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

Union CollegeMechanical Engineering

MER311: Advanced Strength 2

Material Properties

Union CollegeMechanical Engineering

MER311: Advanced Strength 3

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?

Union CollegeMechanical Engineering

MER311: Advanced Strength 4

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?

Union CollegeMechanical Engineering

MER311: Advanced Strength 5

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

Union CollegeMechanical Engineering

MER311: Advanced Strength 6

Typical σ-ε Curves - Brittle

Union CollegeMechanical Engineering

MER311: Advanced Strength 7

Typical σ-ε Curves - Ductile

Union CollegeMechanical Engineering

MER311: Advanced Strength 8

Multi-Axial Loading

Union CollegeMechanical Engineering

MER311: Advanced Strength 9

Multi-Axial Load

Union CollegeMechanical Engineering

MER311: Advanced Strength 10

Maximum Normal Stress TheoryRankine Criteria

Union CollegeMechanical Engineering

MER311: Advanced Strength 11

Maximum Strain TheorySt. Venant Criateria

Union CollegeMechanical Engineering

MER311: Advanced Strength 12

Maximum shear TheoryTresca Criteria

Union CollegeMechanical Engineering

MER311: Advanced Strength 13

Maximum strain Energy TheoryHaig Criterion

Union CollegeMechanical Engineering

MER311: Advanced Strength 14

Maximum energy of Distortion Theory – von Mises Criteria

2 2 21 2 2 3 3 10.5vonMises ys

Union CollegeMechanical Engineering

MER311: Advanced Strength 15

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

Union CollegeMechanical Engineering

MER311: Advanced Strength 16

3ave ave

Comparison with Data

Union CollegeMechanical Engineering

MER311: Advanced Strength 17

Example

Union CollegeMechanical Engineering

MER311: Advanced Strength 18

Example

Union CollegeMechanical Engineering

MER311: Advanced Strength 19