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Beam Analysis Calculator for beam with multiple loads's banner
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Beam Analysis Calculator for beam with multiple loads

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!
Sign convention used in this calculator:
  1. Applied force is negative (-) in the downwards direction
  2. Applied moment is positive (+) in the clockwise direction

Calculator

Parameters used in this calculator

Inputs

Beam Information



Beam Type
:Simply Supported​

❗Note, for Beam Type enter either 'Cantilever' or 'Simply Supported'


Length of beam (L)
:15.00m​



Elastic Modulus (E)
:200.00GPa​



Moment of Inertia (I)
:142,000,000.00mm4​


Beam Loading

Load Type
Enter Point, Moment, UDL, Triangular or Trapezoidal
Distances
For Point or Moment load types, enter b=0
Point Load
For Point load type, enter F1=F and F2=0
Point Moment


Load_1
:Point​




a1
:10.00m​



b1
:0.00m​



F1_1
:-10.00kN​



F2_1
:0.00kN​



M0_1
:0.00kN m​



Load_2
:UDL​




a2
:4.00m​



b2
:8.00m​



F1_2
:-6.00kN​



F2_2
:0.00kN​



M0_2
:0.00kN m​




Load_3
:Moment​




a3
:1.00m​



b3
:0.00m​



F1_3
:0.00kN​



F2_3
:0.00kN​



M0_3
:-5.00kN m​



Click here for more load entries!

Load Type
Distances
Load (kN)
Moment (kNm)


Load_4
:Triangular​




a4
:10.00m​



b4
:9.00m​



F1_4
:7.00kN​



F2_4
:0.00kN​



M0_4
:0.00kN m​




Load_5
:Trapezoidal​




a5
:2.00m​



b5
:6.00m​



F1_5
:5.00kN​



F2_5
:10.00kN​



M0_5
:0.00kN m​




Load_6
:-​




a6
:0.00m​



b6
:0.00m​



F1_6
:0.00kN​



F2_6
:0.00kN​



M0_6
:0.00kN m​




Load_7
:-​




a7
:0.00m​



b7
:0.00m​



F1_7
:0.00kN​



F2_7
:0.00kN​



M0_7
:0.00kN m​



Load_8
:-​




a8
:0.00m​



b8
:0.00m​



F1_8
:0.00kN​



F2_8
:0.00kN ​



M0_8
:0.00kN m​



Load_9
:-​




a9
:0.00m​



b9
:0.00m​



F1_9
:0.00kN​



F2_9
:0.00kN​



M0_9
:0.00kN m​



Load_10
:-​



a10
:0.00m​



b10
:0.00m​



F1_10
:0.00kN​



F2_10
:0.00kN​



M0_10
:0.00kN m​




Outputs



Max Shear
:-112.59kN​


Max Moment
:-402.45kN m​


Max Deflection
:218.98mm​

Can’t display the image because of an internal error. Our team is looking at the issue.


Beam Analysis Equations

For multiple loadings on a single beam, we can use superposition of the

and

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 Beam

Point Load

Point Moment

❗Note:


  1. Shear Force

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}
  1. Bending Moment

M(x)=Ra<x−0>1+M0<x−a>0M(x) = R_a<x-0>^{1} + M_0<x-a>^{0}
  1. Deflection

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}]
See a derivation on this page here!
Simply Supported Beam with Point Moment

Free body diagram


Uniformly Distributed Load (UDL)

Triangular Load

Trapezoidal Load

Cantilever Beam

Point Load

Point Moment

Uniformly Distributed Load (UDL)

Triangular Load

Trapezoidal Load