TABLE OF CONTENTS Reciprocal theorems describe fundamental properties of elastic deformable systems. Displacement computation techniques are presented in this chapter, and the different calculation procedures for obtaining eigenvalues are discussed: among these are Lagrange's equations, Rayleigh, Rayleigh-Ritz and Bubnov-Galerkin's methods, Grammel, Dunker-ley and Hohenemser Prager's formulas, Bernstein and Smirnov's estimations.
| a, b, c, d, e, f | Specific ordinates of the bending moment diagrams | |
| a ik | Inertial coefficients | |
| c ik | Elastic coefficients | |
| E | Young's modulus of the beam material | |
| EI | Bending stiffness | |
| g | Gravitational acceleration | |
| I z | Moment of inertia of a cross-section | |
| k | Stiffness coefficient | |
| L, l, h, a, b | Geometrical parameters | |
| M | Bending moment | |
| m ij, k ij | Mass and stiffness coefficients | |
| M, J | Concentrated mass and moment of inertia of the mass | |
| n | Number of degrees of freedom | |
| Q | Generalized force | |
 | Generalized coordinate, generalized velocity and generalized acceleration | |
| r | Radius of gyration | |
| r ik | Unit reaction | |
| U, T | Potential and kinetic energy | |
| x, y, z | Cartesian coordinates | |
| X(x) | Mode shape | |
| y c | Ordinate of the bending moment diagram in the unit state under centroid of bending moment diagram in the actual state | |
| ? ik | Unit displacement | |
| ? | Area of the bending moment diagram under actual conditions | |
 | Differentiation with respect to space coordinate | |
 | Differentiation with respect to time |
Reciprocal theorems represent the fundamental and useful properties of arbitrary linear elastic systems. The...
