Beam and Crane Check
Find support reactions, protect beams from excessive bending and check a crane against forward and backward tipping. Gravity is 9.81 m/s².
Supported beam
Pin and roller supports provide reactions. A load causes an internal bending moment that varies along the beam.
Bending moment M (N m) vs x (m)
Engineering check
Position the load, then check.
The physics
Beam reactions: RA + RB equals the total downward force. Moment equilibrium about A determines RB. A whole-span UDL acts through the midpoint of the span.
Bending: M(x) = RA x − wx²/2 − Σ P(x − a) for loads to the left of x. The maximum is found at a support, point load, or section with zero shear.
Crane: check the loaded crane about its front edge and the unloaded crane about its rear edge. The crane's own weight and the counterweight both act downwards. The crane and beam are treated as rigid in static equilibrium.