University:
McMaster University
Course:
MATLS 2H04 | Introduction to Materials Engineering
Academic year:

2023
Views:

123

Pages:

2
Author:

Sabrina S.

Hooke's Law, Strain State Analysis, Combined Loading & Buckling 6.3 Strain State Analysis 6.31 Mohr's Circle Strain non-dimensional quantity describing the deformation @ a pt in a body normal strain measures the change in length of a line element (1 + ex)dx Shearing strain measures the change in angle between 2 line elements plane strain only (epsilon_x, epsilon_y, gamma_xy) theta_v'' (1 + eo)ds (1 + es)dy epsilon_x c_2 to Yost T_p Strain Transformations 6.3.2 Strain Rosettes It is easier to measure strain than stress (using a strain gauge) Strain Rosettes epsilon_x = epsilon_a epsilon_y = epsilon_b epsilon(theta) = epsilon_x cos^2(theta) + epsilon_y sin^2(theta) + gamma_xy sin(theta) cos(theta) epsilon(45) = 1/2(epsilon_x + epsilon_y + gamma_xy) gamma_xy = 2epsilon_45 - epsilon_x - epsilon_y 6.4 Combined Loading Assumptions for individual loading case All materials are isotropic All members are homogeneous Remain in the linear elastic region (don't consider any plastic deformations) St Venant's principle applies 10 structures >> one dimension much larger than the other Combined loading method Define coordinate system (x-y-z axis, sign convention for sigma, epsilon) Determine cross-sectional characteristics (area & relevant moments of area) Calculate internal forces (statics) Determine critical stresses in cross-sections Perform stress analysis at critical locations (includes stress transformations/Mohr's Circle) Find relevant deflections to ensure the structure meets any constraints regarding max deformations