Querschnittswerte¶
Note
todos: Abbildungen, Definition der Vektoren h und b, Funktion für I, H, HEB, HEA, ...
In diesem Abschnitt werden die Querschnittswerte für verschieden zusammengesetzte Rechtecksquerschnitte berechnet.
EX01 Rechtecksquerschnitt¶
import numpy as np
import stanpy as stp
import matplotlib.pyplot as plt
b = 0.2 # m
h = 0.4 # m
cs_props = stp.cs(b=b,h=h)
print(cs_props)
offset = 0.2
fig, ax = plt.subplots()
stp.plot_cs(ax, b, h)
ax.set_xlim(-offset, np.max(b) + offset)
ax.set_ylim(-offset, np.max(h) + offset)
ax.grid(linestyle=":")
ax.axis('equal')
plt.show()
{'A': 0.08000000000000002,
'I_y': 0.001066666666666667,
'I_z': 0.00026666666666666673,
'b_render': 0.2,
'h_render': 0.4,
'y_s': 0.1,
'z_s': 0.2}

EX02 Zusammengesetzter Rechtecksquerschnitt¶
import numpy as np
import stanpy as stp
import matplotlib.pyplot as plt
s, t = 0.012, 0.02 # m
b, h = 0.3, 0.4 # m
b_v = np.array([b, s, b])
h_v = np.array([t, h - 2 * t, t])
zsi_v = np.array([t / 2, t + (h - 2 * t) / 2, t + (h - 2 * t) + t / 2]) # von OK
ysi_v = np.array([b/2, b/2, b/2]) # von Links
cs_props = stp.cs(b=b_v, h=h_v, y_si=ysi_v, z_si=zsi_v)
print(cs_props)
offset = 0.2
fig, ax = plt.subplots()
stp.plot_cs(ax, b_v, h_v, ysi_v, zsi_v)
ax.set_xlim(-offset, np.max(b) + offset)
ax.set_ylim(-offset, np.max(h) + offset)
ax.grid(linestyle=":")
ax.axis('equal')
plt.show()
{'A': 0.01632,
'I_y': 0.0004802560000000001,
'I_z': 9.005184000000001e-05,
'b_render': 0.612,
'h_render': 0.4000000000000001,
'y_s': 0.15,
'z_s': 0.20000000000000004}

EX03 I-Querschnitt¶
import numpy as np
import matplotlib.pyplot as plt
import stanpy as stp
import matplotlib.pyplot as plt
s, t = 0.012, 0.02 # m
b, h = 0.3, 0.4 # m
b_v = np.array([b, s, b])
h_v = np.array([t, h - 2 * t, t])
ysi_v = stp.AI_y.dot(b_v) # von OK
zsi_v = stp.AI_z.dot(h_v) # von Links
cs_props = stp.cs(b=b_v, h=h_v, y_si=ysi_v, z_si=zsi_v)
print(cs_props)
offset = 0.2
fig, ax = plt.subplots()
stp.plot_cs(ax, b_v, h_v, ysi_v, zsi_v)
ax.set_xlim(-offset, np.max(b) + offset)
ax.set_ylim(-offset, np.max(h) + offset)
ax.grid(linestyle=":")
ax.axis('equal')
plt.show()
{'A': 0.01632,
'I_y': 0.0004802560000000001,
'I_z': 9.005184000000001e-05,
'b_render': 0.612,
'h_render': 0.4000000000000001,
'y_s': 0.15,
'z_s': 0.20000000000000004}

EX04 H-Querschnitt¶
import numpy as np
import stanpy as stp
import matplotlib.pyplot as plt
s, t = 0.02, 0.02 # m
b, h = 0.3, 0.4 # m
b_v = np.array([t, h - 2 * t, t])
h_v = np.array([b, s, b])
ysi_v = stp.AH_y.dot(b_v) # von OK
zsi_v = stp.AH_z.dot(h_v) # von Links
cs_props = stp.cs(b=b_v, h=h_v, y_si=ysi_v, z_si=zsi_v)
print(cs_props)
offset = 0.2
fig, ax = plt.subplots()
stp.plot_cs(ax, b_v, h_v, ysi_v, zsi_v)
ax.set_xlim(-offset, np.max(b) + offset)
ax.set_ylim(-offset, np.max(h) + offset)
ax.grid(linestyle=":")
ax.axis('equal')
plt.show()
{'A': 0.019200000000000002,
'I_y': 9.024000000000011e-05,
'I_z': 0.0005113600000000001,
'b_render': 0.4000000000000001,
'h_render': 0.62,
'y_s': 0.20000000000000004,
'z_s': 0.14999999999999997}

EX05 Kasten-Querschnitt¶
import numpy as np
import stanpy as stp
import matplotlib.pyplot as plt
s, t = 0.012, 0.02 # m
b, h = 0.3, 0.4 # m
b_v = np.array([b, s, s, b])
h_v = np.array([t, h - 2 * t, h - 2 * t, t])
ysi_v = stp.AK_y.dot(b_v) # von OK
zsi_v = stp.AK_z.dot(h_v) # von Links
cs_props = stp.cs(b=b_v, h=h_v, z_si=zsi_v, y_si=ysi_v)
print(cs_props)
offset = 0.2
fig, ax = plt.subplots()
stp.plot_cs(ax, b_v, h_v, ysi_v, zsi_v)
ax.set_xlim(-offset, np.max(b) + offset)
ax.set_ylim(-offset, np.max(h) + offset)
ax.grid(linestyle=":")
ax.axis('equal')
plt.show()
{'A': 0.020640000000000002,
'I_y': 0.000526912,
'I_z': 0.0002692627199999998,
'b_render': 0.624,
'h_render': 0.7600000000000001,
'y_s': 0.15000000000000002,
'z_s': 0.2}

EX06 - Verstärkter I Querschnitt¶
import numpy as np
import stanpy as stp
import matplotlib.pyplot as plt
s, t = 0.012, 0.02 # m
b, h = 0.3, 0.4 # m
h_i = 0.05 # m
b_v = np.array([b, s, b, s, s, s, s])
h_v = np.array([t, h - 2 * t, t, h_i, h_i, h_i, h_i])
ysi_v = stp.AI_yp.dot(b_v) # von OK
zsi_v = stp.AI_zp.dot(h_v) # von Links
cs_props = stp.cs(b=b_v, h=h_v, z_si=zsi_v, y_si=ysi_v)
print(cs_props)
offset = 0.2
fig, ax = plt.subplots()
stp.plot_cs(ax, b_v, h_v, ysi_v, zsi_v)
ax.set_xlim(-offset, np.max(b) + offset)
ax.set_ylim(-offset, np.max(h) + offset)
ax.grid(linestyle=":")
ax.axis('equal')
plt.show()
{'A': 0.01872,
'I_y': 0.0005384160000000002,
'I_z': 0.00013984703999999986,
'b_render': 0.66,
'h_render': 0.6000000000000002,
'y_s': 0.15000000000000002,
'z_s': 0.20000000000000004}
