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Three Member Frame - Pin/Roller Central Bending Moment

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Three Member Frame - Pin/Roller Central Bending Moment formulas

\large{ R_A = R_B  = \frac{M_C}{L}  }   
\large{ H_A = 0  }   
\large{ M_{max} \;(at \; C)  =  \frac{M_C}{2}   }   
\large{ \theta \;(at \; C) =  \frac{M_C\;L}{12 \; \lambda \; I}  }  

Where:

 Units English Metric
\large{ h } = height of frame \large{in} \large{mm}
\large{ H } = horizontal reaction load at bearing point \large{lbf} \large{N}
\large{ I_h } = horizontal member second moment of area (moment of inertia) \large{in^4} \large{mm^4}
\large{ I_v } = vertical member second moment of area (moment of inertia) \large{in^4} \large{mm^4}
\large{ M } = maximum bending moment \large{lbf-in} \large{N-mm}
\large{ \lambda }  (Greek symbol lambda) = modulus of elasticity \large{\frac{lbf}{in^2}} \large{PA}
\large{ A, B, C, D, E } = point of intrest on frame - -
\large{ \theta } = slope of member \large{deg} \large{rad}
\large{ L } = span length under consideration \large{in} \large{mm}
\large{ R } = vertical reaction load at bearing point \large{lbf} \large{N}

 

diagrams

  • 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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