User`s guide
94
distributed loads and uniformly varying loads over the span and a number of concentrated loads
are conveniently handled using this technique.
For general loadings, the bending moment M can be expressed in the form
The quantity
is a Macaulay bracket, it is defined as
When integrating expressions containing Macaulay brackets, we have
Consider a simple cantilever beam fixed at one end and loaded with a force on the free
end. The dimensions of the cantilever beam are defined in the figure below.
Figure 25 Dimensions of a Simple Cantilever Beam
Figure 3 equations and plots for deflection in terms of distance, deflection in terms of
slope, bending moment and shear stress at arbitrary location in the beam on the neutral axis. In
the equations, x is the distance from the fixed end of the beam to the point of interest, P is the
applied load, L is the length of the beam, E is the elastic modulus, and I is the second moment of
inertia.
Eq.6
Eq.7
Eq.8