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ESO202A: Mechanics of Solids

Stress and Strain

What is Axial stress?

Axial Stress = Load/ Area Axial Strain = Change in length per unit

length Modulus of elasticity = Stress/Strain We will generalize the definition of stress

and define stress equal to force/area

Normal Stress Axial Stress is

also called normal stress

Normal stress results in a volume change.

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

FBD of Bolt Bearing and shearing Force

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

The axial force P can be resolved as:

Q = P cos(θ) V=P sin(θ) Also area of cross section Aθ = A0 / cos(θ)

Stresses on an oblique plane

Magnitude of Normal Stress σ= Q/Aθ

Or, σ= (P/ A0 )cos 2(θ)

Magnitude of Shear stress τ = V/Aθ

Or, τ = (P/ A0 )cos(θ)sin(θ)

Stress on an oblique plane

Stresses on an oblique plane

Normal Stress σx'x'= Fx'x'/Aθ

Or, σx'x'= (P/ A0 )cos 2(θ)

Shear stress τx'y' = Fx'y'/Aθ

Or, τx'y' =- (P/ A0 )cos(θ)sin(θ)

Stresses on an oblique plane

Consider the special case when angle θ=0

Axis x' coincides with x axis Axis y' coincides with y axis Normal stress σxx= (P/ A0 )

Or, σx'x'= σxx cos 2(θ)

Similarly, τx'y' =- σxx 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

Stresses on an oblique plane

Stresses on an oblique plane

Stresses on an oblique plane

Stresses on an oblique plane

Stresses on an oblique plane

Stresses on an oblique plane

Stresses on an oblique plane