def angledComponents(self,
angle: float) -> Tuple[Distributed, Distributed]:
basePolynomial: Polynomial = Polynomial(
self.distribution.coefficients.copy())
if self.distribution.degree < 1:
basePolynomial.coefficients.append(pcot(angle))
basePolynomial.degree = 1
else:
basePolynomial.coefficients[1] += pcot(angle)
return (Distributed(self.length / psin(angle),
pcos(angle) * basePolynomial),
Distributed(self.length / psin(angle),
psin(angle) * basePolynomial))
def __init__(self, master, name: str, beams, polynomials, polyID): self.master = master self.master.geometry(f"1360x768") self.master.title(name) self.canvas = Canvas(self.master, width = 1360, height = 768) self.canvas.pack(fill = BOTH, expand = True, side = TOP) for (i, beam) in enumerate(beams): if polynomials[i] != None: start = Point(beam[1].x, beam[1].y) end = Point(beam[3].x, beam[3].y) self.canvas.create_line((start, end), smooth = True, width = 5, fill="#404040") stressFunctions = polynomials[i] length = beam[0].length angle = beam[2] tipX = start.x tipY = start.y scale = -0.03 if polyID == 2 else 0.3 for j in range(0, 100): fun = stressFunctions(polyID, j * length / 100) self.canvas.create_line(tipX, tipY, tipX + 20 * fun * scale * pcos(90 + angle), tipY - 20 * fun * scale * psin(90 + angle)) tipX += 1 / 10 * length * pcos(angle) tipY -= 1 / 10 * length * psin(angle)
def __init__(self, name: str, angle: float = 0):
# this member is the reaction vector from the support
# its values are used for solving the system
self.reaction: Vector3 = Vector3(0, 0, 0)
if SupportType[name].value[0] > 1:
self.reaction.x = 1
self.reaction.y = 1
else:
self.reaction.x = pcos(angle)
self.reaction.y = psin(angle)
if SupportType[name].value[1] == 1:
self.reaction.z = 1
def updateForce(self):
force_angle = float(self.angleContent.get()) - self.beamAngle if len(self.angleContent.get()) != 0 else 0
length = float(self.lengthContent.get()) if len(self.lengthContent.get()) != 0 else 1
pos = float(self.positionContent.get()) if len(self.positionContent.get()) != 0 else 0
scale = 1 if 0 <= length < 10 else 0.1 if 10 <= length < 100 else 0.01 if 100 <= length < 1000 else 0.001
tipX : float = self.master_force.x + (pos * pcos(self.beamAngle) * 10)
tipY : float = self.master_force.y - (pos * psin(self.beamAngle) * 10)
self.master_window.drawing_area.delete(self.master_window.forcePreview)
self.master_window.forcePreview = self.master_window.drawing_area.create_line(tipX - 20 * length * scale * pcos(force_angle), tipY - 20 * length * scale * psin(force_angle), tipX, tipY, arrow = LAST, width = 4.0, activefill = "blue", smooth = True)
self.master_window.drawing_area.delete(self.master_window.labelPreview)
self.master_window.labelPreview = self.master_window.drawing_area.create_text(tipX + 10 - 40 * pcos(force_angle) if force_angle <= 180 else tipX, tipY - 20 - 40 * psin(force_angle) if force_angle < 180 else tipY - 20, font = "Helvetica", text = f"{length} kN", anchor = W)
def drawBeam(self, start : Point, end : Point, beamAngle : float, size : float, event = None) -> Tuple[object, object]:
if self.beamPreview != None:
event.widget.delete(self.beamPreview)
if self.arcPreview != None:
event.widget.delete(self.arcPreview)
if self.labelPreview != None:
event.widget.delete(self.labelPreview)
if self.anglePreview != None:
event.widget.delete(self.anglePreview)
beam = event.widget.create_line((start, end), smooth = True, width = 5, fill="#404040")
textAngle = beamAngle if 0 <= beamAngle < 90 else beamAngle - 180 if beamAngle > 90 else 360 + beamAngle if - 90 < beamAngle < 0 else beamAngle + 180
length = event.widget.create_text((start.x + end.x) / 2 - 20 * psin(beamAngle), (start.y + end.y) / 2 - 20 * pcos(beamAngle), font = "Helvetica", text = "{0:1.1f} m".format(size), angle = textAngle)
return (beam, length)
def drawBeamPreview(self, start : Point, end : Point, beamAngle : float, size: float, event = None):
if self.beamPreview != None:
event.widget.delete(self.beamPreview)
if self.arcPreview != None:
event.widget.delete(self.arcPreview)
if self.labelPreview != None:
event.widget.delete(self.labelPreview)
if self.anglePreview != None:
event.widget.delete(self.anglePreview)
self.beamPreview = event.widget.create_line((start, end), smooth = True, dash = (10, 10))
self.arcPreview = event.widget.create_arc(start.x - 20, start.y - 20, start.x + 20, start.y + 20, start = 0, extent = beamAngle)
self.anglePreview = event.widget.create_text(start.x + 40, start.y + (20 * sign(beamAngle)) if beamAngle != 0 else start.y + 20, font = "Helvetica", text = "{0:.1f}º".format(beamAngle))
textAngle = beamAngle if 0 <= beamAngle < 90 else beamAngle - 180 if beamAngle > 90 else 360 + beamAngle if - 90 < beamAngle < 0 else beamAngle + 180
self.labelPreview = event.widget.create_text((start.x + end.x) / 2 - 20 * psin(beamAngle), (start.y + end.y) / 2 - 20 * pcos(beamAngle), font = "Helvetica", text = "{0:1.1f} m".format(size), angle = textAngle)
def insertForce(self):
force_angle = float(self.angleContent.get()) - self.beamAngle if len(self.angleContent.get()) != 0 else 0
length = float(self.lengthContent.get()) if len(self.lengthContent.get()) != 0 else 1
pos = float(self.positionContent.get()) if len(self.positionContent.get()) != 0 else 0
scale = 1 if 0 <= length < 10 else 0.1 if 10 <= length < 100 else 0.01 if 100 <= length < 1000 else 0.001
tipX : float = self.master_force.x + (pos * pcos(self.beamAngle) * 10)
tipY : float = self.master_force.y - (pos * psin(self.beamAngle) * 10)
self.master_window.system.beams[self.beamID - 1][0].concentratedList.append((Concentrated(length), pos, force_angle + self.beamAngle))
self.master_window.drawing_area.delete(self.master_window.forcePreview)
self.master_window.drawing_area.delete(self.master_window.labelPreview)
force = self.master_window.drawing_area.create_line(tipX - 20 * length * scale * pcos(force_angle), tipY - 20 * length * scale * psin(force_angle), tipX, tipY, arrow = LAST, width = 4.0, activefill = "blue", smooth = True)
label = self.master_window.drawing_area.create_text(tipX + 10 - 40 * pcos(force_angle) if force_angle <= 180 else tipX, tipY - 20 - 40 * psin(force_angle) if force_angle < 180 else tipY - 20, font = "Helvetica", text = f"{length} kN", anchor = W)
self.master_window.actions.append(Action(related = (force, label, self.beamID), type = ActionType.ADD_CONCENTRATED))
self.master_window.inserting = False
self.master.destroy()
def insertDistributed(self):
force_angle = float(self.angleContent.get()) - self.beamAngle if len(self.angleContent.get()) != 0 else 0
radioOption = self.radioContent.get()
start_pos = float(self.startPosContent.get()) if len(self.startPosContent.get()) != 0 else 0
end_pos = float(self.endPosContent.get()) if len(self.endPosContent.get()) != 0 else 5
if radioOption == 0:
uniformLoad = int(self.distributedParameters[0].get()) if len(self.distributedParameters[0].get()) != 0 else 1
scale = 1 if 0 <= uniformLoad <= 10 else 0.1 if 10 < uniformLoad < 100 else 0.01 if 100 <= uniformLoad < 1000 else 0.001
if len(self.master_window.forcePreview) != 0:
for force in self.master_window.forcePreview:
self.master_window.drawing_area.delete(force)
self.master_window.forcePreview.clear()
self.master_window.drawing_area.delete(self.master_window.labelPreview)
tipX : float = self.master_force.x + (start_pos * pcos(self.beamAngle) * 10)
tipY : float = self.master_force.y - (start_pos * psin(self.beamAngle) * 10)
tipX0 : float = tipX
tipY0 : float = tipY
forces = list()
for i in range(11):
forces.append(self.master_window.drawing_area.create_line(tipX - 20 * uniformLoad * scale * pcos(force_angle), tipY - 20 * uniformLoad * scale * psin(force_angle), tipX, tipY, arrow = LAST, width = 4.0, activefill = "blue", smooth = True))
tipX = tipX + (end_pos - start_pos) * pcos(self.beamAngle)
tipY = tipY - (end_pos - start_pos) * psin(self.beamAngle)
label = self.master_window.drawing_area.create_text((tipX + tipX0) / 2 - 40 * pcos(force_angle) if force_angle <= 180 else (tipX + tipX0) / 2, (tipY + tipY0) // 2 - 30 * (uniformLoad), font = "Helvetica", text = f"{uniformLoad} kN/m")
self.master_window.system.beams[self.beamID - 1][0].distributedList.append((Distributed(end_pos - start_pos, Polynomial([uniformLoad])), start_pos, force_angle + self.beamAngle))
self.master_window.actions.append(Action(related = (forces, label, self.beamID, False, 0), type = ActionType.ADD_DISTRIBUTED))
if radioOption == 1:
startLoad = int(self.distributedParameters[0].get()) if len(self.distributedParameters[0].get()) != 0 else 0
endLoad = int(self.distributedParameters[1].get()) if len(self.distributedParameters[1].get()) != 0 else 1
scale = 1
if len(self.master_window.forcePreview) != 0:
for force in self.master_window.forcePreview:
self.master_window.drawing_area.delete(force)
self.master_window.forcePreview.clear()
self.master_window.drawing_area.delete(self.master_window.labelPreview)
if self.master_window.startLabelPreview != None and self.master_window.startLabelPreview != 0:
self.master_window.drawing_area.delete(self.master_window.startLabelPreview)
tipX : float = self.master_force.x + (start_pos * pcos(self.beamAngle) * 10)
tipY : float = self.master_force.y - (start_pos * psin(self.beamAngle) * 10)
load : int = startLoad
tipX0 : float = tipX
tipY0 : float = tipY
forces = list()
for i in range(11):
forces.append(self.master_window.drawing_area.create_line(tipX - 20 * load * scale * pcos(force_angle), tipY - 20 * load * scale * psin(force_angle), tipX, tipY, arrow = LAST, width = 2.0, activefill = "blue", smooth = True))
tipX = tipX + (end_pos - start_pos) * pcos(self.beamAngle)
tipY = tipY - (end_pos - start_pos) * psin(self.beamAngle)
load = load + (endLoad - startLoad) / 10
startLabel = 0
if startLoad != 0:
startLabel = self.master_window.drawing_area.create_text(tipX0, tipY0 - 5 - 25 * startLoad, font = "Helvetica", text = f"{startLoad} kN/m")
label = self.master_window.drawing_area.create_text(tipX, tipY - 5 - 25 * endLoad, font = "Helvetica", text = f"{endLoad} kN/m")
self.master_window.system.beams[self.beamID - 1][0].distributedList.append((Distributed(end_pos - start_pos, Polynomial([startLoad, (endLoad - startLoad) / (end_pos - start_pos)])), start_pos, force_angle + self.beamAngle))
self.master_window.actions.append(Action(related = (forces, label, self.beamID, startLoad != 0, startLabel), type = ActionType.ADD_DISTRIBUTED))
for force in self.master_window.forcePreview:
self.master_window.drawing_area.delete(force)
self.master_window.forcePreview.clear()
self.master_window.drawing_area.delete(self.master_window.labelPreview)
self.master_window.inserting = False
self.master.destroy()
def updateDistributed(self):
force_angle = float(self.angleContent.get()) - self.beamAngle if len(self.angleContent.get()) != 0 else 0
radioOption = self.radioContent.get()
start_pos = float(self.startPosContent.get()) if len(self.startPosContent.get()) != 0 else 0
end_pos = float(self.endPosContent.get()) if len(self.endPosContent.get()) != 0 else 5
if self.lastRadio != radioOption:
self.distributedParameters.clear()
for entry in self.distributedEntries:
entry.grid_remove()
for label in self.distributedLabels:
label.grid_remove()
self.distributedEntries.clear()
self.distributedLabels.clear()
if radioOption == 0:
uniformLoad = StringVar()
uniformLoad.set("1")
uniformLoad.trace("w", lambda a, b, c: self.updateDistributed())
self.distributedParameters.append(uniformLoad)
loadEntry = Entry(self.frame, textvariable = uniformLoad, width = 4)
loadEntry.grid(row = 4, column = 0)
entryLabel = Label(self.frame, font = "Helvetica", text = "kN/m")
entryLabel.grid(row = 4, column = 1)
self.distributedEntries.append(loadEntry)
self.distributedLabels.append(entryLabel)
elif radioOption == 1:
startLoad = StringVar()
startLoad.set("0")
startLoad.trace("w", lambda a, b, c: self.updateDistributed())
endLoad = StringVar()
endLoad.set("1")
endLoad.trace("w", lambda a, b, c: self.updateDistributed())
self.distributedParameters.append(startLoad)
self.distributedParameters.append(endLoad)
startLabel = Label(self.frame, font = "Helvetica", text = "De")
startLabel.grid(row = 4, column = 0)
startEntry = Entry(self.frame, textvariable = startLoad, width = 4)
startEntry.grid(row = 4, column = 1)
endLabel = Label(self.frame, font = "Helvetica", text = "até")
endLabel.grid(row = 4, column = 2)
endEntry = Entry(self.frame, textvariable = endLoad, width = 4)
endEntry.grid(row = 4, column = 3, padx = 0)
self.distributedEntries.append(startEntry)
self.distributedEntries.append(endEntry)
self.distributedLabels.append(startLabel)
self.distributedLabels.append(endLabel)
if radioOption == 0:
uniformLoad = int(self.distributedParameters[0].get()) if len(self.distributedParameters[0].get()) != 0 else 1
scale = 1 if 0 <= uniformLoad <= 10 else 0.1 if 10 < uniformLoad < 100 else 0.01 if 100 <= uniformLoad < 1000 else 0.001
if len(self.master_window.forcePreview) != 0:
for force in self.master_window.forcePreview:
self.master_window.drawing_area.delete(force)
self.master_window.forcePreview.clear()
self.master_window.drawing_area.delete(self.master_window.labelPreview)
tipX : float = self.master_force.x + (start_pos * pcos(self.beamAngle) * 10)
tipY : float = self.master_force.y - (start_pos * psin(self.beamAngle) * 10)
tipX0 : float = tipX
tipY0 : float = tipY
for i in range(11):
self.master_window.forcePreview.append(self.master_window.drawing_area.create_line(tipX - 20 * uniformLoad * scale * pcos(force_angle), tipY - 20 * uniformLoad * scale * psin(force_angle), tipX, tipY, arrow = LAST, width = 4.0, activefill = "blue", smooth = True))
tipX = tipX + (end_pos - start_pos) * pcos(self.beamAngle)
tipY = tipY - (end_pos - start_pos) * psin(self.beamAngle)
self.master_window.labelPreview = self.master_window.drawing_area.create_text((tipX + tipX0) / 2 - 40 * pcos(force_angle) if force_angle <= 180 else (tipX + tipX0) / 2, (tipY + tipY0) // 2 - 30 * (uniformLoad), font = "Helvetica", text = f"{uniformLoad} kN/m")
self.lastRadio = 0
if radioOption == 1:
startLoad = int(self.distributedParameters[0].get()) if len(self.distributedParameters[0].get()) != 0 else 0
endLoad = int(self.distributedParameters[1].get()) if len(self.distributedParameters[1].get()) != 0 else 1
scale = 1
if self.master_window.startLabelPreview != None and self.master_window.startLabelPreview != 0:
self.master_window.drawing_area.delete(self.master_window.startLabelPreview)
if len(self.master_window.forcePreview) != 0:
for force in self.master_window.forcePreview:
self.master_window.drawing_area.delete(force)
self.master_window.forcePreview.clear()
self.master_window.drawing_area.delete(self.master_window.labelPreview)
tipX : float = self.master_force.x + (start_pos * pcos(self.beamAngle) * 10)
tipY : float = self.master_force.y - (start_pos * psin(self.beamAngle) * 10)
load : int = startLoad
tipX0 : float = tipX
tipY0 : float = tipY
for i in range(11):
self.master_window.forcePreview.append(self.master_window.drawing_area.create_line(tipX - 20 * load * scale * pcos(force_angle), tipY - 20 * load * scale * psin(force_angle), tipX, tipY, arrow = LAST, width = 2.0, activefill = "blue", smooth = True))
tipX = tipX + (end_pos - start_pos) * pcos(self.beamAngle)
tipY = tipY - (end_pos - start_pos) * psin(self.beamAngle)
load = load + (endLoad - startLoad) / 10
if startLoad != 0:
self.master_window.startLabelPreview = self.master_window.drawing_area.create_text(tipX0, tipY0 - 5 - 25 * startLoad, font = "Helvetica", text = f"{startLoad} kN/m")
self.master_window.labelPreview = self.master_window.drawing_area.create_text(tipX, tipY - 5 - 25 * endLoad, font = "Helvetica", text = f"{endLoad} kN/m")
self.lastRadio = 1
def pointPos(self, startPos: Vector3, point: float, angle: float) -> Vector3:
if point > self.length or point < 0:
raise Exception('Point is outside the beam!')
return startPos + Vector3(point*pcos(angle), point*psin(angle), 0)
def forceVector(self, angle: float) -> Vector3:
return Vector3(self.magnitude * pcos(angle),
-self.magnitude * psin(angle), 0)