Postyield

V1.3 — Fixed-fixed beam, uniform load

The same beam and loading as V1.2, but with both ends fixed against rotation instead of pinned — a statically indeterminate case.

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

← Verification — Linear (Frames & Trusses)

V1.3 — Fixed-fixed beam, uniform load

Exact

Description

The same beam and loading as V1.2, but with both ends fixed against rotation instead of pinned — a statically indeterminate case.

Reference

Standard fixed-fixed beam formulas (closed form): δmid = wL⁴/(384EI), Mend = −wL²/12 (hogging), Mmid = wL²/24.

Model

The same elastic frame member and 8-element mesh as V1.2, but with full moment fixity at both ends instead of pin/roller supports.

Uniform load, w0.1 kip/in
Span length, L240 in
Elastic modulus, E29,000 ksi
Section width, b12 in
Section depth, d24 in
Moment of inertia, I13,824 in⁴
Elements8

Comparison

QuantityReferencevfopro% diffStatus
Midspan deflection (in)-0.0022-0.0022-0.00%Exact
Left reaction (kip)12120.00%Exact
Right reaction (kip)12120.00%Exact
Left end moment, hogging (kip-in)-480-4800.00%Exact
Right end moment, hogging (kip-in)4804800.00%Exact
Midspan moment, sagging (kip-in)-240-2400.00%Exact

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