Beam Analysis Calculator for beam with multiple loads

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﻿﻿Status
:Not Started​
 
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Using this calculator you can visualise the shear force, bending moment and deflection of either a simple supported beam or cantilever beam with up to 10 loads acting on it!
Calculator➕Sign convention used in this calculator
📃Parameters used in this calculator
Click on the toggles below to visualise the parameters for each loading condition!
Simply supported beam with:
point load
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Simply Supported Beam with Point Load
Magnitude of load (F)
Distance from left support to load (a)
point moment
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Simply Supported Beam with Point Moment
Magnitude of moment (M0)
Distance from left support to moment (a)
uniformly distributed load (UDL)
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Simply Supported Beam with UDL
Magnitude of load (F)
Distance from left support to start of load (a)
Distance from left support to end of load (b)
triangular load
trapezoidal load
Cantilever beam with:
point load
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Cantilever Beam with Point load
Magnitude of load (F)
Distance from fixed support to load (a)
point moment
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Cantilever beam with Point Moment
Magnitude of moment (M0)
Distance from fixed support to moment (a)
uniformly distributed load (UDL)
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Cantilever beam with UDL
Magnitude of load (F)
Distance from fixed support to start of load (a)
Distance from fixed support to end of load (b)
triangular load
trapezoidal load
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Cantilever beam with Trapezoidal load (Type 1 loading condition)
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Cantilever beam with Trapezoidal load (Type 2 loading condition)
Magnitude of minimum load (F1)
Magnitude of maximum load (F2)
Distance from fixed support to the minimum load end (a)
Distance from fixed support to maximum load end (b)
InputsBeam Information
﻿﻿Beam Type
:Cantilever​
﻿
❗Note, for Beam Type enter either 'Cantilever' or 'Simply Supported'
﻿﻿Length of beam (L)
:15.00m​
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﻿﻿Elastic Modulus (E)
:200.00GPa​
﻿
﻿﻿Moment of Inertia (I)
:142,000,000.00mm4​
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Beam Loading
Outputs﻿﻿Max Shear
:18.14kN​
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﻿﻿Max Moment
:-84.14kN m​
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﻿﻿Max Deflection
:-206.5mm​
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Beam Analysis EquationsFor multiple loadings on a single beam, we can use superposition of the ﻿V(x),M(x)
 and ﻿Y(x)
 equations for each loading to determine the overall Shear Force Diagram (SFD), Bending Moment Diagram (BFD) and Deflection Diagram.
Equations of the individual loading conditions for a simply supported beam and cantilever beam is provided below. Click on the toggle boxes to find the equations you need when combining loads!
Simply Supported BeamPoint Load
Point Moment
❗Note: ﻿ifn<0→⟨x−a⟩n=0
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Shear Force
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V(x)=Ra<x−0>0+M0<x−a>−1=Ra<x−0>0V(x) = R_a<x-0>^{0} + M_0<x-a>^{-1}\\=R_a<x-0>^{0}V(x)=Ra​<x−0>0+M0​<x−a>−1=Ra​<x−0>0
Bending Moment
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M(x)=Ra<x−0>1+M0<x−a>0M(x) = R_a<x-0>^{1} + M_0<x-a>^{0}M(x)=Ra​<x−0>1+M0​<x−a>0
Deflection
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Y(x)=1EI[Ra6<x−0>3+M02<x−a>2+C1x]whereC1=−[Ra6L2+M0(L−a)22L]Y(x) =\frac{1}{EI}[ \frac{R_a}{6}<x-0>^{3} + \frac{M_0}{2}<x-a>^{2} +\hspace{0.1cm} C_{1}x]  \\ \text{where}\hspace{0.3cm} C_1 = -[ \frac{R_a}{6}L^{2} + \frac{M_0(L-a)^{2}}{2L}]Y(x)=EI1​[6Ra​​<x−0>3+2M0​​<x−a>2+C1​x]whereC1​=−[6Ra​​L2+2LM0​(L−a)2​]
See a derivation on this page here!
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Simply Supported Beam with Point Moment
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Free body diagram
Uniformly Distributed Load (UDL)
Triangular Load
Trapezoidal Load
Cantilever BeamPoint Load
Point Moment
Uniformly Distributed Load (UDL)
Triangular Load
Trapezoidal Load