Lecture #10 Stress state of sweptback wing

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15 Νοε 2013 (πριν από 3 χρόνια και 10 μήνες)

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Lecture #10

Stress state of sweptback wing

STRUCTURAL LAYOUT OF SWEPTBACK WINGS

2

Boeing 757

STRUCTURAL LAYOUT OF SWEPTBACK WINGS

3

STRUCTURAL LAYOUT

OF SWEPTBACK WINGS

4

STRUCTURAL LAYOUT

OF SWEPTBACK WINGS

5

STRUCTURAL IDEALIZATION

6

7

STRUCTURAL IDEALIZATION

1


front fuse
-
lage beam;

2


rear fuse
-
lage beam;

3


fuselage
rib;

4


front spar
continuation;

5


root rib;

6


front spar;
7



ribs;

8


rear spar;

9


wingbox;

10


end rib.


STRUCTURAL LAYOUT OF SWEPTBACK WING

8

9

STRUCTURAL IDEALIZATION

DESIGN MODEL OF SWEPTBACK WING

10

ASSUMPTIONS AND SIMPLIFICATIONS

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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.


STRUCTURAL IDEALIZATION

12

Spar caps

Normal forces
only

Quite robust
idealization

Skins (spar
webs, upper and
lower panels)

Shear flows only

Too robust
idealization

Root triangle
beams

Bending
moments and
shear forces

Appropriate
idealization

AIM OF THE PROJECT

13


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.

ANALYSIS OF THE MODEL

14

Kinematical

analysis:


ANALYSIS OF THE MODEL

15

Matrix for statical analysis:














ANALYSIS OF THE MODEL

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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.

ANALYSIS OF THE MODEL

17

FLOWCHART OF SOLUTION USING FORCE METHOD

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Classification

of the problem

Basic system

Loaded and

unit states

Redundant constraints are
removed

In loaded state, external load is
applied. In unit states, unit force
is applied instead of constraint.

Canonical
equations

Total stress state

Forces in removed constraints
are determined

Displacements corresponding to
removed constraints are
determined for each state

BASIC SYSTEM

19

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

23

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.

STRESS STATE OF WINGBOX


SHEAR FLOWS

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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 1
ST

UNIT STATE

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FORCES IN 1
ST

UNIT STATE

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FORCES IN 1
ST

UNIT STATE

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LOADING OF ROOT TRIANGLE IN 1
ST

UNIT STATE

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MOMENTS

IN ROOT

TRIANGLE

IN 1
ST

UNIT

STATE

31

TABLE FOR MOMENTS IN DIFFERENT STATES

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SYSTEM OF CANONICAL EQUATIONS

33

We have twice statically indeterminate problem:






Each of coefficients has three terms; last term is from
bending moments:













TABLE FOR MOMENTS IN DIFFERENT STATES

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EXAMPLE

FOR A TOTAL

STRESS

STATE

NEXT LECTURE

36

EXAM #2

All materials of our course are available at
k102.khai.edu