Determine the force in members ef be bc and bf of the truss...

Determine the force in members EF, BE, BC and BF of the truss and state if these members are in tension or compression. Set $P_1 = 8$ kN, $P_2 = 12$ kN, and $P_3 = 7$ kN. $P_3$ F E A B C 3 m 3 m 3 m 3 m

Transcript

00:01 Hello, so let's take this step by step.

00:03 We need to find the trigonometry of the truss first because we need to determine the angles.

00:08 The vertical rise of diagonal members, b -e -n -e -f, is 4 meters, and the horizontal span between joints is 3 meters.

00:15 So we have our equation, tangent of theta, is equal to the vertical rate over the horizontal span, which is equal to 4 over 3, which gives us data is equal to tangent negative 1 over.

00:37 You know, tangent negative 1 times 4 over 3.

00:41 And so the cosine and sine are, cosine data is equal to 3 over 5.

00:48 And sine data is equal to 4 over 5.

00:52 So now, we need to cut the truss.

00:56 What does that exactly mean? we cut through members b, c, b, e, and ef, and consider the left section of the trust.

01:02 And then we'll also use the following equations of equilibrium for the left section, the summation of the momentum of b, the summation of the horizontal forces and the summation of the vertical forces.

01:15 So first, we need to use the equilibrium equation to find our momentum at point b.

01:22 So taking the counterclockwise momentum as positive, we have 12 times 3 plus the force acting on ef times 3 times 4 over 5 minus p3 times 6 is equal to 0.

01:37 And we're obviously solving for the force of ef here.

01:46 We get 36 plus 12 over 5f ef minus 72 equals 0.

01:56 And so you get 12 over 5f is equal to 36.

02:02 And the force of ef is equal to 36 times 5 over 12, which gives you 15 kiloons...

Question

Determine the force in members EF, BE, BC and BF of the truss and state if these members are in tension or compression. Set $P_1 = 8$ kN, $P_2 = 12$ kN, and $P_3 = 7$ kN. $P_3$ F E A B C 3 m 3 m 3 m 3 m

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