Types of Beams and Beam Supports
Compare simply supported, cantilever, fixed, overhanging and continuous beams with interactive diagrams, support reactions, formulas and worked examples.
Optimal Beam engineering resources
Structural Engineering Guides
Practical explanations, diagrams, formulas and worked examples for structural analysis—with direct links to the tools used to check the results.
Published structural engineering resources
Beam fundamentals
2 resources
Beam Deflection Formulas & Equations
Filter twelve common beam cases and compare reactions, shear, moment, slope and deflection equations with exact calculator handoffs.
Beam analysis guides
5 resources
Cantilever Beam Calculator & Formulas
Calculate fixed-end shear, bending moment and tip deflection, then learn the point-load and UDL formulas, diagrams, assumptions and modeling checks.
Simply Supported Beam Calculator & Formulas
Calculate pin and roller reactions, maximum moment and deflection, then learn central point-load, eccentric-load and UDL formulas.
Fixed Beam Calculator & Formulas
Calculate fixed-end reactions, hogging support moments, positive span moment and deflection for UDL and center point loads.
Continuous Beam Calculator & Formulas
Solve two equal spans under balanced UDL or a point load on one span, including all reactions, support moment and deflection.
Overhanging Beam Calculator & Formulas
Calculate a single-overhang beam under full-length UDL or a free-tip load, including uplift, moment and displacement.
Frame and truss worked examples
5 resources
Pratt Truss Analysis: Solved Example
Follow a verified four-panel Pratt truss calculation from support reactions through member forces, zero-force members and centre deflection.
Warren Truss Analysis: Solved Example
Solve a verified four-panel Warren truss from reactions through alternating diagonal forces, zero-force members and centre deflection.
Howe Truss Analysis: Solved Example
Follow a verified Howe truss calculation from reactions through compression diagonals, the zero-force centre vertical and deflection.
Portal Frame Analysis: Worked Example
Review the solved reactions, sway, rotations and force diagrams first, then follow the direct stiffness calculation for a fixed-base portal frame.
Gable Portal Frame Analysis: Worked Example
See the complete reactions and force diagrams first, then follow the nine-DOF direct stiffness calculation for a fixed-base gable frame with inclined rafters.
Engineering calculators
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Use the calculator or reference that matches the engineering problem.
Beam Calculator
Calculate reactions, shear, bending moment, slope, deflection and stress for a straight beam.
Open Beam Calculator
2D Structural Analysis
Model and analyze frames and trusses with member releases, load cases and combinations.
Open 2D Structural Analysis
Section Properties & Moment of Inertia
Calculate area, centroid, moments of inertia, section modulus and radius of gyration.
Calculate Section Properties
Steel Beam Sizes
Find section dimensions and properties for AISC, CISC, UK, European and Australian steel shapes.
Browse Steel Beam Sizes
Section Builder
Draw or import a custom or arbitrary cross-section and calculate its geometric properties.
Open the free Custom Section Builder
Solver verification
See how the Optimal Beam Solver is checked
Review analytical benchmark cases, tolerances and regression checks used to verify the 2D structural analysis results behind our worked examples.