Final answer:
To determine the force in member AE of the loaded truss, we analyze the equilibrium of forces at point E. By considering the vertical and horizontal forces from members BE and DE, we can apply the Pythagorean theorem to find the magnitude of the force in member AE.
Step-by-step explanation:
To determine the force in member AE of the loaded truss, we need to consider the equilibrium of forces at point E. We can start by analyzing the forces acting on point E:
- The force in member AE, which we want to find
- The vertical force from member BE, which can be calculated using the equation F_BE = F_CE * (BC / BE).
- The horizontal force from member DE, which can also be calculated using the equation F_DE = F_CE * (DC / DE).
Once we have determined the vertical and horizontal forces, we can apply the Pythagorean theorem to find the magnitude of the force in member AE:
F_AE = sqrt((F_BE)^2 + (F_DE)^2)
By substituting the known values into the equation, we can calculate the force in member AE.