def point_cflexure(self):
"""
Returns a Set of point(s) with zero bending moment and
where bending moment curve of the beam object changes
its sign from negative to positive or vice versa.
Examples
========
There is is 10 meter long overhanging beam. There are
two simple supports below the beam. One at the start
and another one at a distance of 6 meters from the start.
Point loads of magnitude 10KN and 20KN are applied at
2 meters and 4 meters from start respectively. A Uniformly
distribute load of magnitude of magnitude 3KN/m is also
applied on top starting from 6 meters away from starting
point till end.
Using the sign convention of upward forces and clockwise moment
being positive.
>>> from sympy.physics.continuum_mechanics.beam import Beam
>>> from sympy import symbols
>>> E, I = symbols('E, I')
>>> b = Beam(10, E, I)
>>> b.apply_load(-4, 0, -1)
>>> b.apply_load(-46, 6, -1)
>>> b.apply_load(10, 2, -1)
>>> b.apply_load(20, 4, -1)
>>> b.apply_load(3, 6, 0)
>>> b.point_cflexure()
[10/3]
"""
from sympy import solve, Piecewise
# To restrict the range within length of the Beam
moment_curve = Piecewise(
(float("nan"), self.variable <= 0),
(self.bending_moment(), self.variable < self.length),
(float("nan"), True))
points = solve(moment_curve.rewrite(Piecewise),
self.variable,
domain=S.Reals)
return points
def point_cflexure(self):
"""
Returns a Set of point(s) with zero bending moment and
where bending moment curve of the beam object changes
its sign from negative to positive or vice versa.
Examples
========
There is is 10 meter long overhanging beam. There are
two simple supports below the beam. One at the start
and another one at a distance of 6 meters from the start.
Point loads of magnitude 10KN and 20KN are applied at
2 meters and 4 meters from start respectively. A Uniformly
distribute load of magnitude of magnitude 3KN/m is also
applied on top starting from 6 meters away from starting
point till end.
Using the sign convention of upward forces and clockwise moment
being positive.
>>> from sympy.physics.continuum_mechanics.beam import Beam
>>> from sympy import symbols
>>> E, I = symbols('E, I')
>>> b = Beam(10, E, I)
>>> b.apply_load(-4, 0, -1)
>>> b.apply_load(-46, 6, -1)
>>> b.apply_load(10, 2, -1)
>>> b.apply_load(20, 4, -1)
>>> b.apply_load(3, 6, 0)
>>> b.point_cflexure()
[10/3]
"""
from sympy import solve, Piecewise
# To restrict the range within length of the Beam
moment_curve = Piecewise((float("nan"), self.variable<=0),
(self.bending_moment(), self.variable<self.length),
(float("nan"), True))
points = solve(moment_curve.rewrite(Piecewise), self.variable,
domain=S.Reals)
return points
def max_deflection(self):
"""
Returns point of max deflection and its coresponding deflection value
in a Beam object.
"""
from sympy import solve, Piecewise
# To restrict the range within length of the Beam
slope_curve = Piecewise((float("nan"), self.variable<=0),
(self.slope(), self.variable<self.length),
(float("nan"), True))
points = solve(slope_curve.rewrite(Piecewise), self.variable,
domain=S.Reals)
deflection_curve = self.deflection()
deflections = [deflection_curve.subs(self.variable, x) for x in points]
deflections = list(map(abs, deflections))
if len(deflections) != 0:
max_def = max(deflections)
return (points[deflections.index(max_def)], max_def)
else:
return None
def max_deflection(self):
"""
Returns point of max deflection and its coresponding deflection value
in a Beam object.
"""
from sympy import solve, Piecewise
# To restrict the range within length of the Beam
slope_curve = Piecewise((float("nan"), self.variable<=0),
(self.slope(), self.variable<self.length),
(float("nan"), True))
points = solve(slope_curve.rewrite(Piecewise), self.variable,
domain=S.Reals)
deflection_curve = self.deflection()
deflections = [deflection_curve.subs(self.variable, x) for x in points]
deflections = list(map(abs, deflections))
if len(deflections) != 0:
max_def = max(deflections)
return (points[deflections.index(max_def)], max_def)
else:
return None
