2.4.3.D.sagews

from sympy.physics.units import *
from sympy import *
from sympy import N as Num

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

symbolic = True
# symbolic = False

if symbolic:
    # quantity = symbol:
    h, b = var("h, b")
    ts, tg = var("t_s, t_g")
    Q = var("Q")
else:
    # quantity =  factor times unit:
    h, b = 190 *mm, 200 *mm
    ts, tg = S(13)/2 *mm, 10 *mm
    Q = 100 *kilo*newton

dev=True
print("\n--- a: -------------------------------")

I_ys = ts * h**3/12
I_yg = (h/2)*(h/2) * tg*b
I_y = I_ys + 2 * I_yg
pprint(["Iy", I_y.simplify()])

print("\n--- b: -------------------------------")
A_1 = b/2*tg
A_2 = h/2*ts

z_1 = h/2
z_2 = h/4

S_A = z_1 * A_1
S_B = 2*z_1*A_1 + z_2*A_2

pprint(["SA:", S_A.simplify()])
pprint(["SB:", S_B.simplify()])

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

tau_A = S_A * Q / I_y / tg
tau_B = S_B * Q / I_y / ts

tau_A = tau_A.simplify()
tau_B = tau_B.simplify()

pprint(["tau_A:", tau_A])
pprint(["tau_B:", tau_B])

print("\n--- d: -------------------------------")
if not (symbolic):
    print(Num(tau_A,3))
    print(Num(tau_B,3))

print("\n--- Check: ---------------------------")
# compare with:
# Gross, Ehlers, Wriggers: Formeln
# und Aufgaben zur Technischen Mechanik 2
Ag = 2*A_1
As = 2*A_2

t1 = As/Ag
t2 = 1+As/6/Ag
t3 = 1+As/4/Ag

tau_max_g = Q/As * t1/t2 * b/2/h
tau_max_g = tau_max_g.simplify()
print(tau_max_g.equals(tau_A))

tau_max_s = Q/As * t3/t2
tau_max_s = tau_max_s.simplify()
print(tau_max_s.equals(tau_B))

--- User input ----------------------- --- a: ------------------------------- 2 h *(6*b*t_g + h*t_s) [Iy, --------------------] 12 --- b: ------------------------------- b*h*t_g [SA:, -------] 4 h*(4*b*t_g + h*t_s) [SB:, -------------------] 8 --- c: ------------------------------- 3*Q*b [tau_A:, -------------------] h*(6*b*t_g + h*t_s) 3*Q*(4*b*t_g + h*t_s) [tau_B:, -------------------------] 2*h*t_s*(6*b*t_g + h*t_s) --- d: ------------------------------- --- Check: --------------------------- True True