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Lecture #12
Stress state of sweptback wing
STRUCTURAL LAYOUT OF SWEPTBACK WINGS
Boeing 757
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STRUCTURAL LAYOUT OF SWEPTBACK WINGS
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STRUCTURAL LAYOUT
OF SWEPTBACK WINGS
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STRUCTURAL LAYOUT
OF SWEPTBACK WINGS
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STRUCTURAL IDEALIZATION
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STRUCTURAL IDEALIZATION
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STRUCTURAL LAYOUT OF SWEPTBACK WING
1 – front fuselage beam;
2 – rear fuselage beam;
3 – fuselage
rib;
4 – front spar
continuation;
5 – root rib;
6 – front spar;
7 – ribs;
8 – rear spar;
9 – wingbox;
10 – end rib. 8
STRUCTURAL IDEALIZATION
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DESIGN MODEL OF SWEPTBACK WING
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ASSUMPTIONS AND SIMPLIFICATIONS
a) deformations are linear;
b) displacements are small;
c) wingbox has absolutely rigid cross section;
d) the axial loads are carried only by spar caps;
e) spar webs and skins carry only shear loads;
f) the elements of the root triangle ABC and the
fuselage structure (RR, FR, FSC, FFB, RFB) are
planar beams, they are finitely rigid in their planes and
absolutely flexible outside them;
g) upper and lower skins of the root triangle do not
carry any loads;
h) the fuselage structure composed of beams FR,
FFB, RFB is a spatial statically determinate system.
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STRUCTURAL IDEALIZATION
Spar caps
Normal forces
only
Skins (spar
webs, upper and Shear flows only
lower panels)
Root triangle
beams
Bending
moments and
shear forces
Quite robust
idealization
Too robust
idealization
Appropriate
idealization
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AIM OF THE PROJECT
The aim is to find the distribution of bending
moments in root triangle beams.
Other data (normal forces, shear flows) could not be
used since it is obtained using very robust idealization.
Actually, the wingbox is studied just to take its rigidity
into account.
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ANALYSIS OF THE MODEL
Kinematical
analysis:
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ANALYSIS OF THE MODEL
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ANALYSIS OF THE MODEL
Matrix for statical analysis:
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ANALYSIS OF THE MODEL
Conclusion:
The system is twice statically indeterminate.
The force method will be used as one being optimal
for systems with small degree of statical
indeterminacy.
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FLOWCHART OF SOLUTION USING FORCE METHOD
Classification
of the problem
Basic system
Loaded and
unit states
Canonical
equations
Redundant constraints are
removed
In loaded state, external load is
applied. In unit states, unit force
is applied instead of constraint.
Displacements corresponding to
removed constraints are
determined for each state
Forces in removed constraints
are determined
Total stress state
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BASIC SYSTEM
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EQUIVALENT SYSTEM
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BASIC SYSTEM IN LOADED STATE
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FORCES IN LOADED STATE
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STRESS STATE OF WINGBOX – NORMAL FORCES
The stress state of wingbox is a problem inside a
problem, twice statically indeterminate.
In contrast to general
problem, it is solved
using Papkovich’
theorem.
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STRESS STATE OF WINGBOX – SHEAR FLOWS
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STRESS STATE
OF WINGBOX –
SUPERPOSITION
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STRESS STATE
OF WINGBOX –
SUPERPOSITION
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LOADS ACTING ON ROOT TRIANGLE BEAMS
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STRESS STATE
OF ROOT
TRIANGLE
BEAMS
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BASIC SYSTEM IN 1ST UNIT STATE
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FORCES IN 1ST UNIT STATE
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FORCES IN 1ST UNIT STATE
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LOADING OF ROOT TRIANGLE IN 1ST UNIT STATE
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MOMENTS
IN ROOT
TRIANGLE
IN 1ST UNIT
STATE
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TABLE FOR MOMENTS IN DIFFERENT STATES
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SYSTEM OF CANONICAL EQUATIONS
We have twice statically indeterminate problem:
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TABLE FOR MOMENTS IN DIFFERENT STATES
Each of coefficients has three terms; last term is from
bending moments:
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EXAMPLE
FOR A TOTAL
STRESS
STATE
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