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Plate section modulus 3
- Thread starter strlengr7
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paddingtongreen
Structural
Is the load a point load or a line load, it makes a difference if you are spanning the 4' way.
Michael.
Timing has a lot to do with the outcome of a rain dance.
Michael.
Timing has a lot to do with the outcome of a rain dance.
- Thread starter
- #9
The plate is 4 feet x 8 feet and is fully supported by beams along both 4 foot sides. Therefore, it is spanning the 4 foot direction. I know b is the width and d is the depth, that is not the question. I know 8x4 is 32, that is irrelevant. It is a point load, and I am not sure what b to use. I would not think I would use the full 8 foot width. So what width do you guys think?
chrislaope
Structural
I agree with paddingtongreen it makes big differentce for line load and point load. For uniformly line load b=8', for concentrated point load at exactly center of the plate, I use 45 degree rule as is shown in attached diagram, therefore b=4'. I also think graybeach's b=1' is too much conservative.
this is primarily a plate theory problem....and you are attempting to use beam theory....one can try to do this but will just about always end up with the plate not working..
a point load on a plate is a very complicated problem and as far as I remember the cases in Roark do not include this...my sugestion would be to add an extra bm underneath the point load and move on...
a point load on a plate is a very complicated problem and as far as I remember the cases in Roark do not include this...my sugestion would be to add an extra bm underneath the point load and move on...
paddingtongreen
Structural
@strlengr7, this is still confusing.
"The plate is 4 feet x 8 feet and is fully supported by beams along both 4 foot sides. Therefore, it is spanning the 4 foot direction."
If the 4" edges are supported, it is spanning the 8'direction. Here's why you need Roarke, the corners of this plate will try to lift up if the effect of the point load exceeds the effect of the plate dead load. If I was winging it, I would calculate the effective width to be the smaller of; the width of the point load + one quarter of the span, or the width of the plate.
Michael.
Timing has a lot to do with the outcome of a rain dance.
"The plate is 4 feet x 8 feet and is fully supported by beams along both 4 foot sides. Therefore, it is spanning the 4 foot direction."
If the 4" edges are supported, it is spanning the 8'direction. Here's why you need Roarke, the corners of this plate will try to lift up if the effect of the point load exceeds the effect of the plate dead load. If I was winging it, I would calculate the effective width to be the smaller of; the width of the point load + one quarter of the span, or the width of the plate.
Michael.
Timing has a lot to do with the outcome of a rain dance.
chrislaope
Structural
SAIL3:
I know it is primarily a very complicated plate theory problem. However, we know every theory has some kind of assumptions and which will leads to errors to cpmpare with "true" solution in engineering practice. My 45 degree approximation theory came from my long time research and I have built several very fine grid element computer models to do calculation verifications and finally I have made an Lab experiment which proved that the 45 degree approximation gives a very good result (a little bit around 5% --- 10% in conservative side).
The experiment is like this:
I take a 32"x32"x0.125" steel plate, put it on 2 long blocks with a span of 16", then apply a 250 lb load on center of the plate, the deflection on center point is 0.26".
Next, I take a 16"x32"x0.125" steel plate and put it on the same 2 long blocks with a span of 16" and with 16” in support width direction. Then I use a very rigid 16” long steel block to apply a 250 lb load on center of the steel plate to form a uniform line load, the deflection is measured around 0.28”.
After above research and experiment I feel very comfortable with this 45 degree approximation. The most advantage is it is very easy and fast to apply in engineering practice.
On the other hand, even if you use Roark's or other more complicated and so called "accurate" theory, you still can not guarantee that it has no error to compare with engineering practice.
strlengr stated:
I think you meant to say fully supported along both 8' sides. That means the ends are held down to prevent them lifting off the supports.
A point load is a singularity resulting in infinite stress at the load point, dying out very quickly as you move away. If the load is spread over a small rectangular area, the problem is addressed in Article 37 of "Theory of Plates and Shells" by Timoshenko and Woinowsky-Krieger for an infinitely long plate with two simply supported edges.
BA
I think you meant to say fully supported along both 8' sides. That means the ends are held down to prevent them lifting off the supports.
A point load is a singularity resulting in infinite stress at the load point, dying out very quickly as you move away. If the load is spread over a small rectangular area, the problem is addressed in Article 37 of "Theory of Plates and Shells" by Timoshenko and Woinowsky-Krieger for an infinitely long plate with two simply supported edges.
BA
Strlengr7:
As Paddington suggested this is really confusing, and it isn’t us who are confusing the issue. So, I am adding that you seem very confused about what you are doing. If you are an engineering professional, you are doing a really poor job of defining your problem: span length and support conditions, load magnitude and its footprint, plate thickness, etc, etc. With such a basic question, so ill expressed, you should not be coming to a forum like Eng-Tips for your fundamental engineering education. We generally don’t do first and second year engineering education here. Given the nature of your question, you probably shouldn’t be doing this problem without the help of a senior engineer from your own office. Your boss should know what you know and what you don’t know, so he can help keep you out of trouble, and guide you in your learning process. If your point load is on some rectangular area in the middle of the plate, what you might be asking is what is an effective width of this plate for these spans and plate thickness and load, so that using simple beam theory, I can take a first long hand shot at this problem. But then, also study how simple beam theory might not be appropriate for a plate bending problem, and come back and tell us. BA’s suggested reading will get you a better answer, once you figure out which edges are supported, and how, and what your span lengths are.
As Paddington suggested this is really confusing, and it isn’t us who are confusing the issue. So, I am adding that you seem very confused about what you are doing. If you are an engineering professional, you are doing a really poor job of defining your problem: span length and support conditions, load magnitude and its footprint, plate thickness, etc, etc. With such a basic question, so ill expressed, you should not be coming to a forum like Eng-Tips for your fundamental engineering education. We generally don’t do first and second year engineering education here. Given the nature of your question, you probably shouldn’t be doing this problem without the help of a senior engineer from your own office. Your boss should know what you know and what you don’t know, so he can help keep you out of trouble, and guide you in your learning process. If your point load is on some rectangular area in the middle of the plate, what you might be asking is what is an effective width of this plate for these spans and plate thickness and load, so that using simple beam theory, I can take a first long hand shot at this problem. But then, also study how simple beam theory might not be appropriate for a plate bending problem, and come back and tell us. BA’s suggested reading will get you a better answer, once you figure out which edges are supported, and how, and what your span lengths are.
- Thread starter
- #18
I did mis-speak, the plate is supported along the 8 foot length, such that it will be spanning the 4 foot direction. Basically, the plate will lay accross an opening to allow for a pallet jack to roll across this opening. I have done this in the past and used a b of 12 inches and everything worked great. But, like chisloape said, I think that is too conservative. Using the smaller of l/4 or the plate width like paddington suggest makes more sense. I just wanted to know if you guys ever spanned a plate one way, put a wheel load on it, and how you justified the b that you used.
as more and more details dribble out about the problem what was suggested before is not valid..
if the pl is just supported along the 8' sides and not held down, the pl can not develop membrane stresses and so would act like a bm.....this results in a very thick pl.
anyway, your original question of what b to use..
sorry don't have a reasonable answer for that, check out what Chrisaope suggested even though I do not understand what theory it is based on..
if the pl is just supported along the 8' sides and not held down, the pl can not develop membrane stresses and so would act like a bm.....this results in a very thick pl.
anyway, your original question of what b to use..
sorry don't have a reasonable answer for that, check out what Chrisaope suggested even though I do not understand what theory it is based on..
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