Two Member Frame - Fixed/Pin Top Point Load

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two Member Frame - Fixed/Pin Top Point Load formulas

 $$\large{ e \;\;=\;\; \frac{h}{L} }$$ $$\large{ \beta \;\;=\;\; \frac{I_h}{I_v} }$$ $$\large{ R_A \;\;=\;\; \frac{P\;x}{L} \; \left[ 1+ \; \frac{2}{L^2} \; \left( \frac{L^2\;-\;x^2}{ 3\;\beta\;e \;+\; 4} \right) \right] }$$ $$\large{ R_D \;\;=\;\; \frac{P\;\left( L\;-\;x \right)}{L} \; \left[ 1- \; \frac{2\;x}{L^2} \; \left( \frac{L\;+\;x}{ 3\;\beta\;e \;+\; 4} \right) \right] }$$ $$\large{ H_A = H_D \;\;=\;\; \frac{3\;P\;x}{h\;L^2} \; \left( \frac{L^2\;-\;x^2}{ 3\;\beta\;e \;+\; 4} \right) }$$ $$\large{ M_A \;\;=\;\; \frac{P\;x}{L^2} \; \left( \frac{L^2\;-\;x^2}{ 3\;\beta\;e \;+\; 4} \right) }$$ $$\large{ M_B \;\;=\;\; \frac{2\;P\;x}{L^2} \; \left( \frac{L^2\;-\;x^2}{ 3\;\beta\;e \;+\; 4} \right) }$$ $$\large{ M_C \;\;=\;\; \frac{P\;a \; \left( L\;-\;x \right) }{L} \; \left[ 1- \; \frac{2\;x}{L^2} \; \left( \frac{L\;-\;x}{ 3\;\beta\;e \;+\; 4} \right) \right] }$$

Where:

 Units English Metric $$\large{ \Delta }$$ = deflection or deformation $$\large{in}$$ $$\large{mm}$$ $$\large{ h }$$ = height of frame $$\large{in}$$ $$\large{mm}$$ $$\large{ x }$$ = horizontal distance from reaction to point on beam $$\large{in}$$ $$\large{mm}$$ $$\large{ H }$$ = 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 $$\large{lbf-in}$$ $$\large{N-mm}$$ $$\large{ A, B, C, D }$$ = point of intrest on frame - - $$\large{ L }$$ = span length under consideration $$\large{in}$$ $$\large{mm}$$ $$\large{ P }$$ = total concentrated load $$\large{lbf}$$ $$\large{N}$$ $$\large{ R }$$ = vertical reaction load at bearing point $$\large{lbf}$$ $$\large{N}$$

diagrams

• 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.
• 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.
• Uniformly distributed load (UDL)  -  A load that is distributed evenly across the entire length of the support area.

Tags: Frame Support