Can someone please explain this example about cantilever beams

In summary, the beam's height at any point is given by the equation h(x) = 2+ (x/L) if x is measured from the point A and the slope of the line through the points (0,ha) and (L,hb) is m.
  • #1
ranaz
4
0
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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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
 

1. What is a cantilever beam?

A cantilever beam is a structural element that is supported at only one end, while the other end is free to move. It is commonly used in construction to create overhangs or balconies.

2. How does a cantilever beam work?

A cantilever beam works by transferring the load applied at the free end to the support at the fixed end. The beam bends under the load, creating tension on the bottom side and compression on the top side.

3. What are the advantages of using cantilever beams?

The main advantage of cantilever beams is their ability to create overhangs without the need for additional support columns or beams. They also offer greater flexibility in design and can be more cost-effective in certain applications.

4. Are there any limitations to cantilever beams?

Yes, cantilever beams have limitations in terms of the amount of load they can support and the length of the overhang they can create. They are also more susceptible to bending and deflection compared to beams with support at both ends.

5. How can I calculate the maximum load a cantilever beam can support?

The maximum load a cantilever beam can support depends on various factors such as its length, material properties, and the type of load applied. To calculate the maximum load, you can use mathematical equations or consult structural engineering guidelines and codes.

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