Shear Stress from Shear Load in closed non symmetric section
Q
t1
t2
Shear load is applied such that (pure) bending occurs
can't use symmetry to determine where to start s = 0 arc length parameter
approach: divide into two problems and superpose:
Q
t1
t2
=
q*
+
q* is the shear flow we have developed to date opening the section and
q1 is a
constant
shear flow in the closed section
superposition => we add the two flows for the actual shear flow
how do we calculate each.
i.e q = q* + q1
We have one condition; the net has to match the applied load
the second comes from the physical situation; the slip at the cut must be 0
q1
1/7
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b
m_star
q s
⌠
slip
=
γ
ds
where integral is circular and
γ
is the shear strain
⌡
⌠
⌠
⌠
γ
ds
=
τ
ds
=
1
⋅
q
ds
=
0
G the shear modulus = constant =>
⌡
G
G
t
⌡
⌡
⌠
⌠
q
1
q_star
ds
+
ds
=
0
q
1
is constant =>
t
t
⌡
⌡
−
q_star s
⌠
( )
ds
t s
⌡
0
( )
where the numerator is the integral around the cross
q
1
:=
⌠
section and the denominator is as well (circular)
1
ds
t s
( )
⌡
⌠
b
⌠
b
( )
ds
=
Q
⋅
m_star s
in this case the example is
q_star s
I
s
⌡
0
( )
I
t s
( )
ds
symmetric wrt z axis Iyz = 0 would
( )
:=
Q
⋅
m_star
( )
and
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 Spring '03
 DavidBurke
 Shear Stress, Shear, Stress, 0 g, Shear strength, Shear strain, Shear modulus

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