Transcript Document

MAE 343 - Intermediate Mechanics of
Materials
Thursday, Sep. 30, 2004
Textbook Section 4.6
Combined Stress Theories of Failure
Maximum Normal Stress Theory (Rankine)
Maximum Shearing Stress Theory (Tresca)
Combined Stress Theories of Failure
• Necessary for Multiaxial States of Stress
– Yielding in any direction influenced by other stresses
– Predictions validated by experimental results
• Based on “Loading Severity Parameter” (LSP)
– Readily calculable and measurable (stress, strain, energy)
• Comparison between two loading scenarios –
failure predicted to occur when:
– Maximum LSP value in multiaxial stress state 
– Value of SAME LSP that causes failure in a simple
uniaxial stress test on specimen made of SAME material
Maximum Normal Stress Theory
(Rankine’s Theory)
• Applicable to brittle, but not ductile materials
• Failure is expected to occur when:
– Maximum principal normal stress in triaxial stress state 
– Maximum normal stress at the time of failure in simple uniaxial
stress test on specimen of the same material, =
– Uniaxial strength of the material for the governing failure mode
• Tension failure strength is different for some materials
from compression failure strength
1   failt  2   failt  3   failt
–
1   failc  2   failc  3   failc
MAE 343-Intermediate Mechanics of Materials
Homework No. 5 - Thursday, Sep. 30, 2004
1) Textbook problems required on Thursday, Oct. 7, 2004:
Problems 2.13 and 2.17
2)Textbook problems recommended for practice before Oct. 7, 04:
Problems 2.1 – 2.18 (except 2.13 and 2.17)