Three Member Frame - Pin/Roller Central Bending Moment

Three Member Frame - Pin/Roller Central Bending Moment formulas

$\large{ R_A = R_B = \frac{M_C}{L} }$
$\large{ H_A = 0 }$
$\large{ M_{max} \;(at \; C) = \frac{M_C}{2} }$
$\large{ \theta \;(at \; C) = \frac{M_C\;L}{12 \; \lambda \; I} }$

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	$\large{lbf-in}$	$\large{N-mm}$
$\large{ \lambda }$ (Greek symbol lambda) = modulus of elasticity	$\large{\frac{lbf}{in^2}}$	$\large{PA}$
$\large{ A, B, C, D, E }$ = point of intrest on frame	-	-
$\large{ \theta }$ = slope of member	$\large{deg}$	$\large{rad}$
$\large{ L }$ = 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.