Forcing a curved beam flat against a rigid surface
Forcing a curved beam flat against a rigid surface
(OP)
Problem: Pre-curved beam, radius of elastic curve constant (r >> thickness), like one leaf of a truck spring.
Rest concave side up on rigid surface (that is, resting at the center of its span, tangent, on the rigid surface.
Apply enough vertical force at the ends of the beam to just bring the beam flat against the rigid surface. (Ends unrestrained in direction of beam's length.)
What is the downward force, and what is the distribution of reaction force on the underside of the beam as it rolls out flat?
I'm told that Roark does not cover this case, but I don't have a copy, so I can't say first hand. If Roark or any reference or text has the problem worked out, I'd be very grateful to have it faxed to 815-371-0649.
Thanks,
Gary Garnier
Raytek Corp.
Rest concave side up on rigid surface (that is, resting at the center of its span, tangent, on the rigid surface.
Apply enough vertical force at the ends of the beam to just bring the beam flat against the rigid surface. (Ends unrestrained in direction of beam's length.)
What is the downward force, and what is the distribution of reaction force on the underside of the beam as it rolls out flat?
I'm told that Roark does not cover this case, but I don't have a copy, so I can't say first hand. If Roark or any reference or text has the problem worked out, I'd be very grateful to have it faxed to 815-371-0649.
Thanks,
Gary Garnier
Raytek Corp.





RE: Forcing a curved beam flat against a rigid surface
For a point the load the formula is:
deflection = PL^3/(48EI)
Solve for load given your deflection. This may or may not get a permament deflection. To achieve permanent deflection you must exceed the yield strength of the steel, probably 36ksi or 50ksi.
If you trying to permanently flatten the beam. I'd suggest that you send it to a bending company and have them reverse bend it through their rollers.
End reactions will depend on the kind of support.
Imagineer
RE: Forcing a curved beam flat against a rigid surface
While your formula (Pl^3/48EI) for deflection applies to a simply supported beam, center-loaded, simply supported, my case is quite different.
Thanks for taking a look at it.
Gary Garnier
RE: Forcing a curved beam flat against a rigid surface
Forgive the crude drawing but... we start something like this:
A B
( )
( )
( )
~
--------------- Flat Surface
Push down end A, we now have:
~~ (sorry no flat curving symbols in ascii)
~~
~~
~~
---------------
Again, we are back to a basic deflection equation, i.e.,
deflection = PL^3/(3EI)
Hope this helps, If not, could you restate?
Imagineer
RE: Forcing a curved beam flat against a rigid surface
Thanks,
Gary Garnier
RE: Forcing a curved beam flat against a rigid surface
/tt
Without Beam With Beam
¦ ¦
/ \ ---------------
/ \ ¦ d ¦
/ \ ---------------
/ \ / \
/ \ / \
/ \ / \
d is the thickness of beam (approximately)
Imagineer
RE: Forcing a curved beam flat against a rigid surface
Thanks again.
RE: Forcing a curved beam flat against a rigid surface
Imagineer
RE: Forcing a curved beam flat against a rigid surface
RE: Forcing a curved beam flat against a rigid surface
RE: Forcing a curved beam flat against a rigid surface
I am also considering using a pre-bowed bar to push something against a relatively flat surface. It is a ~12" length bar mounted on both ends. I calculated the deflection for a STRAIGHT bar under an uniformly distributed load, and I know the deflection will be too much. Since I have no room to "beef" up the bar, I am thinking of using a pre-bowed bar. I would like to know the maximum deflection of the pre-bowed bar at the center (the weakest point) under the same load. Ideally the deflection will be equal to or less than the pre-bowed amount.
Any suggestions as to how to approach this problem?
Thanks.