Calculate reactions, shear, bending moment, stress, and maximum deflection for four basic load cases.
Set the inputs and run the calculation.
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.
Calculate reactions, moment, stress and deflection for basic beam load cases.
Mechanical calculators translate geometry and load into a response such as torque, stress, deflection, spring force or bearing life. The position of the load relative to the effective axis is often decisive.
Euler-Bernoulli EI·w″ = M(x) links moment to curvature; boundary conditions determine deflection.
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.
Select the load case and support type (e.g. a point load on a simply supported beam), then enter length, load and load position plus Young's modulus E and second moment of area I. The calculator returns reactions, moment, stress and deflection.
Doubling I approximately halves deflection for the same load case.
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. The result shows the idealized component response for the selected load case. A small change in diameter, height, length or load can have a large effect because of power laws.
Length in millimetres or metres, load in N or kN, E in MPa or GPa, I in mm⁴, deflection in millimetres.
Estimating whether a beam or girder stays within an allowable deflection limit under a known load, or comparing different sections or supports for stiffness.
Classical small-deflection, linear-elastic beam theory; shear deformation and self-weight are excluded.
Common mistake: Don't swap load case and actual support conditions arbitrarily – a fixed beam deflects noticeably less than a simply supported one under the same load and length, since curvature boundary conditions differ fundamentally. This model assumes small deflections; for very slender parts or large deflections the linear approximation becomes inaccurate.
A fixed support additionally prevents rotation at the support, making the beam curve less over a larger portion of its length than with a pinned support.
Deflection falls to roughly half, since it is inversely proportional to I; stress and reactions are unaffected by this change.
No, the model uses classical Euler-Bernoulli theory without shear deformation; for very short, thick beams or where self-weight matters, this must be added separately.
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.