2.4.3.F.sagews

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

symbolic = True
# symbolic = False

if symbolic:
    F = var("F")
    a, b = var("a, b")
    t = var("t")
else:
    F = 1000 * newton
    a, b = 3*m, 2*m
    t = 1*cm

print("\n--- zS: -------------------------------")
(A1, A2, A3) = (2*t*t, 2*t*t, 4*t*t)
(z1, z2, z3) = (2*t, 2*t, t/2)
zS = z1*A1 + z2*A2 + z3*A3
A = A1 + A2 + A3
zS /= A

print("\n--- Iy: -------------------------------")
Iy1 = t * (2*t)**3 / 12
Iy2 = Iy1
Iy3 = 4*t * t**3 / 12

# Steiner:
Iy =  Iy1 + (z1-zS)**2*A1
Iy += Iy2 + (z2-zS)**2*A2
Iy += Iy3 + (z3-zS)**2*A3

pprint("\nIy:")
pprint(Iy)

print("\n--- Q,M,N: ---------------------------")
M = b*F
Nx = -F

sig_N =  Nx / A
pprint("\nsig_N:")
pprint(sig_N)

z = 7*t/4
sig_M = M/Iy * z
pprint("\nsig_M:")
pprint(sig_M)

sig = sig_N + sig_M
pprint("\nsig:")
pprint(sig)

print("\n---- sig and tau: --------------------")

Q = - b/a * F
zR = 7*t/8
AR = 7*t/4 * t
SyR = zR*AR

# SyR via integration:
s = var("s")
f = (7*t/4 - s)*t
SyR_f = integrate(f, (s, 0, 7*t/4))
SyR_f = integrate(f, s)

# Cousinenformel:
tau = - Q*SyR/Iy/t
tau = tau.simplify()
pprint("\ntau:")
pprint(tau)
# pprint(["tau:", tau])
if not (symbolic):
    pprint("\nsig / MPa:")
    sigMPa = sig/mega/pascal
    pprint(Num(sigMPa,3))

    pprint("\ntau / MPa:")
    tauMPa = tau/mega/pascal
    pprint(Num(tauMPa,3))

--- zS: ------------------------------- --- Iy: ------------------------------- Iy: 4 37*t ----- 6 --- Q,M,N: --------------------------- sig_N: -F ---- 2 8*t sig_M: 21*F*b ------ 3 74*t sig: 21*F*b F ------ - ---- 3 2 74*t 8*t ---- sig and tau: -------------------- tau: 147*F*b -------- 2 592*a*t