Simple Beam - Two Equal Point Loads Unequally Spaced

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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.

 

sb 10D

Simple Beam - Two Equal Point Loads Unequally Spaced formulas

\( R_1 \;=\; V_1 \; ( max.\; when\; a < b )  \;=\; (P\;/\;L)  \; (  L - a + b ) \) 

\( R_2 \;=\; V_2  \; ( max.\; when\; a < b ) \;=\; (P\;/\;L)  \; (  L - b + a ) \)

\( V_x  \; [\; a  <  x < (  L - b ) \;]  \;=\; (P\;/\;L)  \; (  b - a )   \) 

\( M_1 \; ( max.\; when\; a > b  )  \;=\; R_1 \;a     \)

\( M_2 \; (max.\; when\;  a < b )  \;=\; R_2 \;b     \)

\( M_x \; ( max.\; when\; x < a )  \;=\; R_1 \;x     \)

\( M_x \; [\; max. \; when \; a < x <  (  L - b ) \;] \;=\; (R_1 \;x)  - [\;P\; ( x - a )\;]   \)

Symbol English Metric
\( x \) = horizontal distance from reaction to point on beam \(in\) \(mm\)
\( a, b \) = length to point load \(in\) \(mm\)
\( M \) = 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