Can someone please explain this example about cantilever beams

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SUMMARY

The discussion centers on understanding the height equation of a tapered cantilever beam, specifically h(x) = 2 + (x/L). This equation allows users to calculate the height at any point along the beam, with specific values provided for points A and B. The relationship is derived from the standard equation of a straight line, utilizing the points (0, ha) and (L, hb) to establish the slope. The key takeaway is that the equation represents a linear relationship between height and distance along the beam.

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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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