Analysis of a Single-Span Euler-Bernoulli Beam under Different Loading Conditions
Analysis of a Single-Span Euler-Bernoulli Beam under Different Loading Conditions
This Demonstration shows a single-span Euler–Bernoulli beam under four possible support conditions and with three different loading arrangements.
This Demonstration generates the deflection curve of the beam due to the loads, as well as bending moment and shear force diagrams.
You can modify the loading, support conditions, and other parameters, such as Young's modulus and the moment of inertia . Then observe the effect of these changes on the beam's deflection, moment, and shear diagrams.
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The beam deflection is normally found by solving the fourth-order Euler–Bernoulli beam differential equation using the appropriate boundary conditions. The shear force diagram is used as the starting point here and then integrated three times to obtain the deflection .
y(x)
The reactions at the supports are obtained by solving the equilibrium equations for the determinate beam cases (simply supported at both ends) and the cantilever cases. For the indeterminate cases (fixed at both ends or fixed at one end and simply supported at the other end), the slope boundary conditions were used to obtain the additional equations needed to solve for all the unknown reactions.