Determine reactions, shear, bending moment, stress, and maximum deflection for four basic load cases.
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Calculate reactions, moment, stress and deflection for basic beam load cases.
Length, load and position, Young's modulus E, second moment I and section modulus W describe beam and load.
E describes material stiffness, I section distribution and L load leverage. Deflection therefore grows strongly with L and falls strongly with I; adequate strength alone does not guarantee stiffness.
Euler-Bernoulli EI·w″ = M(x) links moment to curvature; boundary conditions determine deflection.
Doubling I approximately halves deflection for the same load case.
Sources and limits: Classical small-deflection, linear-elastic beam theory; shear deformation and self-weight are excluded.
Four basic cases show how support and loading determine deflection. θmax is intentionally omitted.
Length, load, elastic modulus, I, and W describe a prismatic beam. Typical applications include early stiffness estimates for beams, brackets, and machine frames.
Euler-Bernoulli theory assumes small deformation, linear-elastic material, and a slender beam. Shear deformation, self-weight, and stability failure are excluded.