"Propped Cantilever with Partially Distributed Load
'<hr /><div style="max-width:180mm;">
'<img style="width:210pt;" alt="propped-cantilever-beam-distributed-load-p.png" class="side" src="https://calcpad.eu/media/mechanics/beams/propped-cantilever-beam-distributed-load-p.png">
'<p><b>Input data</b></p>
'Beam Length -'l = ?'m
'Load -'q = ?'kN/m
'Distances -'a = ?'m,'b = ?'m
#post
c = l - a - b'm,
d = b + c'm, 'e = a + b'm
'<p><b>Internal forces</b></p>
'Bending at support
M_A = q*((l - c^2/l)^2 - (l - d^2/l)^2)/8'kN·m
'Shear
V_A = q*b/l*(b/2 + c) + M_A/l'kN
V_B = q*b - V_A'kN
'Bending in mid-span
x_max = V_A/q + a'm
M_max = V_A*x_max - (x_max - a)^2*q/2 - M_A'kN·m
'<p><b>Diagrams</b></p>
#hide
PlotWidth = 600
PlotHeight = 150
#show
'Calculate internal forces at'x_1 = ?'m
#pre

#post
'Bending
M(x) = -M_A + V_A*x - q*(x - a)^2/2*(x > a) + q*(x - e)^2/2*(x > e)
$Plot{-M(x) @ x = 0 : l}
M(x_1)'kN·m
'Shear
V(x) = V_A - q*(x - a)*(x > a) + q*(x - e)*(x > e)
$Plot{V(x) @ x = 0 : l}
V(x_1)'kN
#show 
'</div>10	5	2	6	1