Aircraft Structures 1 2011 Part 16 pps

586 Index Materials of aircraft construction 21 1-20 aluminium alloys 214-16 composite materials 2 18-20 glass 218 history 211-14 plastics 217, 218 steel 216,217 titanium 217 analysis of pin-jointed frameworks 500-7 analysis of space frames 507-9 application to statically indeterminate finite element method 516-32 Matrix methods 494-532 frameworks 507 displacement functions beam element 5 18 triangular element 522 quadrilateral element 529 stiffness matrix for a beam element stiffness matrix for a quadrilateral stiffness matrix for a triangular element tetrahedron and rectangular prism 517-21 element 528-30 521-8 elements 532 flexibility method 494 notation 495,496 stiffness influence coefficient 496 stiffness matrix 496 stifkess matrix for a uniform beam 509-16 stiffness matrix for an elastic spring 496, 497 for two elastic springs in line 497-500 stiffness method 494 Maxwell, J.C. 103 Membrane analogy 61-3 Miner and Palmgren’s linear cumulative Model analysis of a fixed beam 106, 107 Modulus of elasticity 24 Modulus of rigidity, shear modulus 25 Modulus of volume expansion, bulk Mohr’s circle of strain 23, 28 Mohr’s circle of stress 12-16 Moment couple (bimoment) 482 Monocoque structures 223 damage law, see Fatigue modulus 26 Neuber beams 316 Neutral axis 281 Open section beams constraint general systems of loading, see Structural shear centre 298-300 stress, strain and displacement relationships 291-5 subjected to bending 276-91 subjected to constraint, see Structural subjected to distributed torque loading subjected to shear, see Shear of open subjected to torsion, see Torsion of open Oscillations of mass/spring and mass/beam constraint 478,479 section beams section beams systems, see Structural vibration Plane strain 20, 21 Plane stress 8, 9 Plastics, see Materials of aircraft construction Plates, thin anticlastic bending 125 anticlastic surface 125 bending and twisting 125-9 bending of plates having a small initial curvature 141 boundary conditions 132-4 buckling 169-78 buckling coefficients 171-3 combined bending and in-plane loading composite, see Stress analysis of aircraft energy method (Rayleigh-Rib) 142-9 experimental determination of buckling failure stress in plates and stiffened panels flexural rigidity 124 Fourier series 135 inelastic buckling 173 instability of stiffened panels 175-7 interrivet buckling 177 Kirchhoff, G.R. 133 maximum values of stress 137 neutral plane 122 plasticity correction factor 173 potential energy of transverse load 144 137-41 components load 174 177-80 of in-plane loads 144-6 Index 587 principal curvatures 127 principal moments 127 pure bending 122-5 secant modulus 173 strain energy in bending and twisting 142, subjected to a distributed transverse load synclastic surface 125 tangent modulus 173 total potential energy 147 limiting value 26 walled column 184 143 129-37 Poisson's ratio 25 Polar second moment of area of a thin- Potential energy 70, 71, 73-6, 144-9, 165-9 Prandtl stress function, see Torsion of solid Principal axes of a beam section 81 Principal planes 11 Principal strains 23 Principal stresses 11, 12 Principle of stationary value of total sections complementary energy 76, 77 application to deflection problems 77-85 application to statically indeterminate systems 85-100 Principle of stationary value of total Principle of superposition 103 Principle of virtual work 71-3 virtual displacements 7 1, 72 virtual forces 72, 73 potential energy 73-6, 142-9 Principles of stressed skin construction 21 1-32 Rayleigh, Lord 103, 565 Rayleigh-Ritz method bending of a beam 75 buckling of columns 168 oscillation of beams 565-8 thin plates 142-9 Reciprocal theorem 68 Reduced elastic modulus of a column 159 Safe life structures, see Fatigue St. Venant, B. de principle 42 semi-inverse method 41, 43-8 warping function, see Torsion of solid sections Sandwich panels 230,23 1 Secant modulus 173 Second moments of area of inclined and Semi-inverse method for elasticity problems Semi-monocoque structures 223 Shear centre 295,298-300, 304-7, 392 Shear lag, see Structural constraint Shear lines 57 Shear of closed section beams 300-7 shear flow distribution 340, 341 curved thin sections 288,289 41,43-8 alternative method for the calculation of shear centre 304-7 shear flow distribution 300-2 twist and warping 303,304 aircraft components alternative method for the calculation of shear centre 298-300 shear flow distribution 295-8 components a closed section beam 445-8 Shear of fuselages, see Stress analysis of Shear of open section beams 295-300 shear flow distribution 340, 341 Shear of wings, see Stress analysis of aircraft Shear stress distribution at a built-in end of Slenderness ratio of a column, see Columns Southwell plot columns 162 plates 174 axial loads 162-5 construction Stability of beams under transverse and Stainless steel, see Materials of aircraft Statically determinate systems 24 Statically indeterminate systems 24, 85-100 Stiffened panels 175-80 failure stress 177-80 instability 175-7 definition 17 experimental measurement 28-32 longitudinal or direct strain 16- 18 maximum shear strain 23 Mohr's circle 23, 28 plane strain 20, 37, 38 principal strains 23 shear strain 16, 18, 19 strain gauge rosette 29 strains on inclined planes 21, 22 Strain 16-32 588 Index Strain cont. volumetric strain 26 Strain energy 68-71, 142, 143, 166 in simple tension 69 Strain gauge rosette 29 Stress 3-16 as a tensor 5 complex stress systems 10-16 components at a point 4, 6 definition 3,4 maximum shear stress 12 Mohr's circle 12-16 normal or direct stress 4 notation for stresses 5-7 plane stress 8, 9 principal stresses, planes 11, 12 resultant of shear and normal stress 4 shear stress 4 sign conventions 6 stresses on inclined planes 10, 11, 12-14 tensile stress 3 Stress analysis of aircraft components 362-432 cut-outs in wings and fuselages 415-25 fuselages 374-80 bending 375, 376 shear 376-9 torsion 379, 380 fuselage frames and wing ribs 406-15 laminated composite structures 425-32 composite plates 429-32 elastic constants 425-9 law of mixtures 426 tapered beams 362-74 beams having variable stringer areas open and closed section beams single web beam 363-6 bending 381-3 deflections 404,405 idealized three-boom shell 380, 381 method of successive approximations shear 387-92 shear centre 392 tapered wings 392-5 torsion 383-6 Stress concentrations 63, 258 Stress functions 38, 39 371-4 366-71 Wings 380-405 395-404 Stress, strain and displacement relationships for open and single cell closed section beams 291-5 Stress-strain relationships 24-8, 37 Structural constraint 443-85 constraint of open section beams 465-85 general systems of loading 479-82 moment couple (bimoment) 482 position of centre of twist 470,471 subject to distributed torque loading torsion-bending constant, 470-4 torsion of a beam of arbitrary section torsion of an I-section beam 465-7 wire analogy 472-4 general aspects 443-5 eigenload 444 flexural axis 444 zero warping axis 444 beam subjected to combined bending beam supported at corner booms only six-boom beam subjected to shear 478,479 467-78 shear lag 455-65 and axial load 461-5 460,461 455-60 shear stress distribution at the built-in end of a closed section beam 445-8 thin-walled rectangular section beam subjected to torsion 449-54 direct stress distribution 453 idealization 449 rate of twist 454 shear stress distribution 453,454 warping 453 booms 328 effect of idealization on analysis 331-41 bending of open and closed section curved web with constant shear flow shear of closed section beams 338-40 shear of open section beams 332-8 torsion of open and closed section of a panel carrying a linearly varying direct stress 328, 329 of a wing section 327,328 Structural instability 153-97 Structural idealization 327-41 beams 331,332 336-8 beams 340 index 589 of columns, see Columns of plates, see Plates primary 153 secondary 153 approximate methods 565-8 flutter, flutter speeds, see Flutter lumped mass concept 552 normal modes 552 oscillation of a mass/spring system 552-4 Structural vibration 551-68 flexibility method 553 stiffness method 553 system 554-7 oscillation of a mass/weightless cantilever oscillation of a uniform beam 560-5 Surface forces 7 Symmetric manoeuvre loads, see Airworthiness Synclastic surface 125 Tail unit components 225 Tangent modulus 157, 159, 173 Tapered beams, see Stress analysis of Temperature effects 107-9 Tension field beams 188-97 aircraft components complete diagonal tension 189-94 diagonal tension factor 194 effect of taper 196 incomplete diagonal tension 194-6 loading (buckling stress) ratio 195 Titanium 217 Torsion of a thin-walled rectangular section beam, see Structural constraint Torsion of closed section beams 307-16 Bredt-Batho theory 307-9 condition for zero warping 315, 316 displacements 309-15 Neuber beams 316 shear flow distribution 307 warping distribution 309-16 aircraft components point of zero warping 320-2 shear stress distribution 317 subjected to constraint, see Structural constraint torsion constant 3 17 warping 3 17-22 primary 318 Torsion of fuselages, see Stress analysis of Torsion of open section beams 316-22 secondary 3 17,3 18 Torsion of solid sections 51-65 bar of elliptical cross-section 57-9 contour lines 62, 63 Laplacian operator 53 membrane analogy 61-3 narrow rectangular strip 63-5 Prandtl stress function solution 51-9 St. Venant warping function solution 59-61 shear lines (lines of shear stress) 57 stress concentrations 63 torsion constant 56, 59, 61. 64 torsional rigidity 56 warping displacement 59, 64 warping function 60 Torsion of wings, see Stress analysis of aircraft components Total complementary energy 68, 76-100, 108 of a beam subjected to a temperature of an end loaded cantilever 81,82 of a multi-redundant system 90 of a pin-jointed framework 77-81 of a propped cantilever 89, 90 of ring frames 93-100 of a statically indeterminate framework of a trussed beam 91-3 of a uniformly loaded cantilever 82, 83 Total potential energy 68, 71, 73-6, 144-9, gradient 107-9 86-9 165-9 of a thin plate 147, 170 Twist and warping of a closed section beam 303, 304, 309-15 Unit load method 68, 100-2, 342-4,404, 405 deflection of open and closed section deflection of multicell wings 404,405 beams 342-4 Vibrations, see Structural vibrations Virtual work 68, 71-3 displacements 7 1, 72 forces 72, 73 Volumetric strain 26 Wagner, theory for tension field beams 188-96 torsion bending theory 468-78 590 Index Warping bars of solid section 59,64 condition for zero warping in a closed section beam 315, 316 of a closed section beam 309-16 of a rectangular section beam 453 narrow rectangular strip 64,65 warping of open section beams 317-22 primary 318 secondary 3 18 zero warping axis 444 Wing bending torsion flutter 569 Wing components 223-5 Wing ribs 223,225,229,230 see also Stress analysis of aircraft components Wing torsional divergence 541-5 Wings, analysis, see Stress analysis of Wire analogy for torsion bending constant Wrinkling in stiffened panels 177 aircraft components 472-4 Young’s modulus 24 Zero warping axis 444 Aircrafi Structures for Engineering Students provides a comprehensive self- contained course in aircraft structures. Starting with the structural mechanics of aircraft this book goes on to cover elasticity, aeroelasticity and airworthiness. The ne\v edition has been thoroughly revised and updated and includes: 0 Extra worked examples and problems 0 Latest materials in aircraft construction 0 Airframe loads produced by manoeuvring 0 Increased Finite Element analysis A solutions manual for lecturers to accompany the book is available free from the Iveb at ~~ww.bh.com/manuals/075065692 1 f4s an introduction to the problem encountered in the structural design of modern aircraff, Megson’s book can be recommended to both students and those already engaged in structural analysis in aerospace design ofices.’ AEROSPACE (OF THE SECOR’D EDITION) ALSO OF INTEREST Chi1 Jet Aircraft Design L. Jenkinson, P. Simpkin and D. Rhodes Aerodjmamics for Engineering Students, 4th Edition E.L. Houghton and P.\Y. Carpenter An imprint of Elsevier Science www.bh.com . Materials of aircraft construction 21 1-20 aluminium alloys 214 -16 composite materials 2 18 -20 glass 218 history 211 -14 plastics 217 , 218 steel 216 , 217 titanium 217 analysis of. shear strain 16 , 18 , 19 strain gauge rosette 29 strains on inclined planes 21, 22 Strain 16 -32 588 Index Strain cont. volumetric strain 26 Strain energy 68- 71, 14 2, 14 3, 16 6 in simple. section beams 307 -16 Bredt-Batho theory 307-9 condition for zero warping 315 , 316 displacements 309 -15 Neuber beams 316 shear flow distribution 307 warping distribution 309 -16 aircraft components