Two Member Frame - Fixed/Free Free End Bending Moment

Two Member Frame - Fixed/Free Free End Bending Moment formulas

$\large{ R_A \;\;=\;\; 0 }$

$\large{ H_A \;\;=\;\; 0 }$

$\large{ M_{max} \;\;=\;\; M_C }$

$\large{ \Delta_{Cx} \;\;=\;\; \frac{M_C\;h^2}{2\; \lambda \; I} }$

$\large{ \Delta_{Cy} \;\;=\;\; \frac{M_C\;L}{2\; \lambda \; I} \; \left( L + 2\;h \right) }$

$\large{ \theta_{C} \;\;=\;\; \frac{M_C}{ \lambda \; L} \; \left( L + h \right) }$

Units	English	Metric
$\large{ \Delta }$ = deflection or deformation	$\large{in}$	$\large{mm}$
$\large{ h }$ = 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	$\large{\frac{lbf}{in^2}}$	$\large{Pa}$
$\large{ A, B, C }$ = 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.