MECHANICS OF MATERIALS
11th Edition
ISBN: 9780137605521
Author: HIBBELER
Publisher: RENT PEARS
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Chapter 10, Problem 3RP
If the material is machine steel having a yield stress of σY = 500 MPa, determine the factor of safety with respect to yielding if the maximum shear stress theory is considered.
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1. We can visualize the factor of safety for an arbitrary stress using a surface in principal stress space. For
a ductile material that yields according to a von Mises criterion with a yield stress σy, sketch the von
Mises surface in σ₁ - 02 space and sketch the stress surface that corresponds to a factor of safety FoS =
2. For a brittle material that yields according to a max normal (Rankine) criterion with a tensile strength
Gyt and a compressive strength σvc = 20yt, sketch the yield surface and the surface that corresponds
to a factor of safety FoS = 2.
The yield stress for a zirconium-magnesium alloy is sY = 15.3 ksi. If a machine part is made of this material and a critical point in the material is subjected to in-plane principal stresses s1 and s2 = -0.5s1, determine the magnitude of s1 that will cause yielding according to the maximum shear stress theory.
Mechanics Of Material I
Chapter 10 Solutions
MECHANICS OF MATERIALS
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 leaf of...Ch. 10.3 - Use the strain transformation equations and...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. 10.5 - The strain at point A on the bracket has...
Ch. 10.5 - Determine (a) the principal strains at A, (b) the...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 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. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - Solve Prob. 1061 using the maximum distortion...Ch. 10.7 - Solve Prob.1063 using the maximum distortion...Ch. 10.7 - Prob. 70PCh. 10.7 - The plate is made of Tobin bronze, which yields at...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 - If Y = 50 ksi, determine the factor of safety for...Ch. 10.7 - Prob. 82PCh. 10.7 - If the yield stress for steel is Y = 36 ksi,...Ch. 10.7 - Prob. 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 - 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...
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- Determine the factor of safety as per tresca's max shear stress theoryarrow_forwardIf the material is machine steel having a yield stress of sY = 700 MPa, determine the factor of safety with respect to yielding if the maximum shear stress theory is considered.arrow_forwardA ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 350 MPa. Using the distortion- energy and maximum-shear-stress theories, determine the factors of safety with the following principal stresses. σA = 90 MPa, and oß = -98 MPa The factor of safety from the maximum-shear-stress theory is " and the factor of safety from the distortion-energy theory isarrow_forward
- A thin-walled cylinder of diameter 40 mm is subjected to an internal pressure of 5 N/mm² and a torque of 100 Nm. If the material of the cylinder has a yield stress in simple tension of 150 N/mm determine the required wall thickness using the Tresca and von Mises theories of elastic failure. Ans. 0.81 mm (Tresca), 0.74 mm (von Mises).arrow_forwardQ1: A ductile bar of aluminum 1010 alloy. Using the distortion-energy and maximum- shear-stress theories determine the factors of safety for the following plane stress states: (α) σχ = 180 MPa, σy = 100 MPa (b) σx = 180 MPa, Txy = (c) σx = -160 MPa, Txy = 150 MPa (d) Txy 100 MPa = 100 MPaarrow_forwardIf a machine part is made of Ti-6A1-4V titanium and a critical point in the material is subjected to plane stress, such that the principal stresses are σ1 and σ2 = 0.501, determine the magnitude of σ1 in MPa that will cause yielding according to (a) the maximum shear stress theory, and (b) the maximum distortion energy theory. Hint: Refer to the inside cover the textbook for material section properties.arrow_forward
- The Mohr's circle for a plane stress for a point in a body is shown. The design is to be on the basis of the maximum shear stress theory of yielding. Then, yielding will just begin of the designer chooses a ductile material whose yield strength is AL σ (+) -10 ✓ T (+) -100arrow_forwardThe state of stress acting at a critical point on a wrench is shown. Determine the smallest yield stress for steel that might be selected for the part, based on the maximum distortion energy theory.arrow_forwardN = 400 N T= 1.8 N-m In order to drill an 8mm hole into a block of steel, a Normal Load of 400N and Torque of 1.8 N-m must be applied to a drill bit. The drill bit H D = 8mm has a diameter of 8mm and is a solid cylinder at point H. Write the stress state for the element H pictured in the diagram.arrow_forward
- Two bolts are used to lap joints two steel plates. The tensile force on the plate is 40 kN. Determine the required diameter of the bolts if the failure shear stress of the bolts is 350 MPa. Use a factor of safety for shear equal to 2.5.arrow_forwardThe supporting wheel on a scaffold is held in place on the leg using a 4-mm-diameter pin as shown. (Figure 1) Figure P 1 of 1 Part A If the wheel is subjected to a normal force of P = 3.3 kN, determine the average shear stress developed in the pin. Neglect friction between the inner scaffold puller leg and the tube used on the wheel. Express your answer to three significant figures and include the appropriate units. μА Tavg= 65.652 N mm² Submit Previous Answers Request Answer Provide Feedback ? X Incorrect; Try Again; 4 attempts remainingarrow_forwardSolve clearly and neatlyarrow_forward
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Understanding Failure Theories (Tresca, von Mises etc...); Author: The Efficient Engineer;https://www.youtube.com/watch?v=xkbQnBAOFEg;License: Standard youtube license