def NAangle(span_position):
M_x, M_y = internal_moments(z)
I_xx, I_yy, I_xy = MOI(z)
y = M_y * I_xx - M_x * I_xy
x = M_x * I_yy - M_y * I_xy
alpha = atan2(y, x)
return alpha * 180 / pi
def Normalstress(span_position):
M_x, M_y = internal_moments(z)
I_xx, I_yy, I_xy = MOI(z)
width, frontheight, rearheight = initial_values(z)[2:5]
centroidx, centroidy = centroid(z)
#x1, y1 = -0.5 * width - centroidx, 0.5 * rearheight - centroidy
#x2, y2 = 0.5 * width - centroidx, 0.5 * frontheight - centroidy
x3, y3 = 0.5 * width - centroidx, -0.5 * frontheight - centroidy
x4, y4 = -0.5 * width - centroidx, -0.5 * rearheight - centroidy
#sigma1 = ((M_x * I_yy - M_y * I_xy) * y1 + (M_y * I_xx - M_x * I_xy) * x1) / (I_xx * I_yy - I_xy ** 2)
#sigma2 = ((M_x * I_yy - M_y * I_xy) * y2 + (M_y * I_xx - M_x * I_xy) * x2) / (I_xx * I_yy - I_xy ** 2)
sigma3 = ((M_x * I_yy - M_y * I_xy) * y3 +
(M_y * I_xx - M_x * I_xy) * x3) / (I_xx * I_yy - I_xy**2)
sigma4 = ((M_x * I_yy - M_y * I_xy) * y4 +
(M_y * I_xx - M_x * I_xy) * x4) / (I_xx * I_yy - I_xy**2)
return -sigma3, -sigma4 #, -sigma3, -sigma4
b = 27.14
dz = 0.1
z = 0.1
k1c = 35.1
c = 0.0025
sigmastar = k1c / (sqrt(pi * c))
sigma1tab, sigma2tab, sigma3tab, sigma4tab = [], [], [], []
alphatab, ztab, ztab1, ztab2, ztab3, ztab4, M_xtab, M_ytab = [], [], [], [], [], [], [], []
I_xxtab, I_yytab, I_xytab = [], [], []
while z <= b:
sigma1, sigma2, sigma3, sigma4 = Normalstress(z)
M_x, M_y = internal_moments(z)
I_xx, I_yy, I_xy = MOI(z)
ztab.append(z)
alphatab.append(NAangle(z))
sigma1margin = sigmastar / (sigma1 / 10**6)
sigma2margin = sigmastar / (sigma2 / 10**6)
sigma3margin = sigmastar / (sigma3 / 10**6)
sigma4margin = sigmastar / (sigma4 / 10**6)
if abs(sigma1 / 10**6) >= 1:
sigma1tab.append(sigma1margin)
ztab1.append(z)
if abs(sigma2 / 10**6) >= 1:
sigma2tab.append(sigma2margin)
ztab2.append(z)
if abs(sigma3 / 10**6) >= 1: