2.4.3.E.sagews

from sympy import *
from sympy import N as Num

hlf = S(1)/2
fth = S(1)/4

# lengths/mm:
b = 130
h = 160
t = 5
B = b + 2*t
H = h + 2*t

# Q_z / N:
Q_z = 100000

# I_y / mm^4:
I_y = (B*H*H*H - b*h*h*h)/12
print(I_y)

# A / mm^2:
A_1 = hlf*h*t
A_2 = B*t
A_3 = A_1
print(A_1, A_2, A_3)

# S_y / mm^3:
S_A = fth*h * A_1
S_B = S_A + hlf*(h + t) * A_2
S_C = S_B + S_A
print(S_A, S_B, S_C)

for S_y in (S_A, S_B, S_C):
    tau = Float(S_y) / I_y / t * Q_z
    print(Num(tau,3))

12945000 (400, 700, 400) (16000, 73750, 89750) 24.7 114. 139.