mer311 mer311: advanced strength of...

MER311 MER311: Advanced Strength of Materials

Failure Criteria

Union CollegeMechanical Engineering

MER311: Advanced Strength 1

Design Factors orFactors of Safety Factor of Safety Factor of Safety

Allowable Stress (strength) SAllowable Stress (strength)Calculated Stress

Sn

Margin of Safety

1m n



Material Properties



Example

000 0 2 2Let P=5000lb and the cross-sectional area = 0.2 in2.What is the Factor of Safety and Margin of Safety?



Example

Let T=200 ft lb and r= 0 2 in (J=2 51x10-3 in4)Let T=200 ft-lb and r= 0.2 in (J=2.51x10 3 in4)What is the Factor of Safety and Margin of Safety?



Unacceptable Deformation Under Load w/ or w/o Fracture Excessive Elastic Deflection Excessive Elastic Deflection Stretching, Twisting, or Bending Buckling

Vib ti Vibration Yielding Plastic Deformation @ Room Tempp Creep at Elevated Temperatures

Fracture Sudden Fracture of Brittle Materials Sudden Fracture of Brittle Materials Fatigue (Progressive Fracture) Stress Rupture at Elevated Temperatures



Typical σ-ε Curves - Brittle



Typical σ-ε Curves - Ductile



Multi-Axial Loading



Multi-Axial Load



Maximum Normal Stress TheoryRankine Criteria



Maximum Strain TheorySt. Venant Criateria



Maximum shear TheoryTresca Criteria



Maximum strain Energy TheoryHaig Criterion



Maximum energy of Distortion Theory – von Mises Criteria

2 2 21 2 2 3 3 10.5vonMises ys



1 2 2 3 3 1vonMises y

Maximum energy of Distortion Theory – von Mises Criteria

x xy xz

xy y yz

0 00 0

xz yz z

ave x ave xy xz

0 0

0 0

0 0 0 0

ave xy y ave yz

ave xz yz z ave

1

2

3

0 0 0 00 0 0 00 0 0 0

ave ave

ave ave

ave ave



3ave ave

Comparison with Data



Example



mer311 mer311: advanced strength of...

Documents