Can someone please explain this example about cantilever beams

AI Thread Summary
The discussion focuses on understanding the equation for the height of a tapered cantilever beam, given as h(x) = 2 + (x/L). Participants clarify that this equation represents a straight line graphically, connecting the heights at points A and B. The relationship is derived using the standard equation for a line, where the slope is calculated based on the heights at these points. The confusion arises from the derivation process, which is explained through graphing and applying the line equation. Overall, the explanation aids in grasping the concept of beam height variation along its length.
ranaz
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This might look a bit stupid but I have just started beams and I can't understand a part in this example it is to do with finding a general equation of the height at any given point on a tapered cantilever beam can someone please explain
 

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The height of the beam at a distance x from point A is given by the relation h(x) = 2 +(x/L)

You can use this relation to check the given heights of the beam at A and B, which are 2 in and 3 in, respectively.

The relation is already developed and given to you. I suspect the problem is asking you to do something besides developing this relation.
 
SteamKing said:
The height of the beam at a distance x from point A is given by the relation h(x) = 2 +(x/L)

You can use this relation to check the given heights of the beam at A and B, which are 2 in and 3 in, respectively.

The relation is already developed and given to you. I suspect the problem is asking you to do something besides developing this relation.

I understand that the relationship has been developed, the part I am confused about is that how he has derived this relationship.
 
If you draw the graph of h against x, it is straight line.

So the relationship is the equation of the straight line through the points (0,ha) and (L,hb).

Plug the values into the standard equation for a line in the form (y-y0) = m(x-x0).

x0 = 0, y0 = ha, and the slope m = (hb-ha)/L.
 
AlephZero said:
If you draw the graph of h against x, it is straight line.

So the relationship is the equation of the straight line through the points (0,ha) and (L,hb).

Plug the values into the standard equation for a line in the form (y-y0) = m(x-x0).

x0 = 0, y0 = ha, and the slope m = (hb-ha)/L.

OO
Thank you that really helped
 
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