beam/plate in bending, is there a difference?
beam/plate in bending, is there a difference?
(OP)
if i have a plate in bending (simply supported, force applied at the center), 15ft long, 5 ft wide, 1 inch thick, can i use standard beam bending formulas or is there a correction factor if it is more of a plate then a beam?





RE: beam/plate in bending, is there a difference?
RE: beam/plate in bending, is there a difference?
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My recollection (just from my prep for the PE exam 4 years ago) was that the formula was very similar... there was just a multiplication by a factor that came from the ratio of the width to the thickness or something.
-Dustin
Professional Engineer
Pretty good with SolidWorks
RE: beam/plate in bending, is there a difference?
what is the load ? distributed ? point ??
also consider membrane loads ... if the plate is deflecting more than 1/2 it's thickness plate bending theory (no axial load on the NA) starts to break-down and the internal membrane loads help react the applied load.
also, if you have a localised load, with a wide plate the edges are probably deflecting so as to increase the load in the remainder of the plate (ie flexing up with a down load).
RE: beam/plate in bending, is there a difference?
Also note that in certain cases, membrane action must be taken into account- particularly if the ends are both attached rather than free to move toward each other.
RE: beam/plate in bending, is there a difference?
Is the last paragraph any different for a beam though? I think that statement is applicable to both.
Brian
www.espcomposites.com
RE: beam/plate in bending, is there a difference?
But - at 5 feet wide, unless the total load is (somehow) applied in a UNIFORM "line of force" exactly across the width of the plate at the center of the plate - and ONLY if the this "line of force" will be resisted by ONLY the two ends of the plate (with neither side being fastened!) will the plate "bend" as you are expecting.
Otherwise, you will get a multi-curved "sagging rectangular trampoline" if all four sides are bolted or welded. The "curve" across ANY section of the plate will depend on how the four edges are fastened: If they are free to flex (free to bend up as if tied by ropes around a stretched tarp) then the curve will have no inflection point and continue from the edges down towards the center of mass of the load. This will also tend to happen (but to a lessor degree) if the edges of the plate are fixed to a frame around all four edges, but that frame is not stiff enough and the frame or its legs twists under load.)
If the edges are firmly welded to a frame that has significant rigidity, then the plate will begin flat at all edges, then bend down towards the load, then inflect and bend up across the middle of the load to the other side.
RE: beam/plate in bending, is there a difference?
RE: beam/plate in bending, is there a difference?
ESP- the membrane situation would also exist with a beam, but is much more likely with a plate due to the much lower bending stiffness. Note that Roark's criteria for when this becomes significant in a 2-D plate is when the deflection exceeds half the thickness, which wouldn't take much in the situation described- plate weight alone might deflect that much.
RE: beam/plate in bending, is there a difference?
Tara
http://tinyurl.com/4ydjg7m
RE: beam/plate in bending, is there a difference?
if you apply plate bending and get a deflection greater than this, then the plate will be reacting (at least some of) the load as a membrane (ie tension on the mid-plane).
mind you, i think hokie is right about the discussion of the side edge restraint ... the OP clearly said his plate is supported on the two ends only.
RE: beam/plate in bending, is there a difference?
Hmmmn. Are you sure you want to do this?
I just supported a 115 inch long 1x1 steel beam at both in the garage, supporting both ends on rollers. Assume 113 between rollers. Zero'ed out the deflection at midpoint (55 inches) with a laser level. (Found 1/16+ some-odd deflection for beam weight alone by the way.)
Put a 68 pound anvil at the midpoint, measured a 11/16 inch deflection at the 55 inch point. If your actual "load" is more than 65-70 pounds per inch of the loaded length of the plate, you can't assume any maximum of "only" 1/2 thickness of the plate deflection.
RE: beam/plate in bending, is there a difference?
RE: beam/plate in bending, is there a difference?
RE: beam/plate in bending, is there a difference?
and i'm not saying it'll deflect only 1/2 the thickness, i'm saying that plate bending theory is valid If it deflects less than 1/2 thickness.
RE: beam/plate in bending, is there a difference?
RE: beam/plate in bending, is there a difference?
Brian
www.espcomposites.com
RE: beam/plate in bending, is there a difference?
Beam theory is only valid for small deflectionns I agree with ESPcomposites and rb1957.
See this paper:-
http://hpfem.org/~pavel/public/book2/p_211.pdf
Also rb1957 is correct, if the plate deflects more than approximately half its thickness, then diaphragm stresses cannot be ignored see R.J.Roark's formula for stress and strain 5th edition page 405
desertfox
RE: beam/plate in bending, is there a difference?
RE: beam/plate in bending, is there a difference?
OK. So why did I measure only about 1/16 inch deflection for a 1x1 bar at 115 inch length, when the bar was also simply supported with o end restraints? It's shorter, obviously, but what am I measuring incorrectly?
RE: beam/plate in bending, is there a difference?
i get hokie'd 1.6" for 180" length, and 0.27" for 115"
d = 12/30E6*5/384*0.3*L^4, assuming t = 1"
RE: beam/plate in bending, is there a difference?
RE: beam/plate in bending, is there a difference?
I used this formula out of Mechanical engineers handbook by Carvill:-
ym = k1*Pa^2/E*t^3 where t=thickness 1"
P= point load at centre of plate
acting over a small radius
a= plate width
b= plate length
k1= b/a
RE: beam/plate in bending, is there a difference?