Prob. 7.29, using Mohr's circle. 7.29 For...Ch. 7.2 - Solve Prob. 7.30, using Mohrs circle. 7.30...Ch. 7.2 - Solve Prob. 7.29, using Mohr's circle and assuming...Ch. 7.2 - 7.54 and 7.55 Determine the principal planes and...Ch. 7.2 - 7.54 and 7.55 Determine the principal planes and...Ch. 7.2 - 7.56 and 7.57 Determine the principal planes and...Ch. 7.2 - 7.56 and 7.57 Determine the principal planes and...Ch. 7.2 - For the element shown, determine the range of...Ch. 7.2 - For the element shown, determine the range of...Ch. 7.2 - For the state of stress shown, determine the range...Ch. 7.2 - For the state of stress shown, determine the range...Ch. 7.2 - For the state of stress shown, determine the range...Ch. 7.2 - For the state of stress shown, it is known that...Ch. 7.2 - The Mohr's circle shown corresponds to the state...Ch. 7.2 - (a) Prove that the expression xy 2xywhere x,...Ch. 7.5 - For the state of plane stress shown, determine the...Ch. 7.5 - For the state of plane stress shown, determine the...Ch. 7.5 - For the state of stress shown, determine the...Ch. 7.5 - For the state of stress shown, determine the...Ch. 7.5 - 7.70 and 7.71 For the state of stress shown,...Ch. 7.5 - 7.70 and 7.71 For the state of stress shown,...Ch. 7.5 - 7.72 and 7.73 For the state of stress shown,...Ch. 7.5 - 7.72 and 7.73 For the state of stress shown,...Ch. 7.5 - For the state of stress shown, determine the value...Ch. 7.5 - For the state of stress shown, determine the value...Ch. 7.5 - Prob. 76PCh. 7.5 - For the state of stress shown, determine two...Ch. 7.5 - For the state of stress shown, determine the range...Ch. 7.5 - Prob. 79PCh. 7.5 - Prob. 80PCh. 7.5 - The state of plane stress shown occurs in a...Ch. 7.5 - Prob. 82PCh. 7.5 - The state of plane stress shown occurs in a...Ch. 7.5 - Solve Prob. 7.83, using the...Ch. 7.5 - The 38-mm-diameter shaft AB is made of a grade of...Ch. 7.5 - Solve Prob. 7.85, using the...Ch. 7.5 - The 1.5-in.-diameter shaft AB is made of a grade...Ch. 7.5 - Prob. 88PCh. 7.5 - Prob. 89PCh. 7.5 - Prob. 90PCh. 7.5 - Prob. 91PCh. 7.5 - Prob. 92PCh. 7.5 - Prob. 93PCh. 7.5 - Prob. 94PCh. 7.5 - Prob. 95PCh. 7.5 - Prob. 96PCh. 7.5 - Prob. 97PCh. 7.6 - A spherical pressure vessel has an outer diameter...Ch. 7.6 - A spherical gas container having an inner diameter...Ch. 7.6 - The maximum gage pressure is known to be 1150 psi...Ch. 7.6 - Prob. 101PCh. 7.6 - Prob. 102PCh. 7.6 - A basketball has a 300-mm outer diameter and a...Ch. 7.6 - The unpressurized cylindrical storage tank shown...Ch. 7.6 - Prob. 105PCh. 7.6 - Prob. 106PCh. 7.6 - Prob. 107PCh. 7.6 - Prob. 108PCh. 7.6 - Prob. 109PCh. 7.6 - Prob. 110PCh. 7.6 - Prob. 111PCh. 7.6 - The cylindrical portion of the compressed-air tank...Ch. 7.6 - Prob. 113PCh. 7.6 - Prob. 114PCh. 7.6 - Prob. 115PCh. 7.6 - Square plates, each of 0.5-in. thickness, can be...Ch. 7.6 - The pressure tank shown has a 0.375-in. wall...Ch. 7.6 - Prob. 118PCh. 7.6 - Prob. 119PCh. 7.6 - A pressure vessel of 10-in. inner diameter and...Ch. 7.6 - Prob. 121PCh. 7.6 - A torque of magnitude T = 12 kN-m is applied to...Ch. 7.6 - The tank shown has a 180-mm inner diameter and a...Ch. 7.6 - The compressed-air tank AB has a 250-rnm outside...Ch. 7.6 - In Prob. 7.124, determine the maximum normal...Ch. 7.6 - Prob. 126PCh. 7.6 - Prob. 127PCh. 7.9 - 7.128 through 7.131 For the given state of plane...Ch. 7.9 - 7.128 through 7.131 For the given state of plane...Ch. 7.9 - Prob. 130PCh. 7.9 - 7.128 through 7.131 For the given state of plane...Ch. 7.9 - Prob. 132PCh. 7.9 - Prob. 133PCh. 7.9 - Prob. 134PCh. 7.9 - 7.128 through 7.131 For the given state of plane...Ch. 7.9 - 7.136 through 7.139 The following state of strain...Ch. 7.9 - Prob. 137PCh. 7.9 - Prob. 138PCh. 7.9 - Prob. 139PCh. 7.9 - Prob. 140PCh. 7.9 - 7.140 through 7.143 For the given state of plane...Ch. 7.9 - Prob. 142PCh. 7.9 - Prob. 143PCh. 7.9 - Prob. 144PCh. 7.9 - The strains determined by the use of the rosette...Ch. 7.9 - Prob. 146PCh. 7.9 - Prob. 147PCh. 7.9 - Show that the sum of the three strain measurements...Ch. 7.9 - Prob. 149PCh. 7.9 - Prob. 150PCh. 7.9 - Solve Prob. 7.150, assuming that the rosette at...Ch. 7.9 - Prob. 152PCh. 7.9 - Prob. 153PCh. 7.9 - Prob. 154PCh. 7.9 - Prob. 155PCh. 7.9 - The given state of plane stress is known to exist...Ch. 7.9 - The following state of strain has been determined...Ch. 7 - A steel pipe of 12-in. outer diameter is...Ch. 7 - Two steel plates of uniform cross section 10 80...Ch. 7 - Prob. 160RPCh. 7 - Prob. 161RPCh. 7 - For the state of stress shown, determine the...Ch. 7 - For the state of stress shown, determine the value...Ch. 7 - The state of plane stress shown occurs in a...Ch. 7 - The compressed-air tank AB has an inner diameter...Ch. 7 - For the compressed-air tank and loading of Prob....Ch. 7 - Prob. 167RPCh. 7 - Prob. 168RPCh. 7 - Prob. 169RP
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
- Please provide detailed solution, thank you. τA = ? psi τB = ? psiarrow_forward(a) Construct Mohr's circle for an element in a uniaxial state of stress (b) Use this Mohr's circle to derive the equation for the normal stress On and shear stress En on the n-face. The equations should depend on Ox and θ (c) Use the Mohr's circle to determine the planes on which the maximum shear stress acts. Sketch a properly oriented maximum-shear-stress element and indicate the normal and shear stresses acting on its faces. Ơn nt o, Note: for (b), the angle θ is between 0 and 90° and is positivearrow_forwardDraw Mohr's circle for the state of stress defined by 01= 80 MPa, o2 = -20 MPa and t12= 40 MPa. (1 points) %3Darrow_forward
- At a point on the surface of a pressurized cylinder, the material element is subjected to stresses; σx = 60 MPa, σy = - 40 MPa, and τxy = - 30 MPa. Construct Mohr’s circle, then use it to determine the following: Do not use the equations of transformations.1- The principal stresses and the maximum shear stress.2- Show these stresses on sketches of properly stress elements.3- A point on the circle where the element is only subjected to pure shear stress. Calculate the value of that pure shear stress.arrow_forwardProblem II. An exhaust gas piping fabricated as shown is subjected to a bending moment, an internal pressure, and a torque. In points A and B, the following stresses occur due to the loading: 0,05 and Txs 72.2 144.4 144.4 MPa A,B A,B A,B a. Determine Gmin, Omax, and its direction (in degrees) from x-axis at point A. b. Determine Omin, Omax, and its direction (in degrees) from x-axis at point B. B S A " O Xarrow_forward2) A 150 lb horizontal force, P, is applied to end D of handle ABD in the direction shown. Section AB has a diameter of 1.2 in. a. Determine the stress state at point H (H has sides parallel to the x and y axes). b. Draw a Mohr's circle representation for the point. What are the principal stresses at point H. 10 in. 4 in. y B 18 in. 1.2 in. P xarrow_forward
- sigma x =10 Mpaarrow_forwardDetermine the state of stress at point A of the rectangular post shown loaded with concentrated forces directed along the y axis equal to 75kN and along the x axis equal to 15kN. 75 KN a) Determine the equivalent internal forces and moments at the section containing points A 50 mm F₂= Fy= F₂= M₂= M,= M,= b) Determine the total normal stress along the x and y axes at point A (include if tensile or compressive in your final solutions) σμ² ƠAy² c) Determine the total shear stress at point A TA= d) Draw the state of stress of point A 15 KN 200 mm A 150 mm 50 mm 800 mmarrow_forwardQuestion 2) arm of Figure B from point x z plane, a horizontal angle of θ = 38 ° angled F = 29 kN force sized and C from the point z direction M = 17 kn.m acts a moment in size. The lengths of the arm are also given as L 1 = 1.5 m and L 2 = 1.1 m . It is desired to determine the stress state of point A on the aa section taken from the arm. The radius r of the section is r=0.015 m and the shear modulus of the arm material is also G = 78 Gpa . According to this; Question 2-C) Find the normal stress caused by the normal force at point A ( Write your result in MPa .) Question 2-D) Find the normal stress caused by the bending moment at point A. (Your result MPa in the size of your font.)arrow_forward
- Question 2) arm of Figure B from point x z plane, a horizontal angle of θ = 38 ° angled F = 29 kN force sized and C from the point z direction M = 17 kn.m acts a moment in size. The lengths of the arm are also given as L 1 = 1.5 m and L 2 = 1.1 m . It is desired to determine the stress state of point A on the aa section taken from the arm. The radius r of the section is r=0.015 m and the shear modulus of the arm material is also G = 78 Gpa . According to this; Question 2-A) Find the shear stress at point A due to the shear force . ( Write your result in MPa .) Question 2-B) Find the shear stress due to the torsional moment at point A. ( Write your result in MPa .) Question 2-C) Find the normal stress caused by the normal force at point A ( Write your result in MPa .)arrow_forwardsolve the question given in the image.arrow_forwardPlease answer the following questions as a reply on this Discussion In relation to Mohr's Circle which shows the relationship between normal and shear stress, at what angle from the principla x-axis does maximum shear stress occurs? Justify your answer.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Understanding Stress Transformation and Mohr's Circle; Author: The Efficient Engineer;https://www.youtube.com/watch?v=_DH3546mSCM;License: Standard youtube license