# sigma = Mmax/Wo = Mmax/(Jz/(H/2)) <= sigD
# Jz >= H/2*Mmax/sigD
# [rectangular cross-section]
# Jz = 1/12*B*H**3 = (H/B=2) =
# = 1/24*H**4
# H**4 >= 24*H/2*Mmax/sigD
# H >= (12*Mmax/sigD)**(1/3)
Mmax = max(abs(Mo))
print('Mmax = {:.4}N'.format(Mmax))
H = (12 * Mmax / sigD)**(1. / 3)
print('H = {:.4}m'.format(H))
print('B = {:.4}m'.format(.5 * H))
Jz = H**4 / 24
beam.Jz = Jz
### computation and plots of deflection and angle ###
v = np.array([beam.deflection(xi) for xi in x]).T
v_C = beam.deflection(C)
print('v_C = {:.4}m\nphi_C = {:.4}rad'.format(v_C[0], v_C[1]))
plt.figure()
plt.plot(x, v[0], '.-', label='deflection')
plt.plot(x, v[1], '.-', label='angle')
plt.grid()
plt.legend(loc='best')
plt.show()
# sigma = Mmax/Wo = Mmax/(Jz/(H/2)) <= sigD
# Jz >= H/2*Mmax/sigD
# [rectangular cross-section]
# Jz = 1/12*B*H**3 = (H/B=2) =
# = 1/24*H**4
# H**4 >= 24*H/2*Mmax/sigD
# H >= (12*Mmax/sigD)**(1/3)
Mmax = max(abs(Mo))
print('Mmax = {:.4}N'.format(Mmax))
H = (12*Mmax/sigD)**(1./3)
print('H = {:.4}m'.format(H))
print('B = {:.4}m'.format(.5*H))
Jz = H**4/24
beam.Jz = Jz
### computation and plots of deflection and angle ###
v = np.array([beam.deflection(xi) for xi in x]).T
v_C = beam.deflection(C)
print('v_C = {:.4}m\nphi_C = {:.4}rad'.format(v_C[0], v_C[1]))
plt.figure()
plt.plot(x, v[0], '.-', label='deflection')
plt.plot(x, v[1], '.-', label='angle')
plt.grid()
plt.legend(loc='best')
plt.show()
