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 vo
Trang 1Materials 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
Trang 2principal 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
Trang 3Strain 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
Trang 4of 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
Trang 5Warping
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
Trang 10contained 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)
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