Three Member Frame - Pin/Pin Side Point Load

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Three Member Frame - Pin/Pin Side Point Load formulas

 $$\large{ e = \frac{h}{L} }$$ $$\large{ \beta = \frac{I_h}{I_v} }$$ $$\large{ R_A = R_E = \frac{ P \; \left(h\;-\;y\right) }{L} }$$ $$\large{ H_A = \frac{P}{2\;h} \; \left( h+y-\; \left( h-y\right) \; \frac{y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left(2\;h\; \beta\;+\; 3\;L\right) } \right) }$$ $$\large{ H_E = \frac{P\; \left( h\;-\;y \right) }{2\;h} \; \left( 1+\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }$$ $$\large{ M_B = \frac{P\;\left( h\;-\;y \right) }{2\;h} \; \left( h+y- \; \left( h-y \right) \; \frac{x\; \beta \; \left( 2\;h\;-\;y \right) }{h\; \left( 2\;h\; \beta\;+\; 3\;L \right) } \right) }$$ $$\large{ M_C = \frac{P\; \left( h\;-\;y \right) }{2} \; \left( 1-\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }$$ $$\large{ M_D = \frac{P\; \left( h\;-\;y \right) }{2} \; \left( 1+\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }$$

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) $$\large{in^4}$$ $$\large{mm^4}$$ $$\large{ M }$$ = 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 $$\large{in}$$ $$\large{mm}$$ $$\large{ P }$$ = total concentrated load $$\large{lbf}$$ $$\large{N}$$ $$\large{ y }$$ = vertical distance from reaction point $$\large{in}$$ $$\large{mm}$$ $$\large{ R }$$ = 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.

Tags: Frame Support