ESO202A: Mechanics of Solids - Stress and Strain, Lecture notes of Mechanics

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ESO202A: MechanicsESO202A: Mechanics

of Solids of Solids

Stress and Strain Stress and Strain

What is AxialWhat is Axial stress? stress?  Axial Stress = Load/Axial Stress = Load/ AreaArea  Axial Strain = Change in length per unitAxial Strain = Change in length per unit length length  Modulus of elasticity = Stress/StrainModulus of elasticity = Stress/Strain  We will generalize the definition of stressWe will generalize the definition of stress and define stress equal to force/area and define stress equal to force/area

Shear Stress  Shear stress acts tangential to the surface of a material element  Shear stress results in a shape change

Shearing stresses Bolt in Single shear Shearing stresses commonly found in bolts and rivets

Shearing stresses Bolt in Double shear Shearing stresses commonly found in bolts and rivets

Stresses on an oblique plane Axial forces cause both normal and shearing stresses on planes which are not perpendicular to the axis.

Stresses on an oblique plane Magnitude of Normal Stress σ= Q/A θ Or, σ= (P/ A 0 )cos 2 (θ) Magnitude of Shear stress τ = V/A θ Or, τ = (P/ A 0 )cos(θ)sin(θ)

Stress on an oblique plane

Stresses on an oblique plane Consider the special case when angle θ= Axis x' coincides with x axis Axis y' coincides with y axis Normal stress σ xx

= (P/ A

0

Or, σ x'x' = σ xx cos 2 (θ) Similarly, τ x'y' =- σ xx cos(θ)sin(θ)

Stresses on an oblique plane Normal force applied to a bar on an inclined sction produces a combination of shear and normal stresses.

Stresses on an oblique plane

Stresses on an oblique plane

Stresses on an oblique plane

Stresses on an oblique plane