Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Textbook Question
Chapter 10.7, Problem 59P
A material is subjected to plane stress. Express the distortion energy theory of failure in terms of σx, σy, and τxy.
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If the material is machine steel having a yield stress of sY = 750 MPa, determine the factor of safety with respect to yielding using the maximum distortion energy theory.
If the material is machine steel having a yield stress of sY = 750 MPa, determine the factor of safety with respect to yielding if the maximum shear stress theory is considered.
The state of plane stress at a critical point in a steel machine bracket is shown. If the yield stress for steel is sY = 36 ksi, determine if yielding occurs using the maximum distortion energy theory.
Chapter 10 Solutions
Mechanics of Materials
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- Indicate the points on the stress-strain diagram which represent the proportional limit and the ultimate stress.arrow_forwardIf sY = 50 ksi, determine the factor of safety for this loading against yielding based on (a) the maximum shear stress theory and (b) the maximum distortion energy theory.arrow_forwardIf a machine part is made of titanium (Ti-6A1-4V) and a critical point in the material is subjected to plane stress, such that the principal stresses are s1 and s2 = 0.5s1, determine the magnitude of s1 in MPa that will cause yielding according to (a) the maximum shear stress theory, and (b) the maximum distortion energy theory.arrow_forward
- The plate is made of Tobin bronze, which yields at sY = 25 ksi. Using the maximum distortion energy theory, determine the maximum tensile stress sx that can be applied to the plate if a tensile stress sy = 1.5sx is also applied.arrow_forwardA material is subjected to plane stress. Express the distortion energy theory of failure in terms of sx, sy, and txy.arrow_forwardThe components of plane stress at a critical point on a thin steel shell are shown. Determine if failure (yielding) has occurred on the basis of the maximum distortion energy theory. The yield stress for the steel is sY = 700 MPa.arrow_forward
- A torque of 2 kip # in. is applied to the tube. If the wall thickness is 0.1 in., determine the average shear stress in the tube.arrow_forwardA loading condition is shown below. The wires at point A and D both made from a steel with the yield strength (Sy) of 190 MPa with 2 mm diameter. Using either maximum shear stress theory or distortion energy theory, determine the maximum load P that can be applied before yielding happens in the wires.arrow_forwardWhat is the Weibull modulus of this material? Would you advise the use of a similar material with a Weibull Modulus of 16.3 and a mean failure stress of 485 MPa, if you anticipate that the peak stress on the material could be 430 MPa? a. 15.7 b. Yes c. 18.6 d. 13.4 e. No f. 17.1arrow_forward
- The five-bolt connection must support an applied load of P = 3500 lb. If the average shear stress in the bolts must be limited to 29 ksi, determine the minimum bolt diameter that may be used for this connection.arrow_forwardDetermine the:1- Shear Strain2- Shear stress3- Friction Coefficientarrow_forwardRefer to the set of bars made of a material with a yield strength of 350 MPa, determine the minimum dimensions h1 and h2 required. Apply a safety factor FS = 1.5 without flux. Each bar is 12 mm thickarrow_forward
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