Distance DC = FE = HG = AB = 2.7m
FH = FD = GE = EC = CB = 2 m
Find the supporting reaction of H, Member BD (Tension Force), Member CE, and Member CF?
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To find the supporting reaction at point H, we need to consider the equilibrium of the forces acting on that point.
Supporting reaction at point H can be determined by resolving the vertical and horizontal forces:
1. Vertical forces:
The only vertical force acting at H is FH, which is equal to 2m. Since there are no other vertical forces acting on H, the supporting reaction at H must be equal in magnitude but opposite in direction to FH. Therefore, the supporting reaction at H is 2m (upward).
2. Horizontal forces:
The horizontal forces acting at point H are HD and HE. HD is the tension force in member HD, and HE is the tension force in member HE. These horizontal forces must balance each other out to maintain equilibrium.
Since the length of member HD and member HE is the same (2.7m) and the directions of the forces are opposite, the magnitudes of HD and HE must be equal.
Therefore, the supporting reaction at point H due to HD and HE is 2m (to the right).
Now, moving on to the tension force in member BD:
To find the force in member BD, we need to consider the equilibrium of the forces acting on point D.
The forces acting on point D include:
1. The vertical force FD (2m downward).
2. The horizontal force HD (to the left).
To maintain equilibrium, the magnitude of the tension force in member BD must balance the horizontal force HD and the vertical force FD.
By using the Pythagorean theorem, we can find the magnitude of the tension force in member BD:
BD^2 = HD^2 + FD^2
BD^2 = (2m)^2 + (2m)^2
BD^2 = 4m^2 + 4m^2
BD^2 = 8m^2
BD = √8m^2
BD = 2√2m
Therefore, the tension force in member BD is 2√2m, acting along the direction from D to B.
Moving on to member CE:
To find the force in member CE, we need to consider the equilibrium of the forces acting on point E.
The forces acting on point E include:
1. The vertical force GE (2m downward).
2. The horizontal force HE (to the right).
The magnitude of the tension force in member CE must balance the horizontal force HE and the vertical force GE.
Using the Pythagorean theorem, we can find the magnitude of the tension force in member CE:
CE^2 = HE^2 + GE^2
CE^2 = (2m)^2 + (2m)^2
CE^2 = 4m^2 + 4m^2
CE^2 = 8m^2
CE = √8m^2
CE = 2√2m
Therefore, the tension force in member CE is 2√2m, acting along the direction from E to C.
Finally, for member CF:
To find the force in member CF, we need to consider the equilibrium of the forces acting on point F.
The forces acting on point F include:
1. The horizontal forces CF (to the left) and FH (to the right).
The magnitude of the tension force in member CF must balance the horizontal forces CF and FH.
Since the lengths of member CF and FH are the same (2.7m) and the directions of the forces are opposite, the magnitudes of CF and FH must be equal.
Therefore, the tension force in member CF is 2m, acting along the direction from F to C.