Calculate beam bending shear force, bending moment, slope and deflection for solid trapezoid beams.
The Euler Bernoulli beam equation is suitable for slender beams (it does not include the effect of shear), and for small angles (θ < 0.5 rad). The calculations are not valid past the beam end points. For combined loads, the shear force, bending moment, slope and deflection are assumed to be additive. The beam end conditions are of the form left end - right end (for example Pin-Fix is left end pinned and right end fixed). All distances are measured from the left end of the beam.
Beam end types include: free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends.
Combined loads include axial loads, point loads, distributed loads, weight loads, concentrated moments, angular displacements, lateral displacements, and uniform temperature gradient.
For beams with compressive axial loads the bending moment, slope and deflection tend to infinity as the axial load tends to the buckling load. For tension loads, the bending moment, slope and deflection decrease with increasing tension. The buckling load can be calculated using either the Euler equation (suitable for long beams), the Johnson equation (suitable for short beams), or the buckling load equation can be determined from the transition length.
The effective length factor should be used for beams on a soft foundation such as soil, where the beam ends are poorly defined. For defined beam ends, such as structures, the effective length factor should be set to one (fe = 1).
Use the Result Plot option to plot the bending moment, shear force, slope, deflection and stress versus position x. Refer to the figures and help pages for more details.
Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill
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