1 / The basic three, two, and one dimensional equations in structural analysis.- 1.1 Introduction.- 1.2 Three dimensional equations.- 1.3 The displacement method of solution.- 1.4 The stress method of solution.- 1.5 The combined method of solution.- 1.6 Two dimensional equations.- 1.7 Saint Venant’s principle.- 1.8 One dimensional beam equations.- 1.9 No shear stresses in the beam.- 1.10 Beam cross section of a thin plate with one shear stress.- 1.11 Thin web beams with large flange areas and one shear stress.- 1.12 Torsion of circular cross section and thin wall closed box.- 1.13 Thin web box beam with general loading.- 1.14 Inelastic effects in beams with temperature.- 1.15 Example of inelastic axial stresses and strains with temperature.- 1.16 Sequence loading and thermal cycling in beams.- 1.17 Load-strain design curves for beams.- 1.18 Problems.- References.- 2 / Virtual displacement and virtual force methods in structural analysis.- 2.1 Introduction.- 2.2 The principle of virtual displacements.- 2.3 The unit displacement theorem.- 2.4 The principle of virtual forces.- 2.5 The unit load theorem.- 2.6 The principle of mixed virtual stresses and virtual displacements.- 2.7 The mixed unit displacement and unit load theorem.- 2.8 Two dimensional form of the virtual principles.- 2.9 One dimensional forms of the virtual principles.- 2.10 The one dimensional virtual principles with temperature, inelastic and large displacement effects.- 2.11 Matrix forms of the virtual principles.- 2.12 Problems.- References.- 3 / The virtual principles for pin-jointed trusses.- 3.1 Introduction.- 3.2 The unit displacement theorem for trusses.- 3.3 The unit load theorem for trusses.- 3.4 Inelastic effects with temperature changes in trusses.- 3.5 Matrix equations for trusses from the unit displacement theorem.- 3.6 Matrix equations for trusses from the unit load theorem.- 3.7 Matrix equations for trusses from the mixed unit displacement and unit load theorem.- 3.8 Problems.- References.- 4 / The virtual principles for simple beams.- 4.1 Introduction.- 4.2 Principle of virtual displacements for beams.- 4.3 Point values for beam elements by the principle of virtual displacements.- 4.4 Principle of virtual forces for beams.- 4.5 Point values for beam elements by the unit load theorem.- 4.6 Principle of mixed virtual stresses and virtual displacements for beams.- 4.7 Inelastic and temperature effects in simple beams.- 4.8 Matrix equations for beams from the unit displacement theorem.- 4.9 Matrix equations for beams from the unit load theorem.- 4.10 Matrix equations for beams from the mixed unit displacement and unit load theorem.- 4.11 The beam column equations.- 4.12 Problems.- References.- 5 / Box beam shear stresses and deflections.- 5.1 Introduction.- 5.2 Shear stresses in beams.- 5.3 Torsional shear stresses in beams.- 5.4 Shear flows in open box beams.- 5.5 Shear flows in single cell box beams.- 5.6 Shear flows in multi-cell box beams.- 5.7 Shear center for closed box beams.- 5.8 Shear flows in tapered box beams.- 5.9 Inelastic and buckling shear stresses in beams.- 5.10 Axial and bending deflections of box beams with inelastic and temperature effects.- 5.11 Shear deflections of beams.- 5.12 Torsional rotation of beams.- 5.13 Rotation of swept wings.- 5.14 Spanwise airload distribution and static wing divergence under rotation.- 5.15 Static aileron effectiveness and reversal speed under wing rotation.- 5.16 Problems.- References.- 6 / Shear lag in thin web structures.- 6.1 Introduction.- 1. Solutions for determinate cases.- 6.2 Shear flows due to concentrated loads into thin webs.- 6.3 Shear flows around cut-outs in thin web beams.- 6.4 Cut-outs in box beams.- 6.5 Shear flows in ribs and bulkheads.- 6.6 Forces on ribs due to airloads and taper effects.- 2. Solutions for redundant cases.- 6.7 Restraint effects in thin web structures.- 6.8 Shear flows in redundant beams in one plane.- 6.9 Deflections of thin web structures.- 6.10 Flexibility matrices for shear web elements and stiffener elements.- 6.11 Matrix solutions for thin web beams in one plane.- 6.12 Matrix solutions for box beams.- 6.13 Load redistribution in swept back wings.- 6.14 Problems.- References.- 1 / Allowable stresses of flight vehicle materials.- 1.1 Introduction.- 1.2 Tension, shear, and bearing allowable stresses.- 1.3 Temperature effects on allowable stresses.- 1.4 Allowable compression stresses.- 1.5 Allowable combined stresses.- 1.6 Creep effects on allowable stresses.- 1.7 Room temperature fatigue effects upon allowable stresses.- 1.8 Temperature effects upon allowable fatigue stresses.- 1.9 Crack effects upon allowable fatigue stresses.- 1.10 Problems.- References.- 2 / Analysis and design of joints and splices.- 2.1 Introduction.- 2.2 Analysis of plate splices with axial tension forces.- 2.3 Multi-row tension splices.- 2.4 Joints with eccentric loading.- 2.5 Minimum weight design of splice for beam with rectangular cross section.- 2.6 Design of splices for I-beams and thin shear webs.- 2.7 Deflection effects on load distribution in splices.- 2.8 Temperature and inelastic effects on load distribution in splices.- 2.9 Welded joints.- 2.10 Bonded joints.- 2.11 Problems.- References.- 3 / Structural design of aircraft components.- 3.1 Introduction.- 3.2 Design of minimum weight columns without local buckling.- 3.3 Design of minimum weight sections with local buckling and crippling.- 3.4 Design of minimum weight columns with local buckling.- 3.5 Minimum weight design for stiffened panels in compression.- 3.6 Effective areas for stiffened panels.- 3.7 Effect of load intensity on wing design.- 3.8 Design of box beam cross sections with four spar caps.- 3.9 Analysis of diagonal tension beams.- 3.10 Problems.- References.- 4 / Analysis and design of pressurized structures.- 4.1 Introduction.- 4.2 Membrane stresses in thin shells.- 4.3 Cut-outs in thin shells with membrane stresses.- 4.4 Bending in circular cylindrical shells with axially symmetric loading.- 4.5 Bending in pressurized aircraft fuselages from stringers and frames.- 4.6 Bending of non-circular cross sections with internal pressure.- 4.7 Bending of non-circular fuselage rings with internal pressure.- 4.8 Bending of non-circular fuselage rings with point loads.- 4.9 Effect of internal pressure on buckling of cylindrical shells.- 4.10 Pressure stabilized structures.- 4.11 Problems.- References.- 5 / Approximate solutions using the virtual principles.- 5.1 Introduction.- 5.2 Approximate solutions for beams using the principle of virtual displacements.- 5.3 Approximate solutions for columns.- 5.4 The tapered cantilever beam with numerical integration.- 5.5 Tapered beam finite element matrices for columns.- 5.6 The unit load theorem and numerical integration.- 5.7 Approximate solutions for beams using the mixed virtual principle.- 5.8 Problems.- References.- 6 / Dynamics of simple beams.- 6.1 Introduction.- 6.2 Bending vibrations of simple beams.- 6.3 Forced motion of uniform beam.- 6.4 Approximate solutions for frequencies and mode shapes.- 6.5 Torsional vibrations of simple beams.- 6.6 Finite element matrices for beam frequencies.- 6.7 Flutter of wing segment with one degree of freedom.- 6.8 Flutter of wing segment with two degrees of freedom.- 6.9 Dynamic loads on beams.- 6.10 Problems.- References.- 7 / The plate equations.- 7.1 Introduction.- 7.2 The plate inplane case using the principle of virtual displacements.- 7.3 The plate inplane case using the principle of virtual forces.- 7.4 The plate inplane case using the mixed virtual principle.- 7.5 The plate bending case using the principle of virtual displacements.- 7.6 The plate bending case using the principle of virtual forces.- 7.7 The plate bending case using the mixed virtual principle.- 7.8 Combined inplane and lateral forces.- 7.9 Combined forces with large bending deflections.- 7.10 Buckling of plates.- 7.11 Plate vibrations.- 7.12 Problems.- References.- 8 / Approximate matrix equations for plate finite elements.- 8.1 Introduction.- 8.2 The point unknowns for the matrices.- 8.3 The methods to obtain the matrix equations.- 8.4 Inplane plate element matrices from the principle of virtual displacements.- 8.5 Inplane plate element matrices from the principle of virtual forces.- 8.6 Inplane plate element matrices from the mixed virtual principle.- 8.7 Bending plate element matrices from the principle of virtual displacements.- 8.8 Bending plate element matrices from the principle of virtual forces.- 8.9 Bending plate element matrices from the mixed virtual principle.- 8.10 Matrices for constant stress triangular elements.- 8.11 Problems.- 9 / Matrix structural analysis using finite elements.- 9.1 Introduction.- 9.2 General beam elements in local coordinates.- 9.3 General beam elements in datum coordinates.- 9.4 Triangular plate elements with inplane forces.- 9.5 Assembly of finite elements by the virtual principles.- References.- 10 / Composite Materials.- 10.1 Introduction.- 10.2 Stress-strain equations for nonisotropic materials.- 10.3 Stress-strain equations for plane stress in an orthotropic material.- 10.4 Forces and moments in laminated plates.- 10.5 Stresses in laminated plates.- 10.6 Allowable stresses for laminated plates.- 10.7 Interlamina stresses.- 10.8 Joints in laminated plates.- 10.9 Bending deflections of laminated plates.- 10.10 Buckling loads for laminated plates.- 10.11 Vibrations of laminated plates.- 10.12 Problems.- References.- Appendix A / Notes on matrix algebra.- A.1 Definition of matrices.- A.2 Addition, subtraction, multiplication of matrices.- A.3 Determinants.- A.4 Matrix inversion.- A.5 Solution of systems of simultaneous equations by matrices.- A.6 Solution of systems of simultaneous equations by tri-diagonal matrices.- A.7 Solution of systems of equations by Jordan successive transformations.- A.8 Matrix representations.- A.9 Orthogonal matrices.- A.10 Eigenvalues and eigenvectors of matrices.- A.11 Note on matrix notation.- References.- Appendix B / External forces on flight vehicles.- B.1 Introduction.- B.2 Inertial forces for rigid body translation and rotation in a vertical plane.- B.3 Air forces on airplane wing.- B.4 Airplane equilibrium equations in flight. Load factors.- B.6 Wing spanwise lift coefficient distribution.- B.7 Spanwise lift coefficient distribution on twisted wings.- B.8 Spanwise airload, shear, and moment distributions on wing.- B.9 Distribution of inertia forces on wing and fuselage.- B.10 Forces and moments on landing gear structures.- B.11 Thermal forces.- B.12 Miscellaneous forces.- B.13 Deflection effects on the external forces.- B.14 Criteria for the structure to support the external forces.- B.15 Problems.- References.- Appendix C / Derivation of the strain energy theorems from the virtual principles.- C.1 Work and strain energy.- C.2 Maximum and minimum strain energy and total potential energy.- C.3 Theorem of minimum total potential energy.- C.4 Theorem of minimum strain energy.- C.5 Castigliano’s theorem (Part I).- C.6 Hamilton’s principle.- C.7 Theorem of minimum total complementary potential theory.- C.8 Theorem of minimum complementary strain energy.- C.9 Castigliano’s theorem (Part II).- C.10 Reissner’s variational principle.- C.11 Comparison of the virtual principles and the strain energy theorems.- References.