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Simply Supported Beam With Uniform Load

Purpose​

This case validates a standard beam benchmark where several independent checks can be compared against closed-form values:

  • midspan deflection
  • support reactions
  • maximum bending moment at midspan
  • basic bending and shear evaluation downstream of the analysis result

Tests in the repository​

The current code already contains a strong cluster of tests for this exact case:

  • CoreBeamTests.SimplySupportedBeam_UniformLoad_CorrectDeflection
  • CoreBeamTests.SimplySupportedBeam_UniformLoad_CorrectReactions
  • CoreBeamTests.SimplySupportedBeam_UniformLoad_CorrectMomentAtCenter
  • AnalysisAndEvaluationTests.SimplySupportedBeam_UniformLoad_BendingAndShearChecks

That makes this one of the best existing candidates for a fully documented validation page.

Model​

Closed-form beam benchmark in CoreBeamTests:

  • span: L = 6.0 m
  • support condition: simply supported
  • distributed load: w = 3 kN/m downward
  • stiffness values taken from the member under test

Design/evaluation benchmark in AnalysisAndEvaluationTests:

  • span: L = 6.0 m
  • distributed load: w = 50 kN/m downward
  • goal: confirm bending and shear checks are created after analysis

The first is the cleaner analytical benchmark. The second is a pipeline-level evaluation check.

Reference solution​

For a simply supported beam with uniform load:

  • support reaction at each end:
R = w L / 2
  • maximum bending moment at midspan:
Mmax = w L^2 / 8
  • maximum deflection at midspan:
δmax = 5 w L^4 / (384 E I)

Armatura result​

Populate this table from a real test run.

QuantityReferenceArmaturaAbs. errorRel. error
Left reactionTODOTODOTODOTODO
Right reactionTODOTODOTODOTODO
Midspan momentTODOTODOTODOTODO
Midspan deflectionTODOTODOTODOTODO

Existing tolerances in the tests​

The current assertions already provide a practical benchmark target:

  • deflection: within 1.0%
  • reactions: within 0.01%
  • moment at center: within 1.0%

Why this page matters​

This is probably the strongest single-page validation case in the current suite because it checks three different result types from one benchmark:

  • displacement
  • reaction
  • internal force

That makes it more informative than a deflection-only page.

Optional extension: design checks​

The SimplySupportedBeam_UniformLoad_BendingAndShearChecks test is a good follow-on section for this page. It does not just confirm numerical response; it confirms that the analysis result is consumed correctly by the design-check pipeline.