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Beam Design Formulas

Simply select the picture which most resembles the beam configuration and loading condition you are interested in for a detailed summary of all the structural properties. Beam equations for Resultant Forces, Shear Forces, Bending Moments and Deflection can be found for each beam case shown. Handy calculators have been provided for both metric and imperial beam design and assessment.

Structural engineering spreadsheet collection for beam design using excel are available for purchase and can be found under each beam type.

Additional information regarding engineering beam design theory and the assumptions that have been made can be found Here.

Simply Supported Beams

Simple Beam - Uniformly Distributed Load

Simple Beam with UDL

Simple Beam - Uniformly Increasing Load to One End

Simple Beam with UIL

Simple Beam - Uniformly Increasing Load to Centre

Simple Beam with Central UIL

Simple Beam - Partially Distributed Uniform Load

Simple Beam with PDUL

Simple Beam - Partially Distributed Uniform Load at One End

Simple Beam with PDUL at One End

Simple Beam - Partially Distributed Uniform Load at Each End

Simple Beam with PDUL at Each End

Simple Beam - Point Load at Centre

Simple Beam with PL at Centre

Simple Beam - Point Load at Any Point

Simple Beam with PL at Any Point

Simple Beam - Two Point Loads Equally Spaced

Simple Beam with PLs Equally Spaced

Simple Beam - Two Equal Point Loads Unequally Spaced

Beam with PLs Unequally Spaced

Simple Beam - Two Unequal Point Loads Unequally Spaced

Beam with UPLs Unequally Spaced

Simple Beam - Uniformly Distributed Load and Variable End Moments

Simple Beam with UDL and EMs

Simple Beam - Central Point Load and Variable End Moments

Simple Beam with PL and EMs

Beams Fixed at one end

Beam Fixed at One End and Pinned at Other End with a Uniformly Distributed Load

Fixed End Beam with UDL

Beam Fixed at One End and Pinned at Other End with a Central Point Load

Fixed End Beam with Central PL

Beam Fixed at One End and Pinned at Other End with a Point Load at Any Point

Fixed End Beam. PL at Any Point

Beams Fixed at Both ends

Fixed Both Ends Beam - Uniformly Distributed Load

Fixed Beam with UDL

Fixed Both Ends Beam - Point Load at Centre

Fixed Beam with Central PL

Fixed Both Ends Beam - Point Load at Any Point

Fixed Beam with PL at Any Point

Cantilever Beams

Cantilever Beam - Uniformly Increasing Load

Cantilever Beam with UIL

Cantilever Beam - Uniformly Distributed Load

Cantilever Beam with UDL

Cantilever Beam - Uniformly Distributed Load and End Bending Moment

Cantilever Beam with UDL and EM

Cantilever Beam - Point Load at Any Point

Cantilever Beam. PL at Any Point

Cantilever Beam - Point Load at Free End

Cantilever Beam with PL at Free End

Cantilever Beam - Point Load and Bending Moment at Free End

Cantilever Beam with PL and EM

Beams with Overhang

Overhanging Beam - Uniformly Distributed Load

Overhanging Beam with UDL

Overhanging Beam - Uniformly Distributed Load on Overhang

Overhanging Beam with UDL on End

Overhanging Beam - Point Load on Beam End

Overhanging Beam with PL on End

Overhanging Beam - Uniformly Distributed Load Over Supported Span

Overhanging Beam with Part UDL

Overhanging Beam - Point Load Between Supports at Any Point

Overhanging Beam PL at Any Point

Overhanging Beam – Overhang Both Supports with a Uniformly Distributed Load

Two Overhang Beam with UDL

Continuous Beams - Two Spans / Three Supports

Continuous Beam - Two Span with Uniformly Distributed Load Over One Span

Two Span Beam with Partial UDL

Continuous Beam - Two Span with Point Load Centrally Located Over One Span

Two Span Beam with PL

Continuous Beam - Two Span with Point Load Over One Span at Any Point

Two Span Beam. PL at Any Point

Continuous Beams – Two Equal Spans with a Uniformly Distributed Load

Two Span Beam with UDL

Continuous Beam – Two Equal Spans with Point Loads Centrally Located Over Both Spans

Two Span Beam with two PLs

Continuous Beam - Two Unequal Span With a Uniformly Distributed Load

Two Unequal Spans with UDL

Continuous Beam - Two Unequal Spans with Point Loads Central to Each Span

Two Unequal Spans with PLs

Continuous Beams - Three Spans / Four Supports

Continuous Beam - Three Span with a Uniformly Distributed Load over Two Spans

Three Span Beam with Partial UDL

Continuous Beam - Three Span with a Uniformly Distributed Load over Both End Spans

Three Span Beam with End UDLs

Continuous Beam - Three Span with a Uniformly Distributed Load

Three Span Beam with UDL

Continuous Beams - Four Spans / Five Supports

Continuous Beam - Four Span with One Span Unloaded

Four Span Beam. Unloaded Span

Continuous Beam - Four Span with Two Spans Unloaded

Four Span Beam. Unloaded Spans

Continuous Beam - Four Span with a Uniformly Distributed Load

Four Span Beam with UDL