University:
Massachusetts Institute of Technology
Course:
16.01 | Unified Engineering I, II, III, & IV
Academic year:

2019
Views:

153

Pages:

12
Author:

Melina Dominguez

Unified Quiz 7MS December 15th, 2003 NAME: Solu hions PROBLEM #1 (25%) a) The stress state given below is applied to an element of the aluminum alloy skin of an aircraft. Calculate the maximum shear stress and the direction(s) in which it acts. Express the direction(s) as counterclockwise angles relative to the x₁ axis. (σ₁₁ σ₁₂ σ₁₃) (200 -100 0) (σ₂₁ σ₂₂ σ₂₃) = (-100 -100 0) MPa (σ₃₁ σ₃₂ σ₃₃) ( 0 0 0) Use Mohr's Circle C = (σ₁₁ + σ₂₂) / 2 = 0 MPa R = √[(σ₁₁ - σ₂₂)/2]^2 + σ₁₂² = 180 MPa θ = 45° - 1/2 tan⁻¹(σ₁₂ / (σ₁₁ - σ₂₂)) = θ = 28.2° and 90° + θ = 118.2° Unified Quiz 7MS December 15th, 2003 NAME: b) For the stress state in part (a), calculate the elongation (in meters, millimeters, or micrometers) of the diagonal, AC, of the 1m x 1m element of the wing skin. The Young's modulus of the aluminum alloy is 70 GPa and its Poisson's ratio is 0.33. Strain @ 45° is σ₁₁, σ₂₂ axes σ₁₁ = -50 + 180 cos 56.3° = -50 MPa σ₂₂ = 50 + 180 cos 56.3° = +150 MPa Want ε₁₁ From Elasticity Tensor: ε₁₁ = -50x10⁶ / 70x10⁹ + (1.50x10⁶ x 0.33) / 70x10⁹ = -1.42x10⁻³ ∴ Elongation = -1.42x10⁻³ x √2 = -2.0 x 10⁻³ m = 2 mm (←) Unified Quiz 7MS December 15th, 2003 NAME: e) With reference to the material selection chart below, explain the relative suitability of Titanium, Aluminum and Steel for (i) the bars of a truss and (ii) for the wings of an airplane. For a truss, compliance: E / ρ (max) Ti, Al, Steel are all similar For aircraft wings, minimize: E¹/² / ρ - bending Al better than Steel Ti better than Steel