def draw_beams(self, bridge: BridgeCalculator):
for beam, beam_property in bridge.bridge.beams.items():
self.draw_line(self.scale_point(beam.joint1),
self.scale_point(beam.joint2),
color=beam_property.beam_group.color)
if beam_property.member_force is not None:
label_position = Vector.from_point(
self.scale_point(
beam.joint2)) + BridgeGUI.flip_vector_on_y(
Vector.from_a_to_b(beam.joint2, beam.joint1)
) / 2 * self.scale_factor
self.draw_label(label_position,
beam_property.member_force.rescale(kN))
def get_direction_vector(self) -> Vector:
"""
Note that this function can return different direction vectors depending on the order of joint1 and joint2
"""
return Vector.from_a_to_b(self.joint1, self.joint2)
def calculate_member_forces(self):
# Loop through every joint repeatedly.
# At each joint look for member forces + external forces + joint load
# In each component, verify if there's only one unknown_opposing_joints. Repeat in other component if solved
# Repeat for other joints
passes = 0
calculated_joints = set()
while passes < len(self.bridge.joints) * 2 and len(calculated_joints) < len(self.bridge.joints):
for joint, joint_property in self.bridge.joints.items():
if joint in calculated_joints:
continue
sum_of_forces = Vector(0 * pq.N, 0 * pq.N)
unknown_opposing_joints = []
# Get forces in members
for connected_joint in joint_property.connected_joints:
direction_vector = Vector.from_a_to_b(joint, connected_joint)
member_force = self.bridge.beams[Beam(joint, connected_joint)].member_force
if member_force is None:
unknown_opposing_joints.append(connected_joint)
else:
sum_of_forces += direction_vector.get_unit_vector() * member_force
if joint_property.external_force is not None:
sum_of_forces += joint_property.external_force
if len(unknown_opposing_joints) > 3:
continue
# If all forces are known make sure sum is zero and you're done
elif len(unknown_opposing_joints) == 0:
if sum_of_forces != Vector(0, 0):
print(f"ERROR: Sum of forces at joint, {joint}, is {sum_of_forces} not (0, 0).")
calculated_joints.add(joint)
# If only one force make sure it's opposite to the current sum of forces.
elif len(unknown_opposing_joints) == 1:
unknown_opposing_joint = unknown_opposing_joints[0]
direction_vector = Vector.from_a_to_b(joint, unknown_opposing_joint)
if sum_of_forces == Vector(0, 0):
self.bridge.beams[Beam(unknown_opposing_joint, joint)].member_force = 0 * pq.N
elif sum_of_forces.is_collinear(direction_vector):
self.bridge.beams[Beam(unknown_opposing_joint, joint)].member_force = sum_of_forces.cos_theta(
direction_vector) * sum_of_forces.get_magnitude() * -1
else:
print(
f"Error. Sum of forces ({sum_of_forces})"
f" is not in the same direction as the only unknown beam (dir: {direction_vector})"
f" for joint {joint}.")
calculated_joints.add(joint)
elif len(unknown_opposing_joints) == 2:
unknown_joint_1 = unknown_opposing_joints.pop()
unknown_joint_2 = unknown_opposing_joints.pop()
unknown_force_1 = Vector.from_a_to_b(joint, unknown_joint_1)
unknown_force_2 = Vector.from_a_to_b(joint, unknown_joint_2)
if unknown_force_1.is_collinear(unknown_force_2):
continue
(force_1, force_2) = BridgeCalculator.solve_for_two_unknowns(sum_of_forces, unknown_force_1,
unknown_force_2)
self.bridge.beams[Beam(joint, unknown_joint_1)].member_force = force_1
self.bridge.beams[Beam(joint, unknown_joint_2)].member_force = force_2
calculated_joints.add(joint)
elif len(unknown_opposing_joints) == 3:
unknown_joint_1 = unknown_opposing_joints.pop()
unknown_joint_2 = unknown_opposing_joints.pop()
unknown_joint_3 = unknown_opposing_joints.pop()
unknown_force_1 = Vector.from_a_to_b(joint, unknown_joint_1)
unknown_force_2 = Vector.from_a_to_b(joint, unknown_joint_2)
unknown_force_3 = Vector.from_a_to_b(joint, unknown_joint_3)
if unknown_force_1.is_collinear(unknown_force_2):
(force_1, force_3) = BridgeCalculator.solve_for_two_unknowns(sum_of_forces, unknown_force_1,
unknown_force_3)
self.bridge.beams[Beam(joint, unknown_joint_3)].member_force = force_3
elif unknown_force_2.is_collinear(unknown_force_3):
(force_1, force_2) = BridgeCalculator.solve_for_two_unknowns(sum_of_forces, unknown_force_1,
unknown_force_2)
self.bridge.beams[Beam(joint, unknown_joint_1)].member_force = force_1
elif unknown_force_3.is_collinear(unknown_force_1):
(force_1, force_2) = BridgeCalculator.solve_for_two_unknowns(sum_of_forces, unknown_force_1,
unknown_force_2)
self.bridge.beams[Beam(joint, unknown_joint_2)].member_force = force_2
passes += 1