1. Prof. Carlos Montestruque
SHEAR LAG
21/04/2017
Prof. Carlos Montestruque

2. SHEAR LAG
 Thin sheet structures under loading conditions that produce
characteristically large and non-uniform axial (stringer) stress.
 More pronounced in shells of shallow section than in shells in
deep section.
 Much more important in wings than in fuselage ( if the basic method
of construction is similar)
 The effect of sheet panel shear strains is to cause some stringers to
resist less or more axial load than those calculated by beam
theory
 In general, the shear lag effect in skin-stringer box beam is not
appreciable except for the following situations:
 Thin or soft (i.e., aluminum) skin
 Cutouts which cause one or more stringers
to be discontinued
 Large abrupt changes in external load applications
 Abrupt changes in stringer areas
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3. Example:
Axial constraint stresses in a doubly symmetrical, single cell,
six boom beam subject to shear.
The bending stress in box beams do not always conform very closely
to the predictions of the simple beam bending theory.
The deviations from the theory are caused primary by the shear
deformations in the skin panels of the box that constitutes the
flanges of the beam.
The problem of analyzing these deviations from the simple beam
bending theory become known as the SHEAR LAG EFFECT
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4. Solution: Top cover of beam Loads on web and corner booms of beam
Equilibrium of an edge boom element
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5. Similarly for an element of the central boom
Now considering the overall equilibrium of a length z of the cover, we have
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6. We now consider the compatibility condition which exists in the displacement of
elements of the boom and adjacent elements of the panel.
in which and are the normal strains in the elements of boom or
Now
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7. Choosing , say, the unknown to be determined initially.
From these equations, we have
Rearranging we obtain or
Where is the shear lag constant
The differential equation solution is
The arbitrary constant C and D are determinate from the boundary conditions of the
cover of the beam.
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8. when z = ;
when z = L
From the first of these C = 0 and from the second
Thus
The normal stress distribution follows
The distribution of load in the edge boom is
whence
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9. The shear flow
whence
The shear stress
Elementary theory gives
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10. Rectangular section beam supported at corner booms only
The analysis is carried out in an identical manner to that in the previous case except
that the boundary conditions for the central stringer are when z = 0 and z = L.
Where is the shear lag constant
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11. Beam subjected to combined bending and axial load
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12. is load in boom 1
is load in boom 2
Equilibrium of boom 2
Equilibrium of central stringer A
Equilibrium of boom 2
Longitudinal equilibrium
Moment equilibrium about boom 2
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13. The compatibility condition now includes the effect of bending in addition to extension
as shown in figure below
Where and z are function of z only
Thus
Similarly for an element of the
lower panel
Subtraction these equation
or, as before
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14. Choose as the unknown, and using these equations
we obtain or
Where is the shear lag constant
The differential equation solution is
The arbitrary constant C and D are determinate from the boundary conditions of the
cover of the beam.
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15. when z = ;
when z = L
we have the distribution load in the central stringer
or, rearranging
The distribution of load in the edge booms 1 and 2
Finally the shear flow distribution are
The shear flow and are self-equilibrating and are entirely produced by shear lag
effect ( since no shear loads are applied).
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