| THEORY & FORMULAE |
Consider a beam simply supported at two points that are not necessarily its endpoints (so that one or both ends may overhang the supports). The beam is subject to the simultaneous action of concentrated later forces, concentrated bending moments (couples) and distributed loads which may either be uniform or vary linearly. The loads can be sequenced in any order but act at known points along the beam.
We aim to determine the shearing force and the bending moment at every point along the length of the beam. The implementation here only considers combinations of 0 to 2 concentrated forces, 0 to 2 couples, and 0 to 2 distributed force.
The algorithm employed is based on the fundamental definitions of shearing force and bending moment. The algebraic sum of all the vertical forces to one side (say, left side) of the cross-section at location x, is called the shear force at x. Similarly, the algebraic sum of the moments of all the external forces to the left of the cross-section at location x, is called the bending moment at x.
The computation begins with the determination of the reactive forces at the supports using static equilibrium equations. Then the shear forces and moments at potential points of stepwise discontinuities (i.e at the load points and supports) are computed. And finally the shear forces and moments at 24 regular intervals along the beam are computed.
The implementation here is essentially a modern-day enhancement of the Basic program in Problem 7.7 by Nash.
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