$M(x)$

$w(x)$

$V(x)$

$w(x)$

$V(x)$

$M(x)$

lb

ft

Scales

Shear

Bending Moment

$R_A$

$R_B$

C = (12, 3)
L = 20 (slider from 10 to 20, step 2)
A = Point(yAxis)
mask, mask1, mask4, mask3, mask2 = Polygon(Corner[2], Corner[3], (L, y(Corner[3])), (L, y(Corner[2])))
B = Point(mask3)
realW = Polynomial({A, B, C})
wmax: {Max[realW, 0, L], Min[realW, 0, L]}
W_T = Integral(realW, 0, L)
Qy = Integral((realW(x) * x), 0, L)
xbar: Qy / W_T
R_B: ((W_T * xbar)) / L
R_A: W_T - R_B
realV(x) = Integral[(-realW(x))] + R_A
vmax: {Max[realV, 0, L], Min[realV, 0, L]}
realM = Integral(realV)
mmax: {Max[realM, 0, L], Min[realM, 0, L]}
mscale = 50
i: (1, 0)
m0 = Point(Line[(0, 0) - (0.25 * i), yAxis])
j: (0, 1)
scaledM = Translate(If[0 ≤ x ≤ L, (AxisStepY[] / mscale * realM(x))], (y(m0) * j))
wscale = 1 (slider from -5 to 20)
w0 = Point(Line[(0, 0) - (0.25 * i), yAxis])
scaledW = Translate(If[0 ≤ x ≤ L, (AxisStepY[] / wscale * realW(x))], (y(w0) * j))
TR: (L + 3, 4)
v0 = Point(Line[(0, 0) - (0.25 * i), yAxis])
vscale = 5
ScaleW = Textfield(wscale)
ScaleV = Textfield(vscale)
ScaleM = Textfield(mscale)
scaledV = Translate(If[0 ≤ x ≤ L, (AxisStepY[] / vscale * realV(x))], (y(v0) * j))
vAxis = Segment(v0, (L, y(v0)))
wAxis = Segment(w0, (L, y(w0)))
mAxis = Segment(m0, (L, y(m0)))
textWlabel1: "" + wscale + "  " + unitsF + "/" + unitsD + ""
textWlabel2: "-" + wscale + "  " + unitsF + "/" + unitsD + ""
textVlabel1: "" + vscale + "  " + unitsF + ""
textVlabel2: "-" + vscale + "  " + unitsF + ""
textWmax: "$ w_{max} = " + (LaTeX[Max[abs(y(wmax))]]) + "$"
scaleFunction(x) = If[x ≤ 1, 1, If[x ≤ 2, 2, If[x ≤ 5, 5, If[x ≤ 10, 10, If[x ≤ 20, 20, If[x ≤ 50, 50, If[x ≤ 100, 100, If[x ≤ 200, 200, If[x ≤ 500, 500, If[x ≤ 1000, 1000, If[x ≤ 2000, 5000, 10000]]]]]]]]]]]
load = Sequence(Vector[(d, scaledW(d)), (d, y(w0))], d, 0, L, 0.75)
vAxis
IntegralV = IntegralBetween(scaledV, vAxis, 0, L)
mAxis
IntegralM = IntegralBetween(scaledM, mAxis, 0, L)
wAxis
IntegralW = IntegralBetween(scaledW, wAxis, 0, L)
showV = true
showW = true
showM = true
r_A = Vector((0, y(w0)) - (2 * j), (0, y(w0)))
r_B = Vector((L, y(w0)) - (2 * j), (L, y(w0)))
studentM(x) = (0 * x)
studentV(x) = (0 * x)
scaledStudentV = Translate(If[0 ≤ x ≤ L, (AxisStepY[] / vscale * studentV(x))], (y(v0) * j))
studentVintegral = IntegralBetween(scaledStudentV, vAxis, 0, L)
BL: (-15, y(m0) - 5)
scaledStudentM = Translate(If[0 ≤ x ≤ L, (AxisStepY[] / vscale * studentM(x))], (y(m0) * j))
studentMintegral = IntegralBetween(scaledStudentM, mAxis, 0, L)
textMlabel2: "-" + mscale + " " + unitsF + "-" + unitsD + ""
textMlabel1: "" + mscale + " " + unitsF + "-" + unitsD + ""