Question

g Questions 1 - 4 compute forces in the members of the 2D truss below. The truss has an overall height of 4 meters and an overall length of 12 meters (there are 8 members along the bottom which each are 1.5 meters long). If the member is in compression, use a negative sign in the answer to indicate compression. Work in units of kJ for forces but do not enter units. Determine the force in member KJ. KJ =

Answer 1

FKJ = 0 (It does not work).

Step-by-step explanation:

The truss has an overall height of 4 meters and an overall length of 12 meters (there are 8 members along the bottom which each are 1.5 meters long). If the member is in compression, use a negative sign in the answer to indicate compression. Work in units of kN for forces but do not enter units. Determine the force in member KJ.

Ax = 0 ⇒ Ix = 0

∑ MA = 0 (counterclockwise +) ⇒ - 10*3 – 6*9 – 6*10.5 + Iy*12 = 0

⇒ Iy = 12.25 N (↑)

∑ Fy = 0 (↑)

Ay – 10 – 6 - 6 + Iy = 0 ⇒ Ay = 10 + 6 + 6 - 12.25 ⇒ Ay = 9.75 N (↑)

∑ MK = 0 (counterclockwise +) ⇒ - FHI*4 + Iy*3 = 0

⇒ FHI = (Iy*3) / 4 = (12.25*3) / 4

⇒ FHI = + 9.1875 N

Node I:

∑ Fx = 0 (→)

FRI*Cos (θ) - FHI = 0 ⇒ FRI = FHI / Cos (θ) = 9.1875 / (3/5) = 15.3125 N

⇒ FRI = - 15.3125 N

Now, for the section in the figure 2 shown we have

∑ Fx = 0 (→)

⇒ FKJ + FRI*Cos (θ) - FHI = 0

⇒ FKJ = FHI - FRI*Cos (θ) = 9.1875 - 15.3125*(3/5)

⇒ FKJ = 0 (It does not work).