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6 February, 07:45

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 =

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  1. 6 February, 08:03
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    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).
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