Mechanics 1P

# Mechanics 1P - ±± 2.001 MECHANICS AND MATERIALS I Lecture...

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±± 2.001 - MECHANICS AND MATERIALS I Lecture # 10/25/2006 Prof. Carol Livermore Recall from last time: ± σ xx σ xy σ xz ± [ σ ]= ± σ yx σ yy σ yz ± . ± σ zx σ zy σ zz ± Diagonal terms are normal stresses. OF diagonal terms are shear stresses. Not as bad as it seems: 1. Linearity 2. Superposition EXAMPLE: Uniaxial Stress 1 13

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±± ± ± σ 0 ± ± 00 ± ± [ σ ]=00 ± ± 0 . 000 EXAMPLE: Hydrostatic Stress ± ± p ± ± ± ± [ σ ]= 0 p 0 ± ± . p Note: p is negative (compressive stresses are negative by convention) EXAMPLE: Plane Stress ± σ a τ 0 ± [ σ τσ b 0 . ± 0 ± 2
±± EXAMPLE: Biaxial Plane Stress ± ± ± ± ± ± σ a 0 0 [ σ ]= 0 σ b 0 ± ± ± ± ± ± 0 0 0 . EXAMPLE: Shear Plane Stress ± 0 τ 0 ± [ σ τ 00 . ± 000 ± Note: The stress at a material point that you see, and its magnitude, depends on the orientation of the coordinates relative to your loading. In other words: the state of stress is a function of the chosen coordinate system.

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Mechanics 1P - ±± 2.001 MECHANICS AND MATERIALS I Lecture...

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