Chapter 6 --- Part 2 Impractical to test _________________________ of stresses. Failure theories are needed to __________________ on the basis of material performance on the ____________________, e.g. __________________. Maximum-Normal-Stress Theory --- correlates well with ______________ Failure will occur whenever the greatest tensile stress > ________________ or whenever the largest compressive stress > _________________. MIE 313 Chapter 6 Part 2 1/13
Transcript
Chapter 6 --- Part 2
Impractical to test _________________________ of stresses. Failure theories are needed to __________________ on the basis of material performance on the ____________________, e.g. __________________. Maximum-Normal-Stress Theory --- correlates well with ______________ Failure will occur whenever the greatest tensile stress > ________________ or whenever the largest compressive stress > _________________.
MIE 313 Chapter 6 Part 2 1/13
Maximum-Shear-Stress Theory
• Correlates o.k. with yielding of ductile materials • Coulomb • Tresca
Failure occurs whenever the maximum shear stress > __________________
MIE 313 Chapter 6 Part 2 2/13
Maximum-Distortion-Energy Theory (Maximum – Octahedral – Shear – Stress Theory)
Failure occurs if σe , equivalent stress, > σyt
=eσ For the case of biaxial stress =eσ
In terms of σx, σy and τxy =eσ
=eσOnly if σx, σxy
MIE 313 Chapter 6 Part 2 3/13
Modified Mohr Theory --- for brittle material
utuc SS >>
MIE 313 Chapter 6 Part 2 4/13
Sample Problem 6.3 Find: Safety factor a). distortion energy theory, b). shear stress theory, c). normal stress theory. σ1=58 ksi → b
66 ksi → a 100 ksi → c
Figure 6.14 Graphical solution to Sample Problem 6.3
MIE 313 Chapter 6 Part 2 5/13
Problem 6.13 Known: A machine frame made of steel having known Sy and Ssy is loaded in a test fixture. The principal stresses at two critical points on the surface are known.
MIE 313 Chapter 6 Part 2 6/13
Problem 6.25 A straight round shaft is subjected to a torque of 5000 lb.in. Determine the required diameter, using steel with a tensile yield strength of 60 ksi and a safety factor of 2 based on initial yielding according to (a). maximum-normal-stress theory, (b). maximum-shear-stress theory, (c). maximum-distortion-energy theory.
MIE 313 Chapter 6 Part 2 7/13
Problem 6.27 A round steel bar having Sy = 800 MPa is subjected to loads producing calculated stresses of P/A = 70MPa, Tc/J = 200 MPa, Mc/I = 300 MPa, and 4V/3A = 170MPa. (a) Sketch Mohr circles showing the relative locations of maximum normal stress and
maximum shear stress. (b) Determine the safety factor with respect to initial yielding according to the maximum-
shear-stress theory and according to the maximum-distortion-energy theory.
MIE 313 Chapter 6 Part 2 8/13
Reliability
Fifure 6.18 Normal distribution curves baving a common µ and various σ.
== meanµ
== deviationdards tanσ
MIE 313 Chapter 6 Part 2 9/13
MIE 313 Chapter 6 Part 2 10/13
Interference Theory of Reliability Predictive
Margin of safety, z = x - y µz=µx - µy
22
yxz σσσ += Sample Problem 6.4 Application of Interference Theory of Reliability (Page 268)
MIE 313 Chapter 6 Part 2 11/13
Problem 6.33 Refer to the conditions specified in Problem 6.32 (on page 273). Assume that the failure rate calculated in Problem 6.32 is unacceptable. (a) To what value would the standard deviation of shaft strength have to be reduced in
order to give a failure rate of 5%, with no other changes? (b) To what value would nominal shaft strength have to be increased in order to give a
