Statics of Rods

1. Equilibrium Equations.- 1.1 Vector Equilibrium Equations.- 1.2 External Loads.- 1.3 Equilibrium Equations in the Attached and Cartesian Coordinate Systems.- 1.4 Equilibrium Equations for Small Displacements and Angles of Rotation.- 1.5 Problems.- 2. Integration of Equilibrium Equations.- 2.1 Integration of Linear Equilibrium Equations.- 2.2 Equilibrium Equations for Rods with Lateral Supports.- 2.3 Method of Step-by-Step Loading.- 3. Static Stability of Rods.- 3.1 Basic Concepts.- 3.2 Equilibrium Equations for a Rod After Loss of Stability.- 3.3 Plane Curvilinear Rods.- 3.4 Increments of Loads at Loss of Stability.- 3.5 Computer-Oriented Methods.- 3.6 Problems.- 4. Straight Rods.- 4.1 Rods of Straight Natural Configuration.- 4.2 Equilibrium Equations for Small Displacements and Angles of Rotation.- 4.3 Naturally Twisted Straight Rods.- 4.4 Straight Rods on Elastic Foundation.- 4.5 Application of Approximate Methods.- 4.6 Stability of Compressed-Twisted Rods.- 4.7 Stability of Straight Rods with Local Constraints.- 4.8 Problems.- 5. Curvilinear Rods.- 5.1 Plane Rods.- 5.2 Elementary Theory of Cylindrical Springs.- 5.3 General Theory of Cylindrical Springs.- 5.4 Flexible Rods in a Rigid Conduit.- 5.5 Stability of Plane Curvilinear Rods.- 5.6 Problems.- 6. Rods Interacting with Liquid or Air Flows.- 6.1 Introduction.- 6.2 Basic Concepts of Aerohydrodynamics.- 6.3 Experimental Results.- 6.4 Aerodynamic Forces Acting on Rods of Circular Cross Section.- 6.5 Stress-Strain State of a Rod Interacting with an Air Flow.- 6.6 Aerodynamic Forces Acting on Rods of Noncircular Cross Section.- 6.7 Increments of Aerodynamic Forces at Small Displacements of Axial Points.- 6.8 Rods Containing Internal Liquid Flows.- A. Appendices.- A.1 Elements of Vector Algebra.- A.1.1 Vector Bases; Coordinates of Vectors.- A.1.2 Scalar Product.- A.1.3 Vector Product.- A.1.4 Scalar Triple Product.- A.1.5 Vector Triple Product.- A.1.6 Transformation of Base Vectors.- A.2 Basics of Differential Geometry.- A.2.1 The Derivative of a Radius Vector.- A.2.2 Spatial Curves.- A.2.3 Derivatives of the Base Vectors.- A.2.4 Geometrical Meaning of the Components of the Vector æ.- A.2.6 Derivatives of a Vector in the Attached Coordinate System.- A.3 Increments of the Components of a Vector under Transformation of the Attached Coordinate System.- A.4 Distributions.- A.4.1 The ?-function.- A.4.2 The Nondimensional ?-function.- A.4.3 The Heaviside Function.- A.4.4 Applications of the ?-function.- A.4.5 Integrals Containing Derivatives of the ?-function.- A.5 Direction Cosines of the Unit Vector Tangent to a Rod Axis.- A.5.1 Plane Curve.- A.5.2 Spatial Curve.- A.6 Equations of the First and Higher Approximation.- B. Solution of the Problems.- B.1 To Chapter 1.- B.2 To Chapter 3.- B.3 To Chapter 4.- B.4 To Chapter 5.- References.