def menu():
print("Welcome to the Macaulay notation plotter.")
print("How long is the beam?")
xend = int(input(""))
b = Beam(xend, E, I)
print("How many forces are acting upon the beam?")
num_forces = int(input(""))
for x in range(num_forces):
print("\nForce number " + str(x+1) + ":")
print("What's the magnitude of the force? (Convention is upwards being positive.)")
mag = int(input(""))
print("How far along the beam is the force?")
dist = int(input(""))
print("What's the power?")
power = int(input(""))
b.apply_load(mag, dist, power-1)
print("The Macaulay equation for the beam is:")
pprint(b.shear_force())
graph_choice(b)
def test_Beam():
E = Symbol('E')
E_1 = Symbol('E_1')
I = Symbol('I')
I_1 = Symbol('I_1')
b = Beam(1, E, I)
assert b.length == 1
assert b.elastic_modulus == E
assert b.second_moment == I
assert b.variable == x
# Test the length setter
b.length = 4
assert b.length == 4
# Test the E setter
b.elastic_modulus = E_1
assert b.elastic_modulus == E_1
# Test the I setter
b.second_moment = I_1
assert b.second_moment is I_1
# Test the variable setter
b.variable = y
assert b.variable is y
# Test for all boundary conditions.
b.bc_deflection = [(0, 2)]
b.bc_slope = [(0, 1)]
assert b.boundary_conditions == {'deflection': [(0, 2)], 'slope': [(0, 1)]}
# Test for slope boundary condition method
b.bc_slope.extend([(4, 3), (5, 0)])
s_bcs = b.bc_slope
assert s_bcs == [(0, 1), (4, 3), (5, 0)]
# Test for deflection boundary condition method
b.bc_deflection.extend([(4, 3), (5, 0)])
d_bcs = b.bc_deflection
assert d_bcs == [(0, 2), (4, 3), (5, 0)]
# Test for updated boundary conditions
bcs_new = b.boundary_conditions
assert bcs_new == {
'deflection': [(0, 2), (4, 3), (5, 0)],
'slope': [(0, 1), (4, 3), (5, 0)]}
b1 = Beam(30, E, I)
b1.apply_load(-8, 0, -1)
b1.apply_load(R1, 10, -1)
b1.apply_load(R2, 30, -1)
b1.apply_load(120, 30, -2)
b1.bc_deflection = [(10, 0), (30, 0)]
b1.solve_for_reaction_loads(R1, R2)
# Test for finding reaction forces
p = b1.reaction_loads
q = {R1: 6, R2: 2}
assert p == q
# Test for load distribution function.
p = b1.load
q = -8*SingularityFunction(x, 0, -1) + 6*SingularityFunction(x, 10, -1) + 120*SingularityFunction(x, 30, -2) + 2*SingularityFunction(x, 30, -1)
assert p == q
# Test for shear force distribution function
p = b1.shear_force()
q = -8*SingularityFunction(x, 0, 0) + 6*SingularityFunction(x, 10, 0) + 120*SingularityFunction(x, 30, -1) + 2*SingularityFunction(x, 30, 0)
assert p == q
# Test for bending moment distribution function
p = b1.bending_moment()
q = -8*SingularityFunction(x, 0, 1) + 6*SingularityFunction(x, 10, 1) + 120*SingularityFunction(x, 30, 0) + 2*SingularityFunction(x, 30, 1)
assert p == q
# Test for slope distribution function
p = b1.slope()
q = -4*SingularityFunction(x, 0, 2) + 3*SingularityFunction(x, 10, 2) + 120*SingularityFunction(x, 30, 1) + SingularityFunction(x, 30, 2) + 4000/3
assert p == q/(E*I)
# Test for deflection distribution function
p = b1.deflection()
q = 4000*x/3 - 4*SingularityFunction(x, 0, 3)/3 + SingularityFunction(x, 10, 3) + 60*SingularityFunction(x, 30, 2) + SingularityFunction(x, 30, 3)/3 - 12000
assert p == q/(E*I)
# Test using symbols
l = Symbol('l')
w0 = Symbol('w0')
w2 = Symbol('w2')
a1 = Symbol('a1')
c = Symbol('c')
c1 = Symbol('c1')
d = Symbol('d')
e = Symbol('e')
f = Symbol('f')
b2 = Beam(l, E, I)
b2.apply_load(w0, a1, 1)
b2.apply_load(w2, c1, -1)
b2.bc_deflection = [(c, d)]
b2.bc_slope = [(e, f)]
# Test for load distribution function.
p = b2.load
q = w0*SingularityFunction(x, a1, 1) + w2*SingularityFunction(x, c1, -1)
assert p == q
# Test for shear force distribution function
p = b2.shear_force()
q = w0*SingularityFunction(x, a1, 2)/2 + w2*SingularityFunction(x, c1, 0)
assert p == q
# Test for bending moment distribution function
p = b2.bending_moment()
q = w0*SingularityFunction(x, a1, 3)/6 + w2*SingularityFunction(x, c1, 1)
assert p == q
# Test for slope distribution function
p = b2.slope()
q = (w0*SingularityFunction(x, a1, 4)/24 + w2*SingularityFunction(x, c1, 2)/2)/(E*I) + (E*I*f - w0*SingularityFunction(e, a1, 4)/24 - w2*SingularityFunction(e, c1, 2)/2)/(E*I)
assert p == q
# Test for deflection distribution function
p = b2.deflection()
q = x*(E*I*f - w0*SingularityFunction(e, a1, 4)/24 - w2*SingularityFunction(e, c1, 2)/2)/(E*I) + (w0*SingularityFunction(x, a1, 5)/120 + w2*SingularityFunction(x, c1, 3)/6)/(E*I) + (E*I*(-c*f + d) + c*w0*SingularityFunction(e, a1, 4)/24 + c*w2*SingularityFunction(e, c1, 2)/2 - w0*SingularityFunction(c, a1, 5)/120 - w2*SingularityFunction(c, c1, 3)/6)/(E*I)
assert p == q
b3 = Beam(9, E, I)
b3.apply_load(value=-2, start=2, order=2, end=3)
b3.bc_slope.append((0, 2))
C3 = symbols('C3')
C4 = symbols('C4')
p = b3.load
q = -2*SingularityFunction(x, 2, 2) + 2*SingularityFunction(x, 3, 0) + 4*SingularityFunction(x, 3, 1) + 2*SingularityFunction(x, 3, 2)
assert p == q
p = b3.slope()
q = 2 + (-SingularityFunction(x, 2, 5)/30 + SingularityFunction(x, 3, 3)/3 + SingularityFunction(x, 3, 4)/6 + SingularityFunction(x, 3, 5)/30)/(E*I)
assert p == q
p = b3.deflection()
q = 2*x + (-SingularityFunction(x, 2, 6)/180 + SingularityFunction(x, 3, 4)/12 + SingularityFunction(x, 3, 5)/30 + SingularityFunction(x, 3, 6)/180)/(E*I)
assert p == q + C4
b4 = Beam(4, E, I)
b4.apply_load(-3, 0, 0, end=3)
p = b4.load
q = -3*SingularityFunction(x, 0, 0) + 3*SingularityFunction(x, 3, 0)
assert p == q
p = b4.slope()
q = -3*SingularityFunction(x, 0, 3)/6 + 3*SingularityFunction(x, 3, 3)/6
assert p == q/(E*I) + C3
p = b4.deflection()
q = -3*SingularityFunction(x, 0, 4)/24 + 3*SingularityFunction(x, 3, 4)/24
assert p == q/(E*I) + C3*x + C4
# can't use end with point loads
raises(ValueError, lambda: b4.apply_load(-3, 0, -1, end=3))
with raises(TypeError):
b4.variable = 1
def test_Beam():
E = Symbol("E")
E_1 = Symbol("E_1")
I = Symbol("I")
I_1 = Symbol("I_1")
b = Beam(1, E, I)
assert b.length == 1
assert b.elastic_modulus == E
assert b.second_moment == I
assert b.variable == x
# Test the length setter
b.length = 4
assert b.length == 4
# Test the E setter
b.elastic_modulus = E_1
assert b.elastic_modulus == E_1
# Test the I setter
b.second_moment = I_1
assert b.second_moment is I_1
# Test the variable setter
b.variable = y
assert b.variable is y
# Test for all boundary conditions.
b.bc_deflection = [(0, 2)]
b.bc_slope = [(0, 1)]
assert b.boundary_conditions == {"deflection": [(0, 2)], "slope": [(0, 1)]}
# Test for slope boundary condition method
b.bc_slope.extend([(4, 3), (5, 0)])
s_bcs = b.bc_slope
assert s_bcs == [(0, 1), (4, 3), (5, 0)]
# Test for deflection boundary condition method
b.bc_deflection.extend([(4, 3), (5, 0)])
d_bcs = b.bc_deflection
assert d_bcs == [(0, 2), (4, 3), (5, 0)]
# Test for updated boundary conditions
bcs_new = b.boundary_conditions
assert bcs_new == {"deflection": [(0, 2), (4, 3), (5, 0)], "slope": [(0, 1), (4, 3), (5, 0)]}
b1 = Beam(30, E, I)
b1.apply_load(-8, 0, -1)
b1.apply_load(R1, 10, -1)
b1.apply_load(R2, 30, -1)
b1.apply_load(120, 30, -2)
b1.bc_deflection = [(10, 0), (30, 0)]
b1.solve_for_reaction_loads(R1, R2)
# Test for finding reaction forces
p = b1.reaction_loads
q = {R1: 6, R2: 2}
assert p == q
# Test for load distribution function.
p = b1.load
q = (
-8 * SingularityFunction(x, 0, -1)
+ 6 * SingularityFunction(x, 10, -1)
+ 120 * SingularityFunction(x, 30, -2)
+ 2 * SingularityFunction(x, 30, -1)
)
assert p == q
# Test for shear force distribution function
p = b1.shear_force()
q = (
-8 * SingularityFunction(x, 0, 0)
+ 6 * SingularityFunction(x, 10, 0)
+ 120 * SingularityFunction(x, 30, -1)
+ 2 * SingularityFunction(x, 30, 0)
)
assert p == q
# Test for bending moment distribution function
p = b1.bending_moment()
q = (
-8 * SingularityFunction(x, 0, 1)
+ 6 * SingularityFunction(x, 10, 1)
+ 120 * SingularityFunction(x, 30, 0)
+ 2 * SingularityFunction(x, 30, 1)
)
assert p == q
# Test for slope distribution function
p = b1.slope()
q = (
-4 * SingularityFunction(x, 0, 2)
+ 3 * SingularityFunction(x, 10, 2)
+ 120 * SingularityFunction(x, 30, 1)
+ SingularityFunction(x, 30, 2)
+ 4000 / 3
)
assert p == q / (E * I)
# Test for deflection distribution function
p = b1.deflection()
q = (
4000 * x / 3
- 4 * SingularityFunction(x, 0, 3) / 3
+ SingularityFunction(x, 10, 3)
+ 60 * SingularityFunction(x, 30, 2)
+ SingularityFunction(x, 30, 3) / 3
- 12000
)
assert p == q / (E * I)
# Test using symbols
l = Symbol("l")
w0 = Symbol("w0")
w2 = Symbol("w2")
a1 = Symbol("a1")
c = Symbol("c")
c1 = Symbol("c1")
d = Symbol("d")
e = Symbol("e")
f = Symbol("f")
b2 = Beam(l, E, I)
b2.apply_load(w0, a1, 1)
b2.apply_load(w2, c1, -1)
b2.bc_deflection = [(c, d)]
b2.bc_slope = [(e, f)]
# Test for load distribution function.
p = b2.load
q = w0 * SingularityFunction(x, a1, 1) + w2 * SingularityFunction(x, c1, -1)
assert p == q
# Test for shear force distribution function
p = b2.shear_force()
q = w0 * SingularityFunction(x, a1, 2) / 2 + w2 * SingularityFunction(x, c1, 0)
assert p == q
# Test for bending moment distribution function
p = b2.bending_moment()
q = w0 * SingularityFunction(x, a1, 3) / 6 + w2 * SingularityFunction(x, c1, 1)
assert p == q
# Test for slope distribution function
p = b2.slope()
q = (
f
- w0 * SingularityFunction(e, a1, 4) / 24
+ w0 * SingularityFunction(x, a1, 4) / 24
- w2 * SingularityFunction(e, c1, 2) / 2
+ w2 * SingularityFunction(x, c1, 2) / 2
)
assert p == q / (E * I)
# Test for deflection distribution function
p = b2.deflection()
q = (
-c * f
+ c * w0 * SingularityFunction(e, a1, 4) / 24
+ c * w2 * SingularityFunction(e, c1, 2) / 2
+ d
+ f * x
- w0 * x * SingularityFunction(e, a1, 4) / 24
- w0 * SingularityFunction(c, a1, 5) / 120
+ w0 * SingularityFunction(x, a1, 5) / 120
- w2 * x * SingularityFunction(e, c1, 2) / 2
- w2 * SingularityFunction(c, c1, 3) / 6
+ w2 * SingularityFunction(x, c1, 3) / 6
)
assert p == q / (E * I)
b3 = Beam(9, E, I)
b3.apply_load(value=-2, start=2, order=2, end=3)
b3.bc_slope.append((0, 2))
p = b3.load
q = -2 * SingularityFunction(x, 2, 2) + 2 * SingularityFunction(x, 3, 0) + 2 * SingularityFunction(x, 3, 2)
assert p == q
p = b3.slope()
q = -SingularityFunction(x, 2, 5) / 30 + SingularityFunction(x, 3, 3) / 3 + SingularityFunction(x, 3, 5) / 30 + 2
assert p == q / (E * I)
p = b3.deflection()
q = (
2 * x
- SingularityFunction(x, 2, 6) / 180
+ SingularityFunction(x, 3, 4) / 12
+ SingularityFunction(x, 3, 6) / 180
)
assert p == q / (E * I)
b4 = Beam(4, E, I)
b4.apply_load(-3, 0, 0, end=3)
p = b4.load
q = -3 * SingularityFunction(x, 0, 0) + 3 * SingularityFunction(x, 3, 0)
assert p == q
p = b4.slope()
q = -3 * SingularityFunction(x, 0, 3) / 6 + 3 * SingularityFunction(x, 3, 3) / 6
assert p == q / (E * I)
p = b4.deflection()
q = -3 * SingularityFunction(x, 0, 4) / 24 + 3 * SingularityFunction(x, 3, 4) / 24
assert p == q / (E * I)
raises(ValueError, lambda: b4.apply_load(-3, 0, -1, end=3))
with raises(TypeError):
b4.variable = 1
def test_Beam():
E = Symbol('E')
E_1 = Symbol('E_1')
I = Symbol('I')
I_1 = Symbol('I_1')
b = Beam(1, E, I)
assert b.length == 1
assert b.elastic_modulus == E
assert b.second_moment == I
assert b.variable == x
# Test the length setter
b.length = 4
assert b.length == 4
# Test the E setter
b.elastic_modulus = E_1
assert b.elastic_modulus == E_1
# Test the I setter
b.second_moment = I_1
assert b.second_moment is I_1
# Test the variable setter
b.variable = y
assert b.variable is y
# Test for all boundary conditions.
b.bc_deflection = [(0, 2)]
b.bc_slope = [(0, 1)]
assert b.boundary_conditions == {'deflection': [(0, 2)], 'slope': [(0, 1)]}
# Test for slope boundary condition method
b.bc_slope.extend([(4, 3), (5, 0)])
s_bcs = b.bc_slope
assert s_bcs == [(0, 1), (4, 3), (5, 0)]
# Test for deflection boundary condition method
b.bc_deflection.extend([(4, 3), (5, 0)])
d_bcs = b.bc_deflection
assert d_bcs == [(0, 2), (4, 3), (5, 0)]
# Test for updated boundary conditions
bcs_new = b.boundary_conditions
assert bcs_new == {
'deflection': [(0, 2), (4, 3), (5, 0)],
'slope': [(0, 1), (4, 3), (5, 0)]}
b1 = Beam(30, E, I)
b1.apply_load(-8, 0, -1)
b1.apply_load(R1, 10, -1)
b1.apply_load(R2, 30, -1)
b1.apply_load(120, 30, -2)
b1.bc_deflection = [(10, 0), (30, 0)]
b1.solve_for_reaction_loads(R1, R2)
# Test for finding reaction forces
p = b1.reaction_loads
q = {R1: 6, R2: 2}
assert p == q
# Test for load distribution function.
p = b1.load
q = -8*SingularityFunction(x, 0, -1) + 6*SingularityFunction(x, 10, -1) + 120*SingularityFunction(x, 30, -2) + 2*SingularityFunction(x, 30, -1)
assert p == q
# Test for shear force distribution function
p = b1.shear_force()
q = -8*SingularityFunction(x, 0, 0) + 6*SingularityFunction(x, 10, 0) + 120*SingularityFunction(x, 30, -1) + 2*SingularityFunction(x, 30, 0)
assert p == q
# Test for bending moment distribution function
p = b1.bending_moment()
q = -8*SingularityFunction(x, 0, 1) + 6*SingularityFunction(x, 10, 1) + 120*SingularityFunction(x, 30, 0) + 2*SingularityFunction(x, 30, 1)
assert p == q
# Test for slope distribution function
p = b1.slope()
q = -4*SingularityFunction(x, 0, 2) + 3*SingularityFunction(x, 10, 2) + 120*SingularityFunction(x, 30, 1) + SingularityFunction(x, 30, 2) + S(4000)/3
assert p == q/(E*I)
# Test for deflection distribution function
p = b1.deflection()
q = 4000*x/3 - 4*SingularityFunction(x, 0, 3)/3 + SingularityFunction(x, 10, 3) + 60*SingularityFunction(x, 30, 2) + SingularityFunction(x, 30, 3)/3 - 12000
assert p == q/(E*I)
# Test using symbols
l = Symbol('l')
w0 = Symbol('w0')
w2 = Symbol('w2')
a1 = Symbol('a1')
c = Symbol('c')
c1 = Symbol('c1')
d = Symbol('d')
e = Symbol('e')
f = Symbol('f')
b2 = Beam(l, E, I)
b2.apply_load(w0, a1, 1)
b2.apply_load(w2, c1, -1)
b2.bc_deflection = [(c, d)]
b2.bc_slope = [(e, f)]
# Test for load distribution function.
p = b2.load
q = w0*SingularityFunction(x, a1, 1) + w2*SingularityFunction(x, c1, -1)
assert p == q
# Test for shear force distribution function
p = b2.shear_force()
q = w0*SingularityFunction(x, a1, 2)/2 + w2*SingularityFunction(x, c1, 0)
assert p == q
# Test for bending moment distribution function
p = b2.bending_moment()
q = w0*SingularityFunction(x, a1, 3)/6 + w2*SingularityFunction(x, c1, 1)
assert p == q
# Test for slope distribution function
p = b2.slope()
q = (w0*SingularityFunction(x, a1, 4)/24 + w2*SingularityFunction(x, c1, 2)/2)/(E*I) + (E*I*f - w0*SingularityFunction(e, a1, 4)/24 - w2*SingularityFunction(e, c1, 2)/2)/(E*I)
assert p == q
# Test for deflection distribution function
p = b2.deflection()
q = x*(E*I*f - w0*SingularityFunction(e, a1, 4)/24 - w2*SingularityFunction(e, c1, 2)/2)/(E*I) + (w0*SingularityFunction(x, a1, 5)/120 + w2*SingularityFunction(x, c1, 3)/6)/(E*I) + (E*I*(-c*f + d) + c*w0*SingularityFunction(e, a1, 4)/24 + c*w2*SingularityFunction(e, c1, 2)/2 - w0*SingularityFunction(c, a1, 5)/120 - w2*SingularityFunction(c, c1, 3)/6)/(E*I)
assert p == q
b3 = Beam(9, E, I)
b3.apply_load(value=-2, start=2, order=2, end=3)
b3.bc_slope.append((0, 2))
C3 = symbols('C3')
C4 = symbols('C4')
p = b3.load
q = -2*SingularityFunction(x, 2, 2) + 2*SingularityFunction(x, 3, 0) + 4*SingularityFunction(x, 3, 1) + 2*SingularityFunction(x, 3, 2)
assert p == q
p = b3.slope()
q = 2 + (-SingularityFunction(x, 2, 5)/30 + SingularityFunction(x, 3, 3)/3 + SingularityFunction(x, 3, 4)/6 + SingularityFunction(x, 3, 5)/30)/(E*I)
assert p == q
p = b3.deflection()
q = 2*x + (-SingularityFunction(x, 2, 6)/180 + SingularityFunction(x, 3, 4)/12 + SingularityFunction(x, 3, 5)/30 + SingularityFunction(x, 3, 6)/180)/(E*I)
assert p == q + C4
b4 = Beam(4, E, I)
b4.apply_load(-3, 0, 0, end=3)
p = b4.load
q = -3*SingularityFunction(x, 0, 0) + 3*SingularityFunction(x, 3, 0)
assert p == q
p = b4.slope()
q = -3*SingularityFunction(x, 0, 3)/6 + 3*SingularityFunction(x, 3, 3)/6
assert p == q/(E*I) + C3
p = b4.deflection()
q = -3*SingularityFunction(x, 0, 4)/24 + 3*SingularityFunction(x, 3, 4)/24
assert p == q/(E*I) + C3*x + C4
# can't use end with point loads
raises(ValueError, lambda: b4.apply_load(-3, 0, -1, end=3))
with raises(TypeError):
b4.variable = 1