Aerospace Structures and Materials: Box Beam Analysis
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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
Aerospace Structures and Materials: Box Beam Analysis
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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 • 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?
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
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
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
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
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
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
h q L t AEnclosed = Lh/2 Torsional Shear Flow • What is the torsional moment caused by a shear flow in a skin?
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
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
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
Multi-Cell, No Stringer Box BeamExample Problem • See Textbook p.230
