Bending moment calculation

It depends where the plate is supported underneath.

Here is the calculations from this site

Use the calculation for each load individually then add them together for the total load.

You should Register.

Help will come.

Follow the link, it may help.

http://www.aps.anl.gov/APS_Engineering_Support_Division/Mechanical_Operations_and_Maintenance/Calculators/ElasticBeam2.html

'Can I treat it as a beam of span of 200 inch and apply these vertical loads on it to calculate its moment and deflection'

I think you know the answer better than anyone.

Interesting Problem

My training asks the following:

Are the five loads normal to the plane of the plate? I assume that from what you say. If not, then solve in the planes, x,y and z direction and find resutant deflection, ect. by each force.

May involve simutaneous equations or calculus formulas for plates, since direction of forces. Refer to "plates and shells" formulas.

Hope this helps. Would help me to see the givens. I am very rusty on effects of forces on plates.

Photon Phreak

If you manage to stract a mathematical model, you will only need a numerical solution. You could do this using odesolver in Scilab (www.scilab.org), it is just great for numerical calculations and work like MatLab. But if you need the complete solution, I haven't tried before but Comsol (www.comsol.com) has a mechanical simulation package. Try the one you need.

Yes, you can consider it as a very simple beam and calculate as an ordinary problem which you learn from school since there are no special considerations required as you mention in your post. And if you're not sure with your solution, you can register as MUKULMAHANT suggested.

That's it. Have a nice day.

Hi MUKULMAHANt;

What is the training classes u r taking about?How can I register.

Please give me the link.I would like to go for it.

Thanks all

take care

Can I treat it as a beam of span of 200 inch and apply these vertical loads on it to calculate its moment and deflection?

That depends on support conditions and location of point loads. If the plate is supported on four edges, you cannot treat it as a beam. You must consider plate action which is considerably more difficult to analyze.

If the plate is supported on only two edges 200 inches apart and the loads are centred on the 85 inch dimension, you would be reasonably accurate in treating it as a beam but would be ignoring the Poisson ratio of steel which affects deflection but not bending moment. If the loads are not centred on the 85 inch dimension, you would also be ignoring torsional effects which affects deflection.

If the plate is supported on two edges 85 inches apart, it would tend to behave more like a beam of span 85 rather than 200. Again, you would be ignoring Poisson ratio and, with loads off center, you would be ignoring torsional effects.

I completelly agree to ba/ael comments.

my case is plate supported on only two edges 200 inches apart and the loads are not centred on the 85 inch dimension,hence u r right i will be neglecting torsional effects.

I went with this approach of beam of 200 inchs span ,supported on 2 sides and vertical load applied on the beam at 5 locations and got total moment of 88000 lbs-in.I think this moment is acting on 85 inches of beam.Am i right?

Then I converted this BM to per width of the beam which is 88000/85=1035 lb-in/in.

Then I calcultaed bending stress MC/I and Margin of Safety , in this case my "I" inertia is per width of the beam as BM is per width.

By the way out of curiosity if plate is supported on one more side along with exsting 2 sides, can i still consider it conservativelly as beam supported only 2 sides of 200 inch apart.

Hi MUKULMAHANt;

What is the training classes u taking about?How can I register.

Please give me the link.

Thanks all

take care

If you sliced your plate into 5 strips, each 17" wide and 200" long, then placed a concentrated load at mid-span, centered on the middle strip, it is evident that it would deflect while the other four strips would remain stationary. If you now, magically pull them all together so that they act as one 85" wide member you must add equal and opposite shears between each strip so that deflections of adjoining strips are compatible along the span. This means you have introduced bending moments in the transverse direction. The plate will dish down in both directions and the deflection will be largest directly under the load. The material near the edges of the plate will be less stressed than the material under the load.

So it is not correct to say that the bending moment you have calculated acts uniformly over the 85" width. However, if the plate is extremely stiff in that direction, the difference may be small or even negligible.

If you are talking about a reinforced concrete plate, you would have to reinforce it in the transverse direction in order to spread the concentrated loads across the total panel width.

If you are talking about a solid metal plate, the strength in the transverse direction would be more than adequate to do that job. However, a solid metal plate spanning 200" does not seem very credible.

And finally, if the plate is supported on three sides, you would be conservative in considering it a 200" span but not very realistic. Evidently, the deflection along three edges of the plate is zero. The deflection along the unsupported edge may be close to the value you calculate but a finite element analysis would be a good way to determine that.

I understand what ur trying to say.

But can u suggest me some links in internet or books or examples where I can get more information about differances in plate and bending theory and when plate becomes beam.

thanks

For years I have referred to "Theory of Plates and Shells" by S. Timoshenko and S. Woinowsky-Krieger and also "Theory of Elasticity" by S. Timoshenko and J. N. Goodier. Both books were published by McGraw-Hill Inc., the first in 1959, the other in 1951.

I have not searched the internet thoroughly, but this article gives the reader a reasonable understanding of the structural engineering approach to the plate problem.

Classical thin plate theory is highly mathematical and not easily applied to everyday structural problems. Structural engineers normally apply simplified methods. For small steel plates, I tend to favor the "Yield Line Analysis" because it is easily understood and applied. For concrete plates, the "Hillerborg Strip Method" is favored by many engineers. Younger engineers seem to prefer computer methods such as "Finite Element Analysis" or a multitude of similar techniques.

Your description of the problem suggests to me that, if the plate is isotropic, the structure is uneconomical because, if it can span 200" under load, its capacity in the 85" span is largely wasted.

Perhaps it would be better to place a beam at each long edge of the plate so that the plate spans 85" instead of 200. This reduces the moments on the plate and permits eccentric point loads to be taken into account using simple structural principals.

Register as member with CR4 THAT'S WHAT I SAID you need doing. Like we all did.

Do not think I was asking you to go to any TRAINING CLASS.

Also you can post a drawing showing Support locations And loads all Vertical Vectors?

Also whether supports to Plate are pin- hinged /anchored/roller/Ball

Do you have access to the Classic book:

Formulas for Stress and Strain by Raymond J.Roark 1938? Library of CongressCARD # 53-5173

If you are serious about Engineering Optimization -you need to hug Roark .