Re: physics of anti topple devices
- From: Jim Black <tramspap@xxxxxxxxx>
- Date: Thu, 6 Nov 2008 15:18:30 -0800 (PST)
sam.n.seab...@xxxxxxxxx wrote:
Hi all,
I've got a basic question about physics in this (offbeat perhaps)
situation.
I am building a "rack" for some computer servers. The basic structure
for the rack is the IKEA GORM shelving unit (see note [1]). I have the
following equipment to place on the rack.
two servers, each is a rectangular box about 6"x16"x18" (width, depth,
height), weighing about 20 lbs each.
LCD monitor about 17"x17"x6" (WxDxH) weighing about 10 lbs.
one printer, a rectangular box about 14"x12"x10" (WxDxH) weighing 20
lbs.
4-5 stacks of standard letter paper (each is about 2 lbs) and
miscellaneous office supplies
[1] Link to IKEA GORM unit: http://www.ikea.com/us/en/catalog/products/S59850857
My main requirement is that this shelf should not topple.
The basic principle here is that the shelf will topple forward if its
center of gravity is further forward than the front edge of its base.
Once that happens, you have a forward torque on your shelf due to the
weight of the objects, which will make the shelf accelerate further
forward, leading to catastrophe.
http://img208.imageshack.us/img208/8210/shelf1pp2.png
Here, the black box is a large mass, significantly larger than that of
the shelf, so that the center of gravity is close to the black box.
In general, you'll want to consider the center of gravity of the shelf
and all the objects on it.
In order to prevent this from happening, you want a large angle
between the front of the shelf and the line from the upper front edge
of the shelf to the center of gravity:
http://img146.imageshack.us/img146/5900/shelf2ol4.gif
This means you want to place stuff low and towards the back. I'm
assuming you're putting the back of the shelf against a wall so that
backward toppling is impossible; otherwise, you want to place stuff
low and towards the center. You also want to avoid having the center
of gravity too far to the left or right, to avoid toppling left or
right.
So, my
questions are:
Q1 Unit stability. The bottom shelf of GORM bolts into the legs about
2 inches above the floor, so the unit rests on the legs. (The pic at
[1] shows this.) I am thinking I should saw off the legs so the bottom
shelf sits flush on the floor.
Well, it will bring the center of gravity down a little. This will
help the most if the weight is concentrated in the bottom shelf. It
also would help with friction, making it harder to jerk the bottom out
from under the top. The only risk I can think of is if you saw off
the legs too far, and put the weight of the upper shelves on the
screws/nails between the bottom shelf and the legs.
I am also thinking of placing 10lb
workout discs on the top shelf, at the rear corners; this seems
intuitive, but is it a sensible topple preventor?
You want the weights low and to the rear. Putting weights on the top
shelf, even toward the rear, could actually make it more likely to
topple. Weight at the center of the rear edge is generally better
than weight at the corners, but weight at the corners will be just as
good provided the weights on the left and right corners are equal,
since it's the center of gravity that matters.
Q2 Equipment placement. The shelves will be at the following
locations: bottom, top, table level (29" above the floor) and mid
(about 55" above the floor). I'm obviously going to put the servers on
the bottom shelf, towards the rear. The LCD monitor and printer will
be at table level shelf and the letter paper will be on the mid level
shelf. I suppose this makes for a visually sensible arrangement, but
is it better, for example, to put the servers at the mid level or top
shelf?
You want the servers on the bottom shelf.
Q3 I've got a few more 10lb workout discs. I'm thinking of putting
them at the rear corners of the mid level shelf as well. Does this
make sense?
You want the additional weights to go as low and as close to the rear
as possible.
Q4 (Inevitable) What would it take, after all these steps, to topple
it? I'm thinking of the most common occurrences: people leaning on it,
a sudden jerk of a wire or cord or a hasty action on my part.
I already talked about how much you'd have to tilt it in order to
topple it, but it might also be useful to know how much force it would
take. To to that, you have to consider one mode of toppling at a time
(for example, forward or to the side), add up all of the torques from
the weights on the shelf, and compare it to the torque that's trying
to pull the shelf over. The formula for torque is
torque = force * moment arm,
where the moment arm is the distance between the axis of rotation and
the line of force, measured perpendicular to the line of force:
http://img208.imageshack.us/img208/9375/shelf3ix5.gif
This can give us some quick numerical estimates of how much you'll
need to topple the shelf.
If we assume the items on the shelf (totaling to 90 pounds if we
include 10 pounds for the shelf) are distributed so as to put the
center of gravity close to the center of their respective shelves (the
height of the center of gravity doesn't matter for this calculation),
the force of gravity has a moment arm of about 10 inches for forward
toppling, and 15 inches for left/right toppling. Multiplying the
force by the moment arm, and dividing by the height of the shelf, we
can estimate that it would take 13 pounds of force forward at the very
top of the shelf, or 20 pounds left/right, to topple it. In practical
terms, that's the force of a 150 pound man leaning at 5 to 7 1/2
degrees.
If you added 50 pounds of weight to the back of the rear shelf, those
weights would have a moment arm of 20 inches for forward toppling and,
as before, 15 inches for left/right toppling. So you'd bring the
needed force up by 15 pounds for forward toppling, and 11 pounds left/
right. Now we're looking at a 150 pound man leaning at 10 1/2 to 11
1/2 degrees, in the worst case scenario that he rests his weight at
the very top of the shelf.
--
Jim E. Black
.
- References:
- physics of anti topple devices
- From: sam . n . seaborn
- physics of anti topple devices
- Prev by Date: Re: Sailing, sailing....
- Next by Date: Re: Sailing, sailing....
- Previous by thread: Re: physics of anti topple devices
- Next by thread: Re: physics of anti topple devices
- Index(es):
Relevant Pages
|
