Normal Stress/Shear Stress ††††††††††††††Click here for discussion of Shear Stress



Key Concepts:Normal stress can be viewed as force per unit area acting normal to
an internal section of a structural element, typically called a bar or an axial member.



In a Nut Shell:Definition of an Axial Member


A structure that is generally long in one direction (perhaps in the x-direction), straight,

and has a constant (or mildly tapered) cross-section is generally termed an axial

member.The cross-section of the axial member will have a centroid.The x-axis of
the axial member is assumed to lie along the centroid of each cross-section.
Click here to view a typical axial member.



Definition of Normal Stress in an Axial Member


The average normal stress. σ, in an axial member is the force, P, in the member divided

by its cross-sectional area, A.†††††††††††††††††† σ=P / A


Common units for stress arepsi,ksi,††† MPa, N/mm2(English/Metric)



Definition of Normal Stress at a Point, P, in an axial member


Itís possible that the axial force might vary over the cross-section of a structural

member.In that case let the element of force beΔFover an element of areaΔA

for the cross-section.


Then the normal stress, σp, at pointPin the cross-section of the axial member is


††††††††††††††††††††††††††††††††††††††††††††††††† σp=†† limΔF / ΔA

†††††††††††††††††††††††††††††††††††††††††††† ΔA→ 0

assuming the limit exists.If the cross-section lies in the y-z plane then the axial stress may be

a function of both y and z so that†† σ=σ(y,z)and the total axial force, F, acts through the

centroid at any given cross-section is simply the integral ofσover the cross-section. Click

here for a review of centroids.


†††† ††††††††††††††††††††††††††††††††††††††††††††F=††† ∫ σ(y,z) dA





Click here for examples of normal stress.


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