1.5.C.sagews

from sympy import *
from sympy import N as Num

print("------ User input ---------------------")
a, b, alpha, q = var("a, b, alpha, q")

print("\n--- a: Resultant force --------------")
R = q*b

print("\n--- b: Reaction forces --------------")
#
# unknowns:
A_h, B_v, C_h, C_v, D_h, D_v = var("A_h, B_v, C_h, C_v, D_h, D_v")

print("\n------ Var 1 ------------------------")

# Version a:
ca = cos(alpha)
sa = sin(alpha)

# Equilibrium conditions:
eq1 = Eq(0, A_h - C_h)
eq2 = Eq(0, B_v + C_v - R)
eq3 = Eq(0, 2*b*R/3 - b*B_v -2*b*C_v)

eq4 = Eq(0, C_h - D_h)
eq5 = Eq(0, C_v - D_v)
eq6 = Eq(0, - D_h*ca + D_v*sa)

eqns = [eq1,eq2,eq3,eq4,eq5,eq6]

# Solve:
unknowns = [A_h, B_v, C_h, C_v, D_h, D_v]
sol = solve(eqns, unknowns)
pprint(sol)

print("\n------ Var 2 ------------------------")
D = var('D')

eq1 = Eq(0, A_h - D*sa )
eq2 = Eq(0, R - B_v - D*ca)
eq3 = Eq(0, -b*B_v + 4*b*R/3)
eqns = [eq1, eq2, eq3]

# Solve equations:
unknowns = [A_h, B_v, D]
sol = solve(eqns, unknowns)
pprint(sol)

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

ta = sa/ca
ta = ta.subs(alpha,pi/6)
pprint(ta)
pprint(Num(ta,3))

------ User input --------------------- --- a: Resultant force -------------- --- b: Reaction forces -------------- ------ Var 1 ------------------------ -b*q*tan(alpha) 4*b*q -b*q*tan(alpha) -b*q -b {A_h: ----------------, B_v: -----, C_h: ----------------, C_v: -----, D_h: -- 3 3 3 3 *q*tan(alpha) -b*q --------------, D_v: -----} 3 3 ------ Var 2 ------------------------ -b*q*tan(alpha) 4*b*q -b*q {A_h: ----------------, B_v: -----, D: ------------} 3 3 3*cos(alpha) --- c: ----------------------------- ___ \/ 3 ----- 3 0.577