2.4.3.B.sagews

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

import matplotlib.pyplot as plt
from numpy import linspace, full_like, array, arange

print("------ User input ----------------------------")

symbolic = True
symbolic = False

if symbolic:
    # quantity = symbol:
    F = var("F")
    (l, b, hl) = var("l, b, hl")
    hx = var("h_x")
else:
    # Werte aus Probeklausur TME 02:
    # F_val = 1000
    # (l,b,hl) = (90, 6, 30) *mm
    #
    # quantity =  factor times unit:
    F = 1 * newton
    (l,b,hl) = (600 *mm, 6 *mm, 30 *mm)

    hx = 10 *mm

print("\n--- c: Section modulus ---------------------")
def Wy(b,h):
    return  b/6 * h**2

Wl = Wy(b, hl)
pprint(["W_y at x=l", Wl])

print("\n--- d: Stress ------------------------------")
x = var("x")

Mx = -x*F
Mx_max = Abs(Mx.subs(x,l))
pprint(["|M(x=l)|", Mx_max])

sig_max = Mx_max / Wl
pprint(["sig_max", sig_max])

print("\n--- e: --------------------------------------")
Wx = Wy(b,hx)
eq = Eq( F*l/Wl, F*x/Wx )
x_star = solve(eq,[x])[0]
pprint(["x^*", x_star])

print("\n--- f: Plot ---------------------------------")
# xi  = x / l
xia = linspace(float(0), float(1))

# function to be plotted:
xi = var("xi")
f = xi**0.5
f = lambdify(xi,f,"numpy")
f = array(f(xia))

# plot:
tmp = plt.plot(xia, f, label="$h_{\\xi} = \sqrt{\\xi}$")

# annotation:
tmp = plt.xlabel("$\\xi = x / l$")
tmp = plt.legend(loc="best")

# save, show:
plt.savefig("2.4.3_B_sqrt.png", transparent=True)
plt.show()

------ User input ---------------------------- --- c: Section modulus --------------------- 3 9*m [W_y at x=l, --------] 10000000 --- d: Stress ------------------------------ 2 3*kg*m [|M(x=l)|, -------] 2 5*s 2000000*kg [sig_max, ----------] 2 3*m*s --- e: -------------------------------------- m [x^*, --] 15 --- f: Plot ---------------------------------