Lecture03

# Bending moment both if applicable iii axial pressure

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Bending moment (both, if applicable) (iii) Axial pressure (if pressure vessel) σ zz = N zz A zz + M xx y I xx M yy x I yy + PR 2 t

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ME 382 Lecture 03 10/ix/07 4 For example, shear stress may have a component from Torque (& shear force - will try to avoid problems with shear forces in ME382) If the problem involves a pressure vessel, there will be one more non-zero normal stress (otherwise, everything else will be zero) 8. Calculate principal normal stresses (and maximum shear stress) acting at point using stress transformation equations or Mohr’s circle. Important because the largest stresses acting at a point are not necessarily aligned with the section. All failure criteria for materials involve either principal stresses or maximum shear stresses σ xx σ yy τ yx τ xy y x Mohr’s circle for stress Center of circle: σ xx + σ yy ( ) /2 Radius of circle: 1 2 σ xx σ yy ( ) 2 + 4 τ xy 2 Principal normal stresses: σ 1 , σ 2 = σ xx + σ yy ( ) 2 ± 1 2 σ xx σ yy ( ) 2 + 4 τ xy 2 (in direction for which τ 12 = 0)
ME 382 Lecture 03 10/ix/07 5 Maximum shear stresses inclined at 45 º (2 θ = 90 º ) to principal axes “Principal” or “maximum” shear stress in x-y plane: τ max = 1 2 σ x σ y ( ) 2 + 4 τ xy 2 Example σ x = 100, σ y = 40, σ z = 0.0, τ xy = 30, τ xz = τ yz = 0.0 MPa
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