Weight distribution on supports of a platform
Greg Neill
so please forgive me if my terminology is off base.
Suppose one has a rectangular platform of uniform
density supported at its corners, with some additional
weight load (with a small footprint relative to the
size of the platform) located at some location on
the platform. What approach is used to determine
the net weight supported at each of the corners?
Finding the center of gravity of the system is not
a problem. Can the individual loads be determined
from that by some geometrical "rule"?
For the sake of argument we can say that in this case
the platform consists of a perfectly rigid plate (is
this a valid approximation to make?).
Brian Whatcott
You would expect to be able to estimate applied loads reacting on
three legs - but four legs is not quite as straightforward.
Brian W
Greg Neill
news:745804h5bfq21193v...@4ax.com
> You would expect to be able to estimate applied loads reacting on
> three legs - but four legs is not quite as straightforward.
Yes, I can see how one can write a consistent and
solvable set of equations for three legs. It's the
case of four or more that I am curious about. Surely
there must be some "standard" approach used?
BobK207
> "Brian Whatcott" <betw...@sbcglobal.net> wrote in message
Greg-
With 4 supports the system is "indeterminate", so simple statics will
not give you a solution.
You must use a stiffness approach, energy approach or virtual work
method. They're all somewhat similar.
If the load is symmetrically placed sometimes you use that to
advantage to simplify the problem.
Roarks Formulas for Stress & Strain is a great reference and should
have your solution
cheers
Bob
Greg Neill
news:b75fe76e-b529-48bb...@k13g2000hse.googlegroups.com
Thanks for the info, Bob. That gives me a starting point.
Kannan
> "BobK207" <rkaza...@gmail.com> wrote in message
Greg,
Since you said the plate is rigid, idealize the plate as a beam with 2
support at the ends and get the reaction. Such reaction you get is the
reaction somewhere along one of the edge. Then again for the two
supports at the edge, find the reaction as same as beam with two
supports. It will be some form of acP/((a+c)(b+d). P is the load. a,
b, c, d are distance to the load along the edges to the load.
Regards
Kannan
Greg Neill
news:f7ddd7a8-60e2-453d...@k1g2000prb.googlegroups.com
>
> Since you said the plate is rigid, idealize the plate as a beam with 2
> support at the ends and get the reaction. Such reaction you get is the
> reaction somewhere along one of the edge. Then again for the two
> supports at the edge, find the reaction as same as beam with two
> supports. It will be some form of acP/((a+c)(b+d). P is the load. a,
> b, c, d are distance to the load along the edges to the load.
>
> Regards
> Kannan
Okay, to make a concrete example, suppose that the setup is
as follows:
A .---------------------------. B
| ^ |
| | c |
| a | b |
|<----- o ----------------->|
| | W |
| | |
| | d |
| | |
| | |
| V |
C .---------------------------. D
Rigid plate is ABCD, uniform weight Wp. An object of weight W
is located at "o" with offsets from the edges as shown.
To calculate the additional load at support A caused by weight
at o:
AC load: AC = W*b/(a+b)
A load: A = AC*d/(c+d) = W*b*d/((a+b)*(c+d))
Is this what you are suggesting?
Kannan
> "Kannan" <vthamara...@gmail.com> wrote in message
Yes exactly! you are right.
Reaction at a support = load x area bounded between diagonally
opposite support and loading point / total area.