Beam bending explorer

Reactions come from vertical-force and moment equilibrium. Piecewise load expressions are integrated analytically to obtain moment, slope, and deflection for constant E and I.

• Simply supported: zero deflection at both ends. Cantilever: zero deflection and slope at the fixed left end.
• Positive applied forces act downward. Positive applied moments act anticlockwise. Reactions are positive upward; the fixed reaction moment is positive anticlockwise.
• Positive bending moment is sagging. Away from applied couples, dM/dx = V. With downward deflection δ positive, EI·δ″ = −M.
• Rectangular section: I = b·h³/12, c = h/2. Elastic extreme-fibre bending stress is σ = |M|c/I.
• The model assumes a straight, prismatic, slender beam, linear elasticity, static loading in one bending plane, and small deflections. E and I remain constant.
• Shear deformation, axial loads, torsion, buckling, plasticity, support settlement, design-code checks, and automatic load combinations are outside this example. It does not give a pass/fail design verdict.
• Peak locations are found between load breakpoints. Plots show sampled curves with jumps preserved at concentrated loads and couples. Values are rounded for display; the CSV retains calculation precision.

Reference: MIT OpenCourseWare — Euler–Bernoulli beams. This demonstration illustrates a custom engineering interface; review its assumptions before using results for a project.