1.3.I.sagews

from sympy import *
from sympy import N as Num

# SI units:
m  = Symbol("m",  positive=True)
s  = Symbol("s",  positive=True)
kg = Symbol("kg", positive=True)

# Derived units:
N = kg*m/s/s

print("\n--- User input -----------------------")

a1 = S(200)/1000 *m
a2 = S(300)/1000 *m
a3 = S(250)/1000 *m
a4 = S(125)/1000 *m

b1 = S(300)/1000 *m
b2 = S(300)/1000 *m

F1 = 380 *N
F2 = 500 *N
F3 = 800 *N

A, B, C = var("A, B, C")

print("\n--- a: -------------------------------")

# Vectors from ref. point B to point at which forces act:
rA = Matrix([ -(a1+a2+a3+a4),    b1, 0 ])
rB = Matrix([              0,     0, 0 ])
rC = Matrix([              0, b1+b2, 0 ])
r1 = Matrix([       -(a3+a4),     0, 0 ])
r2 = Matrix([    -(a2+a3+a4), b1+b2, 0 ])
r3 = Matrix([            -a4,    b1, 0 ])

print("\n--- b: -------------------------------")

# Vectors of forces:
# wrt (ex, ey, ez):
FAv = Matrix([ 0, 0, A ])
FBv = Matrix([ 0, 0, B ])
FCv = Matrix([ 0, 0, C ])
F1v = Matrix([ 0, 0, -F1 ])
F2v = Matrix([ 0, 0, -F2 ])
F3v = Matrix([ 0, 0, -F3 ])

# Moments wrt point B:
MA = rA.cross(FAv)
MB = rB.cross(FBv)
MC = rC.cross(FCv)
M1 = r1.cross(F1v)
M2 = r2.cross(F2v)
M3 = r3.cross(F3v)

# Total moment wrt B (vector):
M = MA + MB + MC + M1 + M2 + M3

# Total force:
F = FAv + FBv + FCv + F1v + F2v + F3v

Mx = M[0]
My = M[1]
Fz = F[2]
eq1 = Eq(Mx)
eq2 = Eq(My)
eq3 = Eq(Fz)

# solve linear system:
eqs = [eq1, eq2, eq3]

sol = solve(eqs, [A,B,C])
A = sol[A]
B = sol[B]
C = sol[C]
pprint(Num(A/N,3))
pprint(Num(B/N,3))
pprint(Num(C/N,3))

--- User input ----------------------- --- a: ------------------------------- --- b: ------------------------------- 663. 449. 569.