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Aerospace Structures and Materials: Box Beam Analysis

Aerospace Structures and Materials: Box Beam Analysis. Dr. Tom Dragone Orbital Sciences Corporation. Motivation. Real structures (like wings and fuselages) are more complex than the simple beams that we have looked at so far

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Aerospace Structures and Materials: Box Beam Analysis

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  1. Aerospace Structures and Materials:Box Beam Analysis Dr. Tom Dragone Orbital Sciences Corporation

  2. Motivation • Real structures (like wings and fuselages) are more complex than the simple beams that we have looked at so far • However, the beam analogy works well to determine internal shear and bending moment • Box beam analysis allows us to determine real, lower-level component loads from idealized, higher-level beam analogs Questions: • How can we analyze complex structures consisting of skins, stringers, caps, and webs? • What is a cell? • What do stringers do to a closed cell structure? • What is the torsional moment caused by shear flow in a skin? • Are box beams determinate or indeterminate?

  3. Box Beam Example

  4. Box Beam Types

  5. Skin Cap Stringer Clip Web Box Beam Analysis • Box Beam is a built-up, multi-component structure • Skins and Webs support shear and torsion loads • Stringers, Caps and Clips support axial and bending loads • Closed box section

  6. tsk Atot=Acap+Aclip+nAst+lwtw+lsktsk Acap Ast Aclip tweb Structure Idealization Process of converting: • Real Section • Stringers • Spar Caps • Skins • Clips • Webs • Ideal Section • Axial-load bearing stringers • Zero-thickness shear-carrying • webs and skins and back into AREAS LOADS

  7. Structure Idealization • Idealization DOES NOT mean that the skin does not carry in-plane loads! • Ptot = sAtot = s (Acap + Aclip + nAstringer + lwebtweb + lskintskin) • Ptot = Pcap+Pclip+nPstringer+Pweb+Pskin • Pskin = NskinLskin • Acap > Askin so Pcap > Pskin • but • Pskinis not insignificant

  8. Box Beam Analysis Box Beams: • Can be single cell, two-cell, or multi-cell • Can have stringers or not • Represent fuselage structures, wing structures, leading edges, etc. TWO CELL SINGLE CELL Fuselage MULTI-CELL Wing

  9. Box Beam Loads • Mx = Beam Bending Moment (=M) • Pz = Vertical Shear (=V) • My = Torsion (=T) • Px = Chordwise Shear • Mz = Chord Moment • Py = Axial Force (=P) Vertical +Pz +Mz Spanwise +Py +My Chordwise +Px +Mx } Not Typically Analyzed During Preliminary Design

  10. All Loads Vertical Loads Only Torsion Only Stringer Effects • Stringers allow the box beam to support bending and shear loads • No stringers => Torsion only • 2 stringers => Vertical Bending and Shear only • 3+ stringers (non-co-planar) => All Loads

  11. h q L t AEnclosed = Lh/2 Torsional Shear Flow • What is the torsional moment caused by a shear flow in a skin?

  12. a t q b T Single Cell, No Stringer Box Beam • Statically Determinate q, q Independent [Niu Fig. 6.8.5] Shear flow defined by applied torsion Twist defined by shear flow and geometry

  13. t1 t2 q1 q2 q1 q2 a t1 t3 t2 q3 A1 A2 b1 b2 t1 t2 T T (1) (2) Multi-Cell, No Stringer Box Beam • Statically Indeterminate q, q Dependent • Combine shear flows in the common web Shear flows sum at a junction • Apply torsion equilibrium Internal shear flows balance applied torsion

  14. Multi-Cell, No Stringer Box Beam • Apply compatibility (Equal twist angles) Each cell deforms (twists) the same amount (3) Can solve equations (1), (2), and (3) for q1, q2, and q3

  15. Multi-Cell, No Stringer Box BeamExample Problem • See Textbook p.230

  16. Multi-Cell, No Stringer Box BeamExample Problem

  17. Multi-Cell, No Stringer Box BeamExample Problem

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