Two Member Frame - Pin/Pin Top Uniformly Distributed Load

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

$\large{ e = \frac{h}{L} }$
$\large{ \beta = \frac{I_h}{I_v} }$
$\large{ R_A = \frac{w\;L}{8} \; \left( \frac{ 4\; \beta \; e \;+\; 5 }{\beta \; e \;+\; 1} \right) }$
$\large{ R_C = \frac{w\;L}{8} \; \left( \frac{ 4\; \beta \; e \;+\; 3 }{\beta \; e \;+\; 1} \right) }$
$\large{ H_A = H_C = \frac{ w\;L^2 }{ 8\;h\; \left( \beta \; e \;+\; 1 \right) } }$
$\large{ H_B = \frac{ w\;L^2 }{ 8\; \left( \beta \; e \;+\; 1 \right) } }$

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	$\large{lbf-in}$	$\large{N-mm}$
$\large{ A, B, C }$ = point of intrest on frame	-	-
$\large{ L }$ = span length under consideration	$\large{in}$	$\large{mm}$
$\large{ R }$ = vertical reaction load at bearing point	$\large{lbf}$	$\large{N}$

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.