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Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

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Lecture #12 Stress state of sweptback wing
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Page 1: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

Lecture #12Stress state of sweptback wing

Page 2: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

STRUCTURAL LAYOUT OF SWEPTBACK WINGS

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Boeing 757

Page 3: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

STRUCTURAL LAYOUT OF SWEPTBACK WINGS

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Page 4: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

STRUCTURAL LAYOUTOF SWEPTBACK WINGS

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Page 5: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

STRUCTURAL LAYOUTOF SWEPTBACK WINGS

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Page 6: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

STRUCTURAL IDEALIZATION

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Page 7: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

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STRUCTURAL IDEALIZATION

Page 8: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

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

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Page 9: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

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STRUCTURAL IDEALIZATION

Page 10: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

DESIGN MODEL OF SWEPTBACK WING

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Page 11: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

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.

Page 12: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

STRUCTURAL IDEALIZATION

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Spar capsNormal forces

onlyQuite 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

Page 13: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

AIM OF THE PROJECT

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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.

Page 14: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

ANALYSIS OF THE MODEL

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Kinematicalanalysis:

Page 15: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

ANALYSIS OF THE MODEL

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Page 16: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

Matrix for statical analysis:

ANALYSIS OF THE MODEL

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Page 17: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

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

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Page 18: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

FLOWCHART OF SOLUTION USING FORCE METHOD

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Classificationof the problem

Basic system

Loaded andunit 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

Page 19: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

BASIC SYSTEM

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Page 20: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

EQUIVALENT SYSTEM

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Page 21: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

BASIC SYSTEM IN LOADED STATE

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Page 22: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

FORCES IN LOADED STATE

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Page 23: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

STRESS STATE OF WINGBOX – NORMAL FORCES

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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.

Page 24: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

STRESS STATE OF WINGBOX – SHEAR FLOWS

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Page 25: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

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STRESS STATE OF WINGBOX – SUPERPOSITION

Page 26: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

STRESS STATE OF WINGBOX – SUPERPOSITION

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Page 27: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

LOADS ACTING ON ROOT TRIANGLE BEAMS

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Page 28: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

STRESS STATE OF ROOT TRIANGLE BEAMS

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Page 29: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

BASIC SYSTEM IN 1ST UNIT STATE

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Page 30: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

FORCES IN 1ST UNIT STATE

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Page 31: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

FORCES IN 1ST UNIT STATE

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Page 32: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

LOADING OF ROOT TRIANGLE IN 1ST UNIT STATE

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Page 33: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

MOMENTSIN ROOTTRIANGLEIN 1ST UNITSTATE

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Page 34: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

TABLE FOR MOMENTS IN DIFFERENT STATES

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Page 35: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

SYSTEM OF CANONICAL EQUATIONS

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We have twice statically indeterminate problem:

Page 36: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

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

TABLE FOR MOMENTS IN DIFFERENT STATES

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Page 37: Lecture #12 Stress state of sweptback wing. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 2 Boeing 757.

EXAMPLEFOR A TOTALSTRESSSTATE


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