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

Answer:

FKJ = 0    (It does not work).

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).