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**Definition of Normal Stress at a Point, P, in an
axial member**
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It’s possible that the
axial force might vary over the cross-section of a structural
member. In that case let the element of force
be ΔF over an element of area ΔA
for the cross-section.
Then the normal stress, σ_{p}, at point P
in the cross-section of the axial member is
σ_{p} =
lim
ΔF / 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 of
σ over the
cross-section. Click
here for a review of centroids.
F
= ∫ σ(y,z) dA
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