8_Axial_Loading_2.ppt.pptVIP

Poisson’s Ratio Generalized Hooke’s Law Dilatation: Bulk Modulus Shearing Strain Example 2.10 Relation Among E, n, and G Sample Problem 2.5 Composite Materials Saint-Venant’s Principle Stress Concentration: Hole Example 2.12 Elastoplastic Materials Plastic Deformations Residual Stresses Overview of Mechanical Engineering MECHANICS OF MATERIALS Fourth Edition Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University CHAPTER ? 2006 The McGraw-Hill Companies, Inc. All rights reserved. text, p. 84 Stress Strain: Axial Loading For a slender bar subjected to axial loading: The elongation in the x-direction is accompanied by a contraction in the other directions. Assuming that the material is isotropic (no directional dependence), Poisson’s ratio is defined as text, p. 85 Stress Strain: Axial Loading For an element subjected to multi-axial loading, the normal strain components resulting from the stress components may be determined from the principle of superposition. This requires: 1) strain is linearly related to stress2) deformations are small With these restrictions: (change in volume)/(unstressed state volume) = e For element subjected to uniform hydrostatic pressure, Subjected to uniform pressure, dilatation must be negative (k 0), therefore text, p. 89 Stress Strain: Axial Loading A cubic element subjected to a shear stress will deform into a rhomboid. The corresponding shear strain is quantified in terms of the change in angle between the sides, A plot of shear stress vs. shear strain is similar to the previous plots of normal stress vs. normal strain except that the strength values are approximately half. For small strains, where G is the modulus of rigidity or shear modulus. text, p. 92 Stress Strain: Axial Loading A rectangular block of material with modulus of rigidity G = 90 ksi is bonded to two rigid horizontal plates. The lower plate is fixed, while the upper plate is subjected to a horizonta