def test_deflection_for_fixed_cantilevered_beam_with_load_at_any_point():
P = -1000 # load in lbs down
a = 7 # position of load in inches
L = 25 # length of beam in inches
E = 29e6 # Young's modulus in psi
Ixx = 345 # area moment of inertia in in**4
b = L - a
# function to calculate deflection anywhere along the length of the beam
d1 = lambda x: P * b**2 / (6 * E * Ixx) * (3 * L - 3 * x - b) # x < a
d2 = lambda x: P * (L - x)**2 / (6 * E * Ixx) * (3 * b - L + x) # x > a
d3 = lambda x: P * b**3 / (3 * E * Ixx) # x == a
beam = Beam(L, [PointLoad(P, a)], [FixedReaction(L)], E, Ixx)
for x in [0, 7, 12.5, 25]:
# check the deflection of the beam at both end points, and the center
if x < a:
exact = d1(x)
elif x > a:
exact = d2(x)
else:
exact = d3(x)
assert pytest.approx(beam.deflection(x), rel=1e-12) == exact, \
f"Calculated deflection does not match expected deflection at {x}"
def test_invalid_deflection_location():
beam = Beam(25, [PointLoad(-100, 25)], [FixedReaction(0)], 29e6, 345)
with pytest.raises(ValueError):
beam.deflection(-4) # a value less than 0
with pytest.raises(ValueError):
beam.deflection(beam.length + 5) # a value greater then the length
with pytest.raises(TypeError):
beam.deflection('a string (not a number)')