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:







            
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BEAM EDITOR:
















EQUATIONS:

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






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.