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RectFootingPressDistribution.py
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RectFootingPressDistribution.py
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from math import sqrt, fabs, pow
from enum import Enum
from scipy.optimize import fsolve
class EccentricityRegions(Enum):
"""
Eccentricity regions
--------------------
A : enumerate
Triangular Compression Zone
B : enumerate
Pentagonal Compression Zone
C : enumerate
Full Compression Zone
D : enumerate
Trapezoidal Compression Zone X Direction
E : enumerate
Trapezoidal Compression Zone Y Direction
"""
Null = 1
A = 2
B = 3
C = 4
D = 5
E = 6
class RectFootingPressDistribution:
"""
Rectangular footing base pressure distribution object
(Determination of base stresses in rectangular footings
under biaxial bending)
Attributes
-------------------------------------------------------
name : str
Name of calculation
p : float
Axial force
mx : float
Bending moment about x axis
my : float
Bending moment about y axis
lx : float
Footing length in x direction
ly : float
Footing length in y direction
ex : float
eccentricity of axial load in x direction
ey : float
eccentricity of axial load in y direction
pm : float
Mean base pressure
pmax : float
Maximum base pressure
pmin : float
Minimum base pressure
po, pp, pq, pr : float
Actual corner pressures
p1, p2, p3, p3 : float
Rearranged footing corner pressures depending on the eccentricities signs
xn : float
Distance of zero pressure point to maximum pressure point (o) in x direction
yn : float
Distance of zero pressure point to maximum pressure point (o) in y direction
xq : float
Distance of zero pressure point to corner q in x direction
yp : float
Distance of zero pressure point to corner p in y direction
"""
def __init__(self, name, p, mx, my, lx, ly):
self.name = name
self.p = p
self.mx = mx
self.my = my
self.lx = lx
self.ly = ly
self.ex = self.my / self.p
self.ey = self.mx / self.p
self.kx = fabs(self.ex)/ self.lx
self.ky = fabs(self.ey) / self.ly
self.pm = self.p / (self.lx * self.ly)
self.po = self.pp = self.pq = self.pr = 0.0
self.pmax = self.pmin = 0.0
self.xn = self.yn = self.xq = self.yp = 0.0
self.eccentricity_region = self.find_eccentricity_region()
if self.eccentricity_region == EccentricityRegions.A:
self.triangular_compression_zone_a()
elif self.eccentricity_region == EccentricityRegions.B:
self.pentagonal_compression_zone_b()
elif self.eccentricity_region == EccentricityRegions.C:
self.full_compression_zone_c()
elif self.eccentricity_region == EccentricityRegions.D:
self.trapezoidal_compression_zone_x_direction_d()
elif self.eccentricity_region == EccentricityRegions.E:
self.trapezoidal_compression_zone_y_direction_e()
self.p1, self.p2, self.p3, self.p4 = self.corner_pressures()
def find_eccentricity_region(self):
x4 = 1.0 + 4.0 * self.kx
y4 = 1.0 + 4.0 * self.ky
x12 = sqrt(1.0 - 12.0 * pow(self.kx, 2.0))
y12 = sqrt(1.0 - 12.0 * pow(self.ky, 2.0))
c12 = 0.50
c16 = 1.0 / 6.0
c14 = 0.25
eccentricity_region = EccentricityRegions.Null
if self.kx >= 0.25 and self.kx < 0.5 and self.ky >= 0.25 and self.ky < 0.5:
eccentricity_region = EccentricityRegions.A
elif self.kx + self.ky >= c16 and self.kx <= c12 - c16 * (2.0 - y12) * (1.0 + 2.0 * self.ky + y12) / y4 and \
self.ky <= c12 - c16 * (2.0 - x12) * (1.0 + 2.0 * self.kx + x12) / x4:
eccentricity_region = EccentricityRegions.B
elif self.kx + self.ky <= c16:
eccentricity_region = EccentricityRegions.C
elif self.kx >= 0 and self.kx <= c14 and self.ky < c12 and \
self.ky >= c12 - c16 * (2.0 - x12) * (1.0 + 2.0 * self.kx + x12) / x4:
eccentricity_region = EccentricityRegions.D
elif self.ky >= 0 and self.ky <= c14 and self.kx < c12 and \
self.kx >= c12 - c16 * (2.0 - y12) * (1.0 + 2.0 * self.ky + y12) / y4:
eccentricity_region = EccentricityRegions.E
return eccentricity_region
def triangular_compression_zone_a(self):
self.xn = 4 * self.lx * (0.5 - self.kx)
self.yn = 4 * self.ly * (0.5 - self.ky)
self.po = self.pmax = 3.0 * self.pm / (8.0 * (0.5 - self.kx) * (0.5 - self.ky))
self.pr = self.pp = self.pq = self.pmin = 0.0
def pentagonal_compression_zone_b(self):
self.xn, self.yn = fsolve(self.pentagonal_compression_zone_b_equations, (self.lx, self.ly))
self.yp = self.yn * (1.0 - self.lx / self.xn)
self.xq = self.xn * (1.0 - self.ly / self.yn)
self.po = self.pmax = 6.0 * self.pm * self.lx * self.ly / (self.xn * self.yn) / \
(1.0 - pow(1.0 - self.lx / self.xn, 3.0) - pow(1.0 - self.ly / self.yn, 3.0))
self.pp = self.pmax * (1.0 - self.lx / self.xn)
self.pq = self.pmax * (1.0 - self.ly / self.yn)
self.pr = self.pmin = 0.0
def pentagonal_compression_zone_b_equations(self, variables):
x, y = variables
a1 = 4 * self.lx * (0.5 - fabs(self.ex) / self.lx)
b1 = 1 - pow(1 - self.lx / x, 3) - pow(1 - self.ly / y, 3)
c1 = 1 - pow(1 - self.lx / x, 4) - pow(1 - self.ly / y, 4) - 4 * pow(1 - self.lx / x, 3) * self.lx / x
f1 = x - a1 * b1 / c1
a2 = 4 * self.ly * (0.5 - fabs(self.ey) / self.ly)
b2 = 1 - pow(1 - self.lx / x, 3) - pow(1 - self.ly / y, 3)
c2 = 1 - pow(1 - self.lx / x, 4) - pow(1 - self.ly / y, 4) - 4 * pow(1 - self.ly / y, 3) * self.ly / y
f2 = y - a2 * b2 / c2
return (f1, f2)
def full_compression_zone_c(self):
self.xn = self.lx * (1.0 + 6.0 * (self.kx + self.ky)) / (12.0 * self.kx)
self.yn = self.ly * (1.0 + 6.0 * (self.kx + self.ky)) / (12.0 * self.ky)
self.yp = 0.0
self.po = self.pmax = self.pm * (1.0 + 6.0 * self.kx + 6.0 * self.ky)
self.pr = self.pmin = self.pm * (1.0 - 6.0 * self.kx - 6.0 * self.ky)
self.pp = self.pm * (1.0 - 6.0 * self.kx + 6.0 * self.ky)
self.pq = self.pm * (1 + 6.0 * self.kx - 6.0 * self.ky)
def trapezoidal_compression_zone_x_direction_d(self):
x12 = sqrt(1.0 - 12.0 * pow(self.kx, 2.0))
x4 = 1.0 + 4.0 * pow(self.kx, 2.0)
c12 = 0.5
self.xn = self.lx * (1.0 + 6.0 * self.kx + x12) / (12.0 * self.kx)
self.yn = c12 * self.ly * (c12 - self.ky) * (2.0 + x12) * (1.0 + 2.0 * self.kx - x12) / (self.kx * x4)
self.yp = c12 * self.ly * (c12 - self.ky) * (2.0 + x12) * (-1.0 + 2.0 * self.kx + x12) / (self.kx * x4)
self.po = self.pmax = (self.pm / 3.0) * (2.0 - x12) * (1.0 + 6.0 * self.kx + x12) / (c12 - self.ky)
self.pp = (self.pm / 3.0) * (2.0 - x12) * (1.0 - 6.0 * self.kx + x12) / (c12 - self.ky)
self.pr = self.pq = self.pmin = 0.0
def trapezoidal_compression_zone_y_direction_e(self):
y12 = sqrt(1.0 - 12.0 * pow(self.ky, 2.0))
y4 = 1.0 + 4.0 * pow(self.ky, 2.0)
c12 = 0.5
self.xn = c12 * self.lx * (c12 - self.kx) * (2.0 + y12) * (1.0 + 2.0 * self.ky - y12) / (self.ky * y4)
self.yn = self.ly * (1.0 + 6.0 * self.ky + y12) / (12.0 * self.ky)
self.xq = c12 * self.lx * (c12 - self.kx) * (2.0 + y12) * (-1.0 + 2.0 * self.ky + y12) / (self.ky * y4)
self.po = self.pmax = self.pm * (2.0 - y12) * (1.0 + 6.0 * self.ky + y12) / (c12 - self.kx) / 3.0
self.pq = self.pm * (2.0 - y12) * (1.0 - 6.0 * self.ky + y12) / (c12 - self.kx) / 3.0
self.pp = self.pr = self.pmin = 0.0
def corner_pressures(self):
if self.ex >= 0.0 and self.ey >= 0.0:
return self.po, self.pp, self.pr, self.pq
elif self.ex < 0.0 and self.ey > 0.0:
return self.pp, self.po, self.pq, self.pr
elif self.ex <= 0.0 and self.ey < 0.0:
return self.pr, self.pq, self.po, self.pp
elif self.ex > 0.0 and self.ey < 0.0:
return self.pq, self.pr, self.pp, self.po
else:
return 0.0, 0.0, 0.0, 0.0
def arrange_pressure_point(self, x, y):
if self.p3 == self.pmax:
x = self.lx - x
y = self.ly - y
elif self.p2 == self.pmax:
x = self.lx - x
elif self.p4 == self.pmax:
y = self.ly - y
return x, y
def arrange_pressure_point_by_centroid_cs(self, x, y):
if self.p3 == self.pmax:
x = - x
y = - y
elif self.p2 == self.pmax:
x = - x
elif self.p4 == self.pmax:
y = - y
return x, y
def pressure_at_point(self, x, y):
x, y = self.arrange_pressure_point(x, y)
return self.pmax * (-x / self.xn - y / self.yn + 1)
def pressure_at_point_by_centroid_cs(self, x, y):
x, y = self.arrange_pressure_point_by_centroid_cs(x, y)
return self.pmax * (-x / self.xn - y / self.yn + 1 - 0.5 * (self.lx / self.xn + self.ly / self.yn))