In figure 1 w 12 text lbft2 determine the reaction at the...

In (Figure 1), $w = 1.2 \text{ lb/ft}^2$. Determine the reaction at the ball supports $B$ and $C$ and the components of reaction at the ball-and-socket $A$ (not shown) for the uniformly loaded plate. What are the components of reaction at $A$? Express your answers in pounds to three significant figures. Enter your answers separated by commas. $A_x, A_y, A_z = \text{lb}$ Part B What are the reactions at $B$ and $C$? Express your answers in pounds to three significant figures. Enter your answer separated by a comma. $B_z, C_z = \text{lb}$ Figure

Transcript

00:02 Consider a weight this plate, or tangular plate that is being supported with a ball and socket joint at point a and a roller pin at point b and a tension string along cd parallel to the z axis.

00:22 On our plate we have a uniform leadership load, which has a magnitude of 60 pounds per feet.

00:47 And we have a couple moments being applied of 100 pounds per feet.

01:00 So we're going to want to write our equations for equilibrium, which will involve summing our forces equal to zero and our moment equal to zero.

01:13 But first, let's determine.

01:15 Oh, excuse me, moment is pounds times weight.

01:18 So first, let's determine the total weight.

01:24 W applied to our plate.

01:29 So small caps is the distributed load and capital w is the total load.

01:36 So we have 60 pounds per feet over a distance of 5 feet, so 300 pounds.

01:45 Because the uniform distribution, we could assume it is being applied at midway through the beam.

01:53 Now let's draw the remaining of our forces.

01:55 So here we have our upward tension force.

01:58 We have, in theory we could have three reaction forces for a because it's a ball and a socket joint, but there are no other horizontal forces.

02:07 When i mean horizontal, we'll be along the x -y plane, so there will be nothing to equal amount, so they have to be equal to zero.

02:13 So we have a -y and a -z, x equal to zero, and we're looking for a -z.

02:19 Similarly, we want to find b -z.

02:22 And b -z because the roller pin, it only had one reaction force to begin with.

02:29 So now let's look at our conditions for it.

02:31 The sum of the forces along z multiple to zero, which means that a z plus b z is equal to 300 pounds.

02:50 To the couple of these two forces, we're going to need, oh excuse me, i forgot tangent force.

02:58 Tension force, c...

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