Beam Deflection Simulation



INTRODUCTION:

This is a simulator/calculator for beam deflections using Euler-Bernoulli Beam Theory.
The INPUT section contains general controls for the simulation.
The BEAM EDITOR section contains controls for designing a beam.
The EQUATIONS section contains equations used to generate the diagrams.




Controls:

  • - Beam Type:  This drop down menu changes the scenario to simulate/calculate.
  • - Zoom Buttons:  Both buttons adjust the diagram zoom levels so the plots are visible.
  • - "diagram" Zoom:  Changes the zoom level of the related diagram.
  • - Load (F) (kN):  Changes the value of point loads.
  • - Distrubuted Load (w) (kN/m):  Changes the value of distributed loads.
  • - Moment (M0) (kNm):  Changes the value of moments.
  • - Load Position (a) (m):  Changes the position of various loads.
  • - Beam Length (L) (m):  Changes the beam's length.
  • - Moment of Inertia (I) (mm4):  Changes the beam's moment of inertia about the neutral axis.
  • - Young's Modulus (E) (GPa):  Changes the Young's modulus of the beam.
  • - Beam Shape:  This drop down menu changes the shape of beam being designed.
  • - Dimension "variable" (mm):  Changes the value of the related dimension.




Instructional Video:
INPUT:







            
%    %       %    %




















BEAM EDITOR:
















EQUATIONS:

Below are the equations used to generate the diagrams.
The equations change depending on the selected scenario.


Deflection:δ=−Fx26EI(3L−x)δmax=FL33EI,x=LShear:Vmax=FMoment:M=−F(L−x)Mmax=−FL,x=0




The equations are only valid if the following assumptions are satisfied according to Euler-Bernoulli Beam Theory:

  • - The longitudinal axis does not experience any change in length.
  • - The cross-sections of the beam remain plane and perpendicular to the longitudinal axis.
  • - The cross-section is constant and retains its shape.
  • - The material is in the linear elastic range according to Hooke's Law.
  • - The deformed angles and displacements are small.
  • - The beam is made of a homogeneous material.