ABSTRACT

The relationships between displacement v, slope θ, bending moment M, shear force V and load q for a uniform beam are as follows:

d

d

x

v θ (7.1)

EI d

d

x

2v 2 M (7.2)

EI d

d

x

3v 3 V (7.3)

EI d

d

x

4v 4 q (7.4)

Equation 7.2 indicates that the displacement function v for a loaded beam can be obtained by integrating the bending moment function, M, twice with respect to the coordinate x. Equation 7.4 shows that the displacement function v for a loaded beam can be obtained by integrating the loading function q four times with respect to the coordinate x. When carrying out the integrations, the integration constants can be uniquely determined using the available boundary conditions of the beam.