Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 10.6, Problem 10.43P
The principal strains at a point on the aluminum surface of a tank are ε1 = 630 (10−6) and ε2 = 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, val = 0.33. Hint: See Prob.10−30.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The 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.
Electrical strain gauges were applied to a notched specimen, the results were εx = 0.19 and Ey
= -0.068.
If the material is aluminum (E = 71700 MPa and v = 0.333), find σy in MPa to determine the
stresses in the notch. Use Excel spreadsheet posted on Canvas and give correct answer to
one decimal place.
Εγ
Y
Ex
A 60 ̊ strain rosette measures the following strain at a point on the aluminum skin of an airplane. ε0 = 160 ×10-6 m/m, ε60 = -220 ×10-6 m/m and ε120 = 360 ×10-6 m/m. Using E= 10 ×106 psi and v = 0.3, Determine the principle stresses and the maximum in-plane shear stress.
Chapter 10 Solutions
Mechanics of Materials (10th Edition)
Ch. 10.3 - Prove that the sum of the normal strains in...Ch. 10.3 - The state of strain at the point on the arm has...Ch. 10.3 - The state of strain at the point on the pin leaf...Ch. 10.3 - The state of strain at the point on the pin leaf...Ch. 10.3 - The state of strain at the point on the leaf of...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Use the strain- transformation equations to...
Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Determine the equivalent state of strain on an...Ch. 10.3 - Determine the equivalent state of strain which...Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Determine the equivalent state of strain, which...Ch. 10.3 - Solve Prob.103 using Mohrs circle. 103. The state...Ch. 10.3 - using Mohrs circle. 103. The state of strain at...Ch. 10.3 - Solve Prob.105 using Mohrs circle. 105. The state...Ch. 10.3 - Solve Prob.108 using Mohrs circle 108. The state...Ch. 10.3 - using Mohrs circle. 106. The state of strain at a...Ch. 10.5 - The strain at point A on the bracket has...Ch. 10.5 - Determine (a) the principal strains at A, (b) the...Ch. 10.5 - Determine (a) the principal strains at A, in the...Ch. 10.5 - The following readings are obtained for each gage:...Ch. 10.5 - The following readings are obtained for each gage:...Ch. 10.5 - The following readings are obtained for each gage:...Ch. 10.5 - The following readings are obtained from each...Ch. 10.6 - For the case of plane stress, show that Hookes law...Ch. 10.6 - to develop the strain tranformation equations....Ch. 10.6 - Determine the modulus of elasticity and Polssons...Ch. 10.6 - If it is subjected to an axial load of 15 N such...Ch. 10.6 - If it has the original dimensions shown, determine...Ch. 10.6 - If it has the original dimensions shown, determine...Ch. 10.6 - A strain gage having a length of 20 mm Is attached...Ch. 10.6 - Determine the bulk modulus for each of the...Ch. 10.6 - The strain gage is placed on the surface of the...Ch. 10.6 - Determine the associated principal stresses at the...Ch. 10.6 - Determine the applied load P. What is the shear...Ch. 10.6 - If a load of P = 3 kip is applied to the A-36...Ch. 10.6 - The cube of aluminum is subjected to the three...Ch. 10.6 - The principal strains at a point on the aluminum...Ch. 10.6 - A uniform edge load of 500 lb/in. and 350 lb/in....Ch. 10.6 - Prob. 10.45PCh. 10.6 - A single strain gage, placed in the vertical plane...Ch. 10.6 - A single strain gage, placed in the vertical plane...Ch. 10.6 - If the material is graphite for which Eg = 800 ksi...Ch. 10.6 - Determine the normal stresses x and y in the plate...Ch. 10.6 - The steel shaft has a radius of 15 mm. Determine...Ch. 10.6 - Prob. 10.51PCh. 10.6 - The A-36 steel pipe is subjected to the axial...Ch. 10.6 - Air is pumped into the steel thin-walled pressure...Ch. 10.6 - Air is pumped into the steel thin-walled pressure...Ch. 10.6 - Prob. 10.55PCh. 10.6 - The thin-walled cylindrical pressure vessel of...Ch. 10.6 - The thin-walled cylindrical pressure vessel of...Ch. 10.6 - Prob. 10.58PCh. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - The yield stress for a zirconium-magnesium alloy...Ch. 10.7 - Solve Prob. 1061 using the maximum distortion...Ch. 10.7 - If a machine part is made of tool L2 steel and a...Ch. 10.7 - Solve Prob.1063 using the maximum distortion...Ch. 10.7 - Prob. 10.65PCh. 10.7 - If a shaft is made of a material for which y = 75...Ch. 10.7 - Solve Prob.1066 using the maximum shear stress...Ch. 10.7 - If the material is machine steel having a yield...Ch. 10.7 - The short concrete cylinder having a diameter of...Ch. 10.7 - Prob. 10.70PCh. 10.7 - The plate is made of Tobin bronze, which yields at...Ch. 10.7 - The plate is made of Tobin bronze, which yields at...Ch. 10.7 - An aluminum alloy is to be used for a solid drive...Ch. 10.7 - If a machine part is made of titanium (TI-6A1-4V)...Ch. 10.7 - The components of plane stress at a critical point...Ch. 10.7 - The components of plane stress at a critical point...Ch. 10.7 - The 304-stainless-steel cylinder has an inner...Ch. 10.7 - The 304-stainless-steel cylinder has an inner...Ch. 10.7 - If the 2-in diameter shaft is made from brittle...Ch. 10.7 - If the 2-in diameter shaft is made from cast iron...Ch. 10.7 - If Y = 50 ksi, determine the factor of safety for...Ch. 10.7 - Prob. 10.82PCh. 10.7 - If the yield stress for steel is Y = 36 ksi,...Ch. 10.7 - Prob. 10.84PCh. 10.7 - The state of stress acting at a critical point on...Ch. 10.7 - The shaft consists of a solid segment AB and a...Ch. 10.7 - The shaft consists of a solid segment AB and a...Ch. 10.7 - Prob. 10.88PCh. 10.7 - If Y = 50 ksi, determine the factor of safety for...Ch. 10.7 - The gas tank is made from A-36 steel and has an...Ch. 10.7 - The internal loadings at a critical section along...Ch. 10.7 - If the material is machine steel having a yield...Ch. 10.7 - If the material is machine steel having a yield...Ch. 10 - In the case of plane stress, where the in-plane...Ch. 10 - The plate is made of material having a modulus of...Ch. 10 - If the material is machine steel having a yield...Ch. 10 - Determine if yielding has occurred on the basis of...Ch. 10 - The 60 strain rosette is mounted on a beam. The...Ch. 10 - Use the strain transformation equations to...Ch. 10 - If the strain gages a and b at points give...Ch. 10 - Use the strain-transformation equations and...Ch. 10 - Use the strain transformation equations to...Ch. 10 - Specify the orientation of the corresponding...
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
- A 60˚ strain rosette measures the following strain at a point on the aluminum skin ofan airplane. ϵ0 = 160 ×10-6 m/m, ϵ60 = -220 ×10-6 m/m and ϵ120 = 360 ×10-6 m/m. Using E = 10 ×106 psi and v = 0.3, Determine the principle stresses and the maximum in-plane shear stress.arrow_forwardThe material is subjected to biaxial loading producing uniform normal stress x and y as shown. The strains are Strainx=−0.00065 and Strainy=−0.00040. Use E=30×106 psi and v=0.30. Determine the following: (a) stress at x. Indicate tension or compression. Use 2 decimal places. (b) stress at y. Indicate tension or compression. Use 2 decimal places. (c) Change in the thickness of the material. Indicate elongation or contraction. Use 5 decimal places and scientific notation of ×10−3(Example: _ . _ _ _ _ _ ×10−3)arrow_forwardNonearrow_forward
- A tri-axial state of stress, σx , σy, and σz ,exists in a steel machine part. For steel, E = 200GPa and ν = 0.3. Determine the normal strain in the x-direction if σx = 100MPa, σy = 35MPa, σz = 70MPa. Determine the dilatation. Determine the modulus of rigidity.arrow_forwardThe state of stress at a point in a member is shown on the element. Take σx = 90 MPa , σy= 65 MPa , τxy = 40 MPa . A) Determine the normal stress component acting on the inclined plane AB. Solve the problem using the method of equilibrium. B)Determine the shear stress component acting on the inclined plane AB. Solve the problem using the method of equilibrium.arrow_forwardDetermine the normal strains at the point associated with the x and y axes. Determine the shear strain at the point associated with the x and y axes. Determine the normal stresses at the point associated with the x and y axes. Determine the shear stress at the point. Determine the normal stress that acts along an axis rotated at θ= 45° counterclockwise from the positive x-axis.arrow_forward
- . The normal stresses at a point in a steel member are δx = 8 ksi, δy = -4 ksi and δz = 10 ksi. Using E = 29 x 103 ksi and v = 0.3, determine the normal strains at this point.arrow_forwardhe state of stress at a point in a member is shown on the element. Take σx = -3 ksi , σy= 4 ksi , τxy = -3 ksi . A) Determine the shear stress component acting on the inclined plane AB. Solve the problem using the method of equilibrium. B) Determine the normal stress component acting on the inclined plane AB. Solve the problem using the method of equilibrium.arrow_forward2. The stress-strain diagram for a bone is shown and, according to the data analysis curve fitting tool, it can be described by the equation ε = 0.45 · 10-6 +0.36 10-12³, where stress is in kPa. Determine the modulus of toughness and the amount of elongation of a 200-mm-long region just before it fractures if failure occurs at ε = 0.12 mm/mm. -€ = 0.45(106) + 0.36(10-12)³ € ↑Parrow_forward
- A rectangular aluminum plate of uniform thickness has a strain gauge at the center. It is placed in a test rig which can apply a biaxial force system along the edges of the plate as shown below. If the measured strains are +0.0005 and +0.001 in the x and y directions respectively, a) Determine the corresponding stresses set up in the plate and the strain through the thickness, εz. Take E=72 GPa and ν=0.32. b) Construct the Mohr’s circle for the loaded plate. c) State the values of the principal stresses. d) Determine the maximum shearing stresses and the directions of the planes on which they occur.arrow_forwardA state of stress at a point A is given by σx = 25 MPa, σy = 122 MPa, and τxy = 60 MPa. Determine the equivalent state of stress on an element at the point which represents the principal stresses.arrow_forwardIn the following structure if the temperature increases by 20 °C, determine the normal stress in Links (1) and (2). E (GPa) A (mm2) a (1/°C) 11.9x10-6 Link 1 200 310 Link 2 70 620 22.5x106 500mm 350mm B to A 100mm 300mm (2) 6kN 400mmarrow_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
Material Properties 101; Author: Real Engineering;https://www.youtube.com/watch?v=BHZALtqAjeM;License: Standard YouTube License, CC-BY