TABLE OF CONTENTS This chapter focuses on Bernoulli Euler uniform one-span beams with classical boundary conditions. Classical methods of analysis are discussed. Frequency equations and fundamental characteristics such as eigenvalues, eigenfunctions and their nodal points, as well as integrals of eigenfunctions and their derivatives, are presented.
The initial parameter method is convenient to use for the calculation of different types of uniform beams: statically determinate and indeterminate beams, one span and multispan beams, as well as beams with non-classical boundary conditions. Different cases are considered.
The force method may be applied for calculation of non-uniform beams as well as frames. Both cases are considered.
The slope-deflection method is convenient to apply for the calculation of frames with a high degree of statical indeterminancy.
| A | Cross-sectional area | |
| A, B, C, E, S 1 | Hohenemser Prager functions | |
| E, G | Youngs' modulus and modulus of rigidity | |
| EI | Bending stiffness | |
| f 1, f 2 | Correction functions | |
| g | Acceleration due to gravity | |
| I z | Moment of inertia of a cross-section | |
| k | Shear factor | |
| k n | Frequency parameter, | |
| k tr, k rot | Translational and rotational stiffness coefficients | |
| l | Length of the beam | |
| M | Bending moment | |
| M, J | Lumped mass and moment of inertia of the mass | |
| Q | Shear force | |
| r | Dimensionless radius of gyration, r 2 Al 2 = I | |
| s | Dimensionless parameter, s 2 kAGl 2 = EI | |
| S, T, U, V | Krylov Duncan functions | |
| t | Time |
