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V1.7 — Propped cantilever beam, uniform load

A beam fixed at one end and simply supported (propped) at the other, under a uniform load — a third statically indeterminate configuration.

Time
About 5 minutes
Level
All levels
You'll need
None — this is a reference document
You're done when
You can see how V1.7 compares to its reference
On this page
  1. Description
  2. Reference
  3. Model
  4. Comparison
  5. Conclusion

← Verification — Linear (Frames & Trusses)

V1.7 — Propped cantilever beam, uniform load

Exact

Description

A beam fixed at one end and simply supported (propped) at the other, under a uniform load — a third statically indeterminate configuration.

Reference

Standard propped-cantilever beam-table formulas (closed form): Mfixed = wL²/8 (hogging), Rfixed = 5wL/8, Rprop = 3wL/8.

Model

An elastic frame member fixed at one end and pinned at the other (a roller "prop"), under a uniform load along its full length.

Uniform load, w0.3 kip/in
Span length, L180 in
Elastic modulus, E29,000 ksi
Section width, b10 in
Section depth, d20 in
Moment of inertia, I6,666.7 in⁴

Comparison

QuantityReferencevfopro% diffStatus
Fixed-end reaction (kip)33.7533.750.00%Exact
Prop reaction (kip)20.2520.25+0.00%Exact
Fixed-end moment, hogging (kip-in)-1,215-1,2150.00%Exact
Prop vertical displacement (in)00n/aExact

Conclusion

Every reported quantity matched the closed-form value to at least 6 significant figures.

Last updated September 22, 2026 · applies to vfopro 20260922.0.0 or later