Three Member Frame - Pin/Pin Top Uniformly Distributed Load

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Three Member Frame - Pin/Pin Top Uniformly Distributed Load formulas

\(\large{ e  = \frac{h}{L}  }\)
\(\large{ \beta = \frac{I_h}{I_v}  }\)
\(\large{ R_A  = R_E = \frac{ w\;L }{2}  }\)
\(\large{ H_A  = H_E = \frac{ w\;L }{4\;e\; \left( 2\;\beta\;e \;+\; 3 \right)  }  }\)
\(\large{ M_B  = M_D = \frac{ w\;L^2 }{4\; \left( 2\;\beta\;e \;+\; 3 \right)  }  }\)
\(\large{ M_C  =   \frac{w\;L^2}{8}   \;   \left(  \frac{ 2\;\beta\;e \;+\; 1 }{ 2\;\beta\;e \;+\; 3 } \right)  }\)

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)	\(\large{in^4}\)	\(\large{mm^4}\)
\(\large{ w }\) = load per unit length	\(\large{\frac{lbf}{in}}\)	\(\large{\frac{N}{m}}\)
\(\large{ M }\) = maximum bending moment	\(\large{lbf-in}\)	\(\large{N-mm}\)
\(\large{ A, B, C, D, E }\) = point of intrest on frame	-	-
\(\large{ L }\) = 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.