def test_moment_for_fixed_cantilevered_beam_with_load_at_end():
P = -1000 # load in lbs down
L = 25 # length of beam in inches
E = 29e6 # Young's modulus in psi
Ixx = 345 # area moment of inertia in in**4
# function to calculate moment anywhere along the length of the beam
m = lambda x: P * x
beam = Beam(L, [PointLoad(P, 0)], [FixedReaction(L)], E, Ixx)
for x in [7, 12.5, 25]:
# check the deflection of the beam at both end points, and the center
assert pytest.approx(beam.moment(x), rel=0.01) == m(x), \
f"Calculated moment does not match expected moment at {x}"
with pytest.warns(UserWarning):
beam.moment(0)
def test_cantilevered_beam_load_at_end():
"""fixed beam with concentrated load at free end
case 13
"""
R = -P
M_max = P * L # at fixed end
d_max = P * L**3 / (3 * EI) # at free end
beam = Beam(
length=L,
loads=[PointLoad(magnitude=P, location=0)],
reactions=[FixedReaction(L)],
E=E,
Ixx=Ixx,
)
beam.solve()
validate(beam, loc=0, R=[(R, M_max)], M_loc=0, d_loc=d_max)
assert pytest.approx(beam.moment(L), rel=TOL) == M_max
