Overhang beam with a UDL on the end.

support action first

See the hogging at the internal support.

Let L be the distance between the two supports and a the unloaded overhang length beyond support B. A UDL w acts over the overhang only, so the resultant wa acts at a/2 beyond B.

Equilibrium relationships

The free-end movement is evaluated from the elastic beam solution using the supplied E and I. The sign convention reports the support moment as hogging and flags uplift where the idealised reaction becomes negative.

Assumptions and limits

• Two simple supports with a single right overhang and constant section stiffness.
• One downward UDL on the overhang only; no loads are applied on the support span.
• Small-deflection Euler-Bernoulli response without shear deformation or support flexibility.
• Uplift, hold-down, bearing, lateral stability, self-weight, load combinations, and code design require separate review.