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MBD Chapter 4 - 2 Material = homogeneous stresses within...

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a T b Chapter 4: Static Body Stresses 4.2.Axial Loading = σ PA If the load is uniformly distributed over the cross-section: 1. Section being considered must be well removed from the loaded ends 2. Load is applied exactly along the centroidal axis of the bar 3. Bar = straight cylinder (no holes, notches, threads, internal imperfections, or surface scratches) 4. Bar is free of stress when external loads are removed 5. Bar is in stable equilibrium when loaded 6. Bar is homogenous 4.3.Direct Shear Loading = τ PA Direct shear: rivets, pins, keys, splines 4.4.Torsional Loading Compression (negative axial loading) can cause buckling Chain/cable can withstand Tension (positive axial loading) = τ TrJ = τ 16Tπd3 Assumptions for = τ TrJ 1. Bar is straight and round; torque is longitudinal 2. Material is homogenous and perfectly elastic 3. Cross section is sufficiently remote from load points For Non-round Bars: = ( + . ) τ T 3a 1 8b a2b2 4.5.Pure Bending Loading, Straight Beams = σ MyI 1. Bar must be initially straight and loaded in plane symmetry
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Unformatted text preview: 2. Material = homogeneous; stresses within elastic range 3. Section shouldn’t be too close to stress raisers Solid Round Bar → σmax = 32Mπd3 4.6 Pure Bending Loading, Curved Beams Strain on a fiber: = ( + ) ϵ ydφ rn y φ Strain on an elastic material: = ( + ) σ Eydφ rn y φ Curved Beams: = σi McieAri = -σ0 Mc0eAr0 = σi KiMcI = KiMZ = -= -σi K0McI K0MZ 4.7 Transverse Shear Loading in Beams = = = τ VIby y0y cydA Thin Walled: = τmax 2VA Round: = τmax 43VA Rectangle: = τmax 32VA 4.10 Stress Equations Related to Mohr’s Circle , = + ± + (-) σ1 σ2 σx σy2 τxy2 σx σy2 2 = ( -); = + +-; = ± +(-2φ arctan 2τxyσx σy σφ σ1 σ22 σ1 σ22cos2φ τmax τxy2 σx ) σy2 2 =-( ) τφ σ1 σ22sin 2φ 4.12 Stress Concentration Factors, K t = ; = σmax Ktσnom τmax Ktτnom 4.16 Thermal Stresses = ϵ α∆T-; -; -ϵ strain α coefficient of thermal expansion ∆T temperature change...
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