Question

Determine the length b of the triangular load and its position a on the beam such that the equivalent resultant force is zero and the resultant couple moment is 8 kN*m clockwise. 6 kN/m 2 kN/m 4 m

          Determine the length b of the triangular load and its position a on the beam such that the equivalent resultant force is zero and the resultant couple moment is 8 kN*m clockwise.
6 kN/m
2 kN/m
4 m

Determine the length b of the triangular load and its position a on the beam such that the equivalent resultant force is zero and the resultant couple moment is 8 kN*m clockwise.
6 kN/m
2 kN/m
4 m

Added by Roberto B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Supreeta N

05/23/2023

Step 1

First, we need to find the equivalent resultant force (F_R) of the triangular load. The triangular load has a base of b meters and a height of 6 kN/m at one end and 2 kN/m at the other end. The area of the triangle represents the equivalent resultant force. Area Show more…

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Determine the length b of the triangular load and its position a on the beam such that the equivalent resultant force is zero and the resultant couple moment is 8 kN*m clockwise.

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Transcript

00:01 Hello students in this question what we have is a road of 4 meter length and we have a distance from the center from the side a in which 2 kilo newton per meter is applied.

00:17 We have a distance which is smaller than a which is b.

00:21 We have 6 kilo newton per meter added.

00:25 We need to determine the equivalent net force equal to 0.

00:32 We need to find the length b so that the equivalent force equal to 0.

00:39 So that is what we need to find out.

00:44 And let's find out first thing.

00:48 So the resultant force will be equal to integral of weight distributed times dx.

00:57 You can just say that w times dx.

01:02 So here what we have is for length b this weight is given as so resultant force is equal to force on the bottom to the bottom is equal to 6 newton per meter times b.

01:19 That is what you will get and resultant force to the top is equal to 2 times a.

01:28 So what it means is that this force must balance each other.

01:33 So 6b must be equal to 2a 2 times a to balance this whole thing.

01:43 Ok.

01:44 So b must be equal to 2a by 6 to balance this.

01:49 That is when the resultant force is equal to is balanced is counterbalanced.

01:55 So now this is a condition and now we need to calculate from the image we can identify that this happens from the half region.

02:13 Right.

02:14 So this area so a region will be in the clockwise direction.

02:19 So a will be acting on clockwise direction.

02:23 So if you take the torque which is the moment the moment will be equal to a times 2 newton kilo newton per meter plus plus b times the half the second half of the area.

02:47 So that is equal to 6 newton's minus b times 2 newton will be equal to 2 kilo newton per meter will be equal to 8.

03:02 It will be 8 kilo newton per meter kilo newton meter...

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