Cantilever Beam - Load at Free End Deflection Vertically with No Rotation

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diagram Symbols

  • Bending moment diagram (BMD)  -  Used to determine the bending moment at a given point of a structural element.  The diagram can help determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.
  • Free body diagram (FBD)  -  Used to visualize the applied forces, moments, and resulting reactions on a structure in a given condition.
  • Shear force diagram (SFD)  -  Used to determine the shear force at a given point of a structural element.  The diagram can help determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.
  • Uniformly distributed load (UDL)  -  A load that is distributed evenly across the entire length of the support area.

 

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Cantilever Beam - Load at Free End Deflection Vertically with No Rotation formulas

\( R \;=\; V \;=\;  P  \) 

\( M_{max} \; (at\; both\; end )  \;=\; P \;L\;/\;2  \) 

\( M_x  \;=\;   P \; [\; (L \;/\;2) - x \;]  \) 

\( \Delta_{max} \; (at\; free \;end )   \;=\; P\; L^3\;/\;12 \;\lambda\; I  \)

\( \Delta_x   \;=\; [\;P \; ( L - x )^2  \;/\; 12\; \lambda\; I\;] \; ( L + 2\;x ) \)

Symbol English Metric
\( \Delta \) = deflection or deformation \(in\) \(mm\)
\( x \) = horizontal distance from reaction to point on beam \(in\) \(mm\)
\( M \) = maximum bending moment \(lbf-in\) \(N-mm\)
\( V \) = maximum shear force \(lbf\) \(N\)
\( \lambda  \)   (Greek symbol lambda) = modulus of elasticity \(lbf\;/\;in^2\) \(Pa\)
\( R \) = reaction load at bearing point \(lbf\) \(N\)
\( I \) = second moment of area (moment of inertia) \(in^4\) \(mm^4\)
\( L \) = span length of the bending member \(in\) \(mm\)
\( P \) = total concentrated load \(lbf\) \(N\)

 

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Tags: Beam Support