ME 3502 Stress Analysis and Design HOMEWORK #1: SOLUTIONS PROBLEM 1 Define the following terms and concepts: a) Shear Stress: Stress Component acting on ‘shear planes’ coplanar with a material cross-section. b) Normal Strain Relative Geometric Deformation normal to a material cross-section parallel to its respective normal stress vector. c) Young’s Modulus: Material Property characterizing the linear relationship between stress and strain within the linear elastic region of material exhibiting linear elastic properties. d) Isotropic: A material is called isotropic if it exhibits the same material properties under loading in any direction. e) Coefficient of Thermal Expansion: Material Property characterizing the tendency for a material to change in volume with respect to a change in temperature. f) Stress Concentration Factor: Multiplication Factor describing the amplification of stresses at sudden or sharp features due to the nonlinearity of the local stress distribution. Defined as the ratio between maximum and average stresses. g) Classical Beam Theory See Euler-Bernoulli Beam Theory. Its primary assumption is such that a beam cross-section remains perpendicular to the bending axis before and after deformation. This applies for lateral loading for small deflections only. Euler-Bernoulli Beam Theory is a special case of Timoshenko Beam Theory which has a larger range of application. PROBLEM 2 A can of paint with a mass of 4kg and a diameter of 20cm sits on a desk. (a) Assuming the can has a perfectly flat bottom, what is the average normal stress that it creates on the desk? (b) If the paint is subsequently spread over the entire surface of the desk which happens to measure 5 m by 1.5 m, what is the new average normal stress created (assuming that all 4kg are applied)? 𝐹 𝑚𝑔 𝐹 𝑚𝑔 𝑎𝑏 4(9.81) a) 𝜎 = 𝐴 = 𝜋𝑟2 = 𝜋(0.12 ) = 1249 𝑃𝑎 b) 𝜎 = 𝐴 = = 4(9.81) 5(1.5) = 5.23 𝑃𝑎