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}
../_images/cross_section_0_1.png

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}
../_images/cross_section_1_1.png

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}
../_images/cross_section_2_1.png

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}
../_images/cross_section_3_1.png

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}
../_images/cross_section_4_1.png

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}
../_images/cross_section_5_1.png