A uniformly distributed load and a sloped load with...

A uniformly distributed load and a sloped load with magnitude of W = 250 lb./ft., and a point load with magnitude of F = 2075 lb are applied to the beam shown in the figure. Required Calculate the reaction force at point B, Rg in kip, to the nearest 100th (i.e., two decimal places). W F A 9 ft 9 ft B

Transcript

00:01 So in this problem we have our beam under loading and two supports, a pin at a and a roller at b.

00:08 In part a, we need to draw a free body diagram, which means we need to free the body from these supports and represent the reactions there, as well as all of the forces that are applied.

00:24 So we have our applied forces, 48 .7 kip per feet.

00:31 In the triangle of load, 68 kips at point b and the 37 kip at the end of the beam.

00:47 So now we need to look at the reactions.

00:49 Point a is a pin.

00:51 So first let's put an axis here.

00:54 We have the y -axis and the x -axis as conventional.

00:59 So at a, we have a pin, which means we have reactions in both directions.

01:08 Here, putting them in the positive directions as an assumption.

01:12 The reaction at point a in the y direction, and the reaction at point a in the x direction.

01:21 Point b is a roller, so it cannot resist force in the x direction.

01:27 As you see here, it just roll along the beam.

01:29 So it will only resist in the y direction, so the reaction at point b at y.

01:39 We also are asked to decompose the, you don't need to decompose the reaction today, but we can represent that now.

01:51 So the 48 .7 kip, feet, tip per feet.

02:00 And we want to find the total force applied in all of this, so that we want to find, the total force applied in all of this.

02:04 So that would be times the length.

02:09 I guess we can put lengths in here.

02:11 16 feet, 8 feet, and 10 feet times the 16 feet times 1⁄2 due to this being a triangle.

02:26 So you see this is the area of a triangle with the base, with the height and the base.

02:33 So that works out to 389 .6 kips.

02:42 So we can represent this triangular force as we have.

02:45 Or alternatively represented as a distributed load of 389 .6 kips.

02:57 And that is based on geometry.

03:00 We know that this is one -third and two -thirds the distance of the triangle.

03:06 So that distance would be 10 .6 -7 feet.

03:14 And then the other side of the dimension would be 5 .33.

03:22 So it's important to only put one of these on the diagram, why there's a different color.

03:27 We'll need this later...

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