MAE 311 Lecture Notes - Lecture 4: Shear Modulus, Infinitesimal Strain Theory, Plane Stress

• School: University at Buffalo
• Department: Mechanical & Aerospace Engr
• Course: MAE 311
• Professor: Phillip Cormie

Document Summary

Internal forces stress strains displacement. Displacement strains stress internal forces. Macroscopic level: treat the body the as a continuum (part dimension, grain structure, molecules etc. ) Linearity: mapping between stress and strain is linear. Small strain: strain is very small to make sure the deformation formulations hold true. G: shear modulus or modulus of rigidity (unit force/area) : poison"s ratio ratio between lateral strain and axial strain (unit dimensionless) : coefficient of thermal expansion (unit reciprocal of temperature) Using super position (we can do this because we assumed we are in the linear elastic region) 2 zz xx zz xx yy zz x. G0 xx yy zz xy yz zx x y z xy yz zx. Example 1: a 500 lb sculpture need to be 10ft below the ceiling for an exhibit. Choose a steel rod such that the maximum stress is less than 5000 psi. Young"s modulus for steel is e = 30 106 psi.