Simple Beam Questions 4

[Spoonful]

Hi All,

For a simple been both end fixed,under uniform distributed load, as per Roark's table 8.1 case 2d. Max moment is at edge of Wl^2/12, and hence max stress at edge. If we apply a load which will result a stress at edge exceed the allowable stress, or even exceed material yield stress, the beam will starts to plastic bending.

The question is as long as the load is applied, and the beam will start to bend, no longer straight,The beam geometry changed. will the formula M max = wl^2 / 12 remain true? Or the max moment will be shifted to elsewhere along the beam.

My point is how to find out the true load that will break the beam, or cause into plastic bending.

Thanks in advance for any comment.

Regards

Spoonful

 

[BAretired]

Not true. The ends of beams are neither fixed nor hinged. They are connected to a member at each end which has a known stiffness. The rotation at the ends of each beam must match the rotation of its extension. Moments, shears and axial forces will emerge from the frame analysis which is, in reality a finite element analysis.

The midspan beam will interact and be supported by other shorter beams and cannot be considered in isolation. Depending on the magnitude of sag, cable action will play a role in carrying load. Cable tension will stretch the entire length of cable, not just the portion covering the 3mm hole. That strain will contribute to the sag and tend to make cable action more dominant than beam action.

It is not a simple problem and I cannot suggest an easy way of solving it.

BA

 

[paddingtongreen]

Another wrinkle is that the wires will already have been taken through the yield point when they were weaved into the mesh and then flattened.

I'm not sure I could run this on an FE program. The wires are continuous and linked to the perpendicular wires only perpendicular to the plane of the grid.

Do a thought experiment on paper. Draw your circle and grid in isometric, assume all joints are supported to start with, then think what happens when you put a load on the members connected at the central point and remove its support. Next imagine the removal of the joints at the far end of the original members with their connected members. Follow in stages, the removal of the supports until you reach the edges of the circle. Do it again with loads on all members. You will get only a general idea from this, what doesn't show here is the effect of redistribution to achieve mutually consistent joint deflections.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[dhengr]

It absolutely staggers the imagination how the OP in this thread could morph into a woven steel screen over a hole in a plate or a bunch of holes in a plate; With the screen being assumed to act like a beam which developed plastic moments and hinges and having fixed end moments. This thread got ridiculouser and ridiculouser by the day and by the post. And, it only took about 23 posts to get all the way from some pretty poor first assumptions and misguided comparisons in the OP, which lead some smart people off on a wild goose chase, interesting nonetheless, and finally to a more realistic problem description. Why not start out with a description of the real problem, since you’re not sure what you are doing anyway? And, I’ll bet this would have elicited completely different responses. Correct proportions and the full picture of the problem mean a lot to an experienced engineer looking at a problem for the first time. And you would learn a lot by just paying attention to how they approach the problem and why. And, pay real close attention to what they say, they are not just twits, twittering. Look for the full meaning of what they say.

People who don’t have a good idea how to approach their problem, would be so much better off, if they did a good job of laying out and describing their problem, just the facts, but all the facts; and then letting some of the smart people here, who are willing to help and have the experience and judgement to make good sound determinations about the tack to take on solving the problem, what assumptions to make and how to approach their problem. Then, the OP’er. should read what they have to say, a couple times, for the deeper meaning, the whole meaning and thought process. Why is it so difficult to get engineers to show a sketch, with dimensions, loads, etc. and to do a good job of describing their basic problem without a bunch of their preconceived notions which just hiding the real facts of the matter?

Now consider, a woven steel screen with .16mm wires and .26mm spacing btwn. wires and wires woven at 90̊ is fairly fine mesh. The wire is probably a pretty hard, brittle and notch sensitive, with pretty high yield and tensile strengths, cold drawn, cold worked in the weaving,, etc.; probably won’t weld worth a darn either. The top edges of the 3mm holes better be pretty finely finished and shaped so that as the screen it bent over these edges into its dished shape, it is not kinked and fractured.

BA.... You would have made one hell of a good teacher (Prof.) if you hadn’t become such a good Structural Engineer and mentor instead. The patience and fortitude of a saint, the ability to boil things down to their basics, posts 17MAY13 @ 14:43 and 21MAY13 @ 2:13, nice presentation on, 20MAY13 @ 12:21, even checking the algebra, etc.

GregL.... You must be clairvoyant if you saw the wire mesh net idea coming, by the third or forth post.

Spoonful.... I think BA’s post 21MAY13 @ 23:11 suggests the proper way to analyze this problem, but you seem to be quite a difficult person to convince. And, his post 22MAY13 @ 11:02 adds some significant detail to the thought process. He’s spent (wasted?) a fair amount of time trying to help you and offer sound advice, but in almost ever cycle you have only half read what he said and meant, or misinterpreted it in some way. Paddington is also offering some good advice and a thought process/method that we often use on these kinds of problems. What is your engineering educational and experience background, please tell us. If you won’t do that, I think you should take some engineering courses, so you gain some better fundamental understanding of what the guys have been talking about. They can’t solve the problem for you. They can explain and suggest, but you have to grasp what they’re telling you from the engineering standpoint. They can’t make you an engineer in one difficult post, and Roark’s book won’t make you an engineer either, if you don’t vaguely understand where that stuff came from. You need to have a good fundamental understanding of the engineering concepts involved if you want to do what you are trying to do.

 

[BAretired]

We don't know how the mesh was fabricated. This may be a problem. I am assuming that each wire acts like a member with a known area and a known stiffness (EI).

I do not claim any expertise with FEA, but FE programs can analyze 3 dimensional objects, so I'm not sure why they would have difficulty analyzing this. It is like analyzing the strings of a tennis racket except that the strings are not fastened to the frame of the racket. Instead, they run through the frame and fasten to a square frame further out.

BA

 

[Spoonful]

dhengr,
First appreciate that you have spend all the time reading through all the previous posts. It is the fact that I do not have extensive experience/knowledge in structural, that is why I am seeking advise here. It is Ok that you not helping, and you may save your precious time to spend on something else.

I appreciate all your kind helpful posts, especially BA, and I do due to my limited knowledge, having trouble understand some posts. I don't see anything inappropriate here by asking further questions for things that I don't clearly understand, if there are people willing to help.

Paddingtongreen,
Good point, the wire would have already been yielded during woven process. To just have a conservative result, could we assume there are 14 wire in the same direction? rather than 7 by 7 wire at 90 degrees? and ignore the effect of its joints?

 

[GregLocock]

If I were analysing it I would treat it as a rubber membrane, incapable of resisting moments. This is very similar to a catenary. I would use smeared properties over the whole disc.



Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[BAretired]

Interesting, Greg...I suppose that would yield a simpler solution but I wonder about the legitimacy of neglecting bending in the wires. If we scale the whole thing up by a factor of 1000, we would be dealing with an opening of 3m (about 10') diameter and 160mm (6.3") diameter solid bars spaced at 420mm (16") centers. The span to depth ratio is 18.75 and I don't think bending can be ignored if you expect to obtain a legitimate result.

BA

 

[GregLocock]

I agree that it is likely to overestimate the deflected shape, but must admit I haven't actually been following along all that closely and have forgotten what the OP actually wants solved. I was thinking of the plastically deformed shape of gauzes I have seen.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[BAretired]

He wants to know the failure capacity of the orthogonal steel mesh.

Typical Wire Spanning 3mm

Diameter D = 0.16mm
Area A = 0.020mm²
Yield strength Fy = 170MPa
Yield tension Ty = 3.4N
Unit Load w = 0.21N/mm
Factored Unit Load w_f = 0.42 (using S.F. of 2)
Factored Moment Simple Span M_f = 0.42*3²/8 = 0.472 N-mm
Sag required = 0.472/3.4 = 0.139mm

Neglecting bending moments and considering only cable action, the longest wire can resist its tributary factored load w_f if it can strain enough to sag 0.139mm at midspan. The remainder of the wires will be less critical.

Ultimate failure will occur when the wire reaches its ultimate stress which will occur when it reaches its ultimate strain (a property of the wire). Sag and failure load will vary accordingly.

Assumptions made above

1. For a cable T = wL²/8s where s = sag
2. Cables are anchored adequately at the ends to develop not less than yield strength and preferably ultimate strength.



BA