Stress_and_Strain

Stress_and_Strain - Stress and Strain (3.1-3.11) MAE 316...

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Stress and Strain (3.1-3.11) MAE 316 – Strength of Mechanical Components C. Heeter Tran Stress and Strain 1
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troduction Introduction ` MAE 316 is a continuation of MAE 314 (solid mechanics) ` Review topics ` Beam theory olumns ` Columns ` Pressure vessels ` Principle stresses ` New topics ` Contact stress ` Press and shrink fits ` Fracture mechanics ` Fatigue Stress and Strain 2
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tress and Strain Review .2) Stress and Strain Review (3.2) ` Normal Stress (axial loading) F A σ ` Sign Convention ` σ൐0 Tensile (member is in tension) ` σ൏0 Compressive (member is in compression) Stress and Strain 3
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tress and Strain Review .3) Stress and Strain Review (3.3) ` Shear stress (transverse loading) ` “Single” shear average shear stress A F A P ave = = τ ` “Double” shear A F A F A P ave 2 2 = = = Stress and Strain 4
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tress and Strain Review Stress and Strain Review ` Normal strain (axial loading) δ L ε= ` Hooke’s Law ε σ E = Where E = Modulus of Elasticity (Young’s modulus) Stress and Strain 5
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tress and Strain Review .5) Stress and Strain Review (3.5) ` Torsion (circular shaft) ear strain T ` Shear strain L ρφ γ= ` Shear stress J Tc = τ ` Angle of twist J TL = φ GJ Where G = Shear modulus (Modulus of rigidity) and J = Polar moment of inertia of shaft cross-section Stress and Strain 6
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tress and Strain Review .4) Stress and Strain Review (3.4) ` Thin-walled pressure vessels ylindrical ` Cylindrical pr pr t = 1 σ t 2 2 = Circumferential “hoop” stress Longitudinal stress ` Spherical t pr 2 2 1 = = σ Stress and Strain 7
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tress and Strain Review .7) Stress and Strain Review (3.7) ` Beams in pure bending rain ` Strain y υ y h P i ’ R ti ress ρ ε x = z y = = Where υ = Poisson’s Ratio ` Stress EI My Where I = 2 nd moment of inertia of the M = I x = σ cross-section and ρ = radius of curvature of the beam Stress and Strain 8
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tress and Strain Review .7 & 3.8) Stress and Strain Review (3.7 & 3.8) ` Beams (non-uniform bending) ear and bending moment `
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Stress_and_Strain - Stress and Strain (3.1-3.11) MAE 316...

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