Structural Analysis

The authors and their colleagues developed this text over many years, teaching undergraduate and graduate courses in structural analysis courses at the Daniel Guggenheim School of Aerospace Engineering of the Georgia Institute of Technology.

The emphasis is on clarity and unity in the presentation of basic structural analysis concepts and methods. The equations of linear elasticity and basic constitutive behaviour of isotropic and composite materials are reviewed. The text focuses on the analysis of practical structural components including bars, beams, and plates. Particular attention is devoted to the analysis of thin-walled beams under bending, shearing, and torsion. Advanced topics such as warping, non-uniform torsion, shear deformations, thermal effect and plastic deformations are addressed. A unified treatment of work and energy principles is provided that naturally leads to an examination of approximate analysis methods including an introduction to matrix and finite element methods.

This teaching tool based on practical situations and thorough methodology should prove valuable to both lecturers and students of structural analysis in engineering worldwide.

Contenu

Part I Basic tools and concepts; 1 Basic Equations of Linear Elasticity .1.1 The concept of stress; 1.1.1 The state of stress at a point; 1.1.2 Volume equilibrium equations; 1.1.3 Surface equilibrium equations; 1.2 Analysis of the state of stress at a point; 1.2.1 Stress components acting on an arbitrary face; 1.2.2 Principal stresses; 1.2.3 Rotation of stresses; 1.2.4 Problems; 1.3 The state of plane stress; 1.3.1 Equilibrium equations; 1.3.2 Stresses acting on an arbitrary face within the sheet; 1.3.3 Principal stresses;1.3.4 Rotation of stresses; 1.3.5 Special states of stress; 1.3.6 Mohr's circle for plane stress; 1.3.7 Lamé's ellipse; 1.3.8 Problems; 1.4 The concept of strain; 1.4.1 The state of strain at a point; 1.4.2 The volumetric strain; 1.5 Analysis of the state of strain at a point; 1.5.1 Rotation of strains 1.5.2 Principal strains; 1.6 The state of plane strain; 1.6.1 Strain-displacement relations for plane strain; 1.6.2 Rotation of strains; 1.6.3 Principal strains; 1.6.4 Mohr's circle for plane strain; 1.7 Measurement of strains; 1.7.1 Problems; 1.8 Strain compatibility equations; 2 Constitutive Behavior of Materials; 2.1 Constitutive laws for isotropic materials; 2.1.1 Homogeneous, isotropic, linear elastic materials; 2.1.2 Thermal effects; 2.1.3 Problems; 2.1.4 Ductile materials; 2.1.5 Brittle materials; 2.2 Allowable stress; 2.3 Yielding under combined loading; 2.3.1 Tresca's criterion; 2.3.2 Von Mises' criterion; 2.3.3 Comparing Tresca's and von Mises' criteria;2.3.4 Problems; 2.4 Material selection for structural performance; 2.4.1 Strength design; 2.4.2 Stiffness design 2.4.3 Buckling design; 2.5 Composite materials; 2.5.1 Basic characteristics;2.5.2 Stress diffusion in a composite; 2.6 Constitutive laws for anisotropic materials; 2.6.1 Constitutive laws for a lamina in the fiber aligned triad; 2.6.2 Constitutive laws for a lamina in an arbitrary triad; 2.7 Strength of a transversely isotropic lamina; 2.7.1 Strength of a lamina under simple loading conditions; 2.7.2 The Tsai-Wu failure criterion; 2.7.3 The reserve factor; 3 Linear Elasticity Solutions; 3.1 Solution procedures; 3.1.1 Displacement formulation; 3.1.2 Stress formulation; 3.1.3 Solutions to elasticity problems; 3.2 Plane strain problems; 3.3 Plane stress problems; 3.4 Plane strain and plane stress in polar coordinates; 3.5 Problem featuring cylindrical symmetry; 3.5.1 Problems; 4 Engineering Structural Analysis; 4.1 Solution approaches; 4.2 Bar under constant axial force; 4.3 Hyperstatic systems; 4.3.1 Solution procedures; 4.3.2 The displacement or stiffness method; 4.3.3 The force or flexibility method; 4.3.4 Problems; 4.3.5 Thermal effects in hyperstatic system; 4.3.6 Manufacturing imperfection effects in hyperstatic system; 4.3.7 Problems; 4.4 Pressure vessels; 4.4.1 Rings under internal pressure; 4.4.2 Cylindrical pressure vessels; 4.4.3 Spherical pressure vessels; 4.4.4 Problems; 4.5 Saint-Venant's principle; Part II Beams and thin-wall structures5 Euler-Bernoulli Beam Theory; 5.1 The Euler-Bernoulli Assumptions; 5.2 Implications of the Euler-Bernoulli assumptions; 5.3 Stress resultants; 5.4 Beams subjected to axial loads; 5.4.1 Kinematic description; 5.4.2 Sectional constitutive law; 5.4.3 Equilibrium equations; 5.4.4 Governing equations; 5.4.5 The sectional axial stiffness; 5.4.6 The axial stress distribution; 5.4.7 Problems; 5.5 Beams subjected to transverse loads; 5.5.1 Kinematic description; 5.5.2 Sectional constitutive law; 5.5.3 Equilibrium equations; 5.5.4 Governing equations; 5.5.5 The sectional bending stiffness; 5.5.6 The axial stress distribution; 5.5.7 Rational design of beams under bending; 5.5.8 Problems; 5.6 Beams subjected to axial and transverse loads; 5.6.1 Kinematic description; 5.6.2 Sectional constitutive law; 5.6.3 Equilibrium equations; 5.6.4 Governing equations; 6 Three-Dimensional Beam Theory; 6.1 Kinematic description; 6.2 Sectional constitutive law; 6.3 Sectional equilibrium equations; 6.4 Governing equations; 6.5 Decoupling the three-dimensional problem; 6.5.1 Definition of the principal axes of bending; 6.5.2 Decoupled governing equations; 6.6 The principal centroidal axes of bending; 6.6.1 The bending stiffness ellipse; 6.7 Definition of the neutral axis; 6.8 Evaluation of sectional stiffnesses; 6.8.1 The parallel axis theorem; 6.8.2 Thin-walled sections; 6.8.3 Triangular area equivalence method; 6.8.4 Useful results; 6.8.5 Problems; 6.9 Summary of three-dimensional beam theory; 6.9.1 Examples; 6.9.2 Discussion of the results; 6.10 Problems; 7 Torsion; 7.1 Torsion of circular cylinders; 7.1.1 Kinematic description; 7.1.2 The stress field;7.1.3 Sectional constitutive law; 7.1.4 Equilibrium equations; 7.1.5 Governing equations; 7.1.6 The torsional stiffness; 7.1.7 Measuring the torsional stiffness; 7.1.8 The shear stress distribution; 7.1.9 Rational design of cylinders under torsion; 7.1.10 Problems; 7.2 Torsion combined with axial force or bending; 7.2.1 Problems; 7.3 Torsion of bars with arbitrary cross-sections; 7.3.1 Introduction; 7.3.2 Saint-Venant's solution; 7.3.3 Saint-Venant's solution for a rectangular cross-section; 7.3.4 Problems; 7.4 Torsion of a thin rectangular cross-section; 7.5 Torsion of thin-walled open sections; 7.5.1 Problems; 8 Thin-Walled Beams; 8.1 Basic equations for thin-walled beams; 8.1.1 The thin wall assumption; 8.1.2 Stress flows; 8.1.3 Stress resultants; 8.1.4 Local equilibrium equation; 8.2 Bending of thin-walled beams; 8.2.1 Problems; 8.3 Shearing of thin-walled beams; 8.3.1 Shearing of open sections; 8.3.2 Evaluation of stiffness static moments; 8.3.3 Shear flow distributions in open sections; 8.3.4 Problems; 8.3.5 Shear center for open sections; 8.3.6 Problems; 8.3.7 Shearing of closed sections; 8.3.8 Shearing of multi-cellular sections; 8.3.9 Problems; 8.4 The shear center; 8.4.1 Calculation of the shear center location; 8.4.2 Problems; 8.5 Torsion of thin-walled beams; 8.5.1 Torsion of open sections; 8.5.2 Torsion of closed section; 8.5.3 Comparison of open and closed sections; 8.5.4 Torsion of combined open and closed sections; 8.5.5 Torsion of multi-cellular sections; 8.5.6 Problems; 8.6 Coupled bending-torsion problems; 8.6.1 Problems; 8.7 Warping of thin-walled beams under torsion;8.7.1 Kinematic description; 8.7.2 Stress-strain relations; 8.7.3 Warping of open sections; 8.7.4 Problems; 8.7.5 Warping of closed sections; 8.7.6 Warping of multi-cellular sections; 8.8 Equivalence of the shear and twist centers; 8.9 Non-uniform torsion; 8.9.1 Non-uniform torsion: a classical approach; 8.9.2 Problems; 8.10 Structural idealization; 8.10.1 Lumping the thin-walled section into sheet and stringer components 8.10.2 Axial stress in the stringers; 8.10.3 Shear flow in the sheet components; 8.10.4 Torsion of sheet-…