Buckling of a simple Plate HELP!
Buckling of a simple Plate HELP!
(OP)
Hi,
I am trying to work out the deflection of a plate when at a certain loading force. There are a number of end conditions so a general formual would be much appreciated.
The plate is 3mm x 410mm in cross section and then 1640mm long. The load is appled to the top the far end is definately fixed. Other possible conditions for the top end are guided or pinned - depending on final design.
I just need a simple or complex way of calculating the max deflection (assuming I know material characteristics) at a load less than the critical buckling load.
Thanks
I am trying to work out the deflection of a plate when at a certain loading force. There are a number of end conditions so a general formual would be much appreciated.
The plate is 3mm x 410mm in cross section and then 1640mm long. The load is appled to the top the far end is definately fixed. Other possible conditions for the top end are guided or pinned - depending on final design.
I just need a simple or complex way of calculating the max deflection (assuming I know material characteristics) at a load less than the critical buckling load.
Thanks





RE: Buckling of a simple Plate HELP!
RE: Buckling of a simple Plate HELP!
RE: Buckling of a simple Plate HELP!
TTFN
RE: Buckling of a simple Plate HELP!
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Tobalcane
RE: Buckling of a simple Plate HELP!
RE: Buckling of a simple Plate HELP!
If the long sides are supported, you'll probably find a buckling load in Roark & Young, but won't find anything giving the deflection of a semi-buckled shape.
RE: Buckling of a simple Plate HELP!
I have only recently joined a design company - and hence want to get the calcs right. Apologies for any offense caused to those seeing it as a trivial question.
RE: Buckling of a simple Plate HELP!
Y=d(1-cospx)
where d is the offset at the point of application and
p=sqrt(P/E)
Y= deflection
P=load
E= modulus of elasticity
I= moment of inertia of crossection
Since Y=d at Y=L i.e. Y(L)=d, cospL must be 0 which leads to
pL=(2n+1)*pi/2
the smallest P would coincide with n=0 and is the critical value.
If P is any other value less than critical, cospL would be different from zero and therefore the only remaining possibility is that d=0 i.e. no deflection.
RE: Buckling of a simple Plate HELP!
RE: Buckling of a simple Plate HELP!
You can envision the problem as stringing a bow, where the bow is initially straight. In the tank world, come-alongs are used to bend steel plate in a similar manner.
The problem is that the moment cannot be easily integrated along the length of the plate because it is a function of the deflection.
A similar problem is that of beams with combined axial and transverse loads. This is discussed in Roark and Young, but the information given there assumes that the transverse load is always non-zero, so there's no way to get a solution for the column effect only.
And FYI, note that when a plate bends like a beam, the stiffness varies slightly from that of a beam due to restraint of transverse strain.
RE: Buckling of a simple Plate HELP!
Unfortunately I have no ready to work solutions for the clamped ends condition, only hinged ends.
And JStephen the deflection would not be calculated as a function of force, but only as a function of end axial displacement: as what we are talking about is a post buckling condition, the load cannot increase beyond the buckling value (or failure would occur).
prex
http://www.xcalcs.com
Online tools for structural design
RE: Buckling of a simple Plate HELP!
preach
RE: Buckling of a simple Plate HELP!