Yiel line theory for point loads 2

[slobo7]

Hi, I would like to know how to define a reasonable yield line for a rectangular slab. Two perpendicular sides of the slab are fixed and the other two are free. The only applied load is a force acting on the center of the plate. Thank you!!!

 

[BAretired]

There should be two negative yield lines, one at each of the fixed edges and one positive yield line extending from the corner where the two fixed edges meet to the long free edge. The direction of the positive yield line would be variable, depending on the aspect ratio of the rectangular slab.

If the weight of slab is considered in addition to the concentrated load, the direction of the positive yield line would be different than the case for the point load by itself.

BA

 

[slobo7]

Thank you so much!!! I am looking for other cases of point loads in rectangular and square plates under different support configurations. Can you please tell me where to find references where I can learn how to tackle these problems?

 

[BAretired]

In the current problem, if the length is large compared to the width, another pattern is possible which also consists of three yield lines. One is positive through the concentrated load and perpendicular to the long side. Two are negative starting from the intersection of the positive yield line and the fixed edge and running diagonally to meet the opposite free edge. In this case, the fixity of the short edge is too far away to play any part in failure of the slab.

I first learned about Yield Line Theory from "Reinforced Concrete Fundamentals" by Phil M. Ferguson. It is mentioned in Chapter 10 "Yield Line Theory for Slabs" but is a relatively small portion of his book.

BA

 

[KootK]

Link

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[BAretired]

I have used Yield Line Theory many times in checking the capacity of steel plates; not so much with concrete slabs. The advantage of using it with steel plates is that the unit moment capacity is equal in all directions whereas with concrete slabs, the unit moment capacity varies with the amount of reinforcement in each direction. One must be very careful to ensure the slab has sufficient reinforcement in locations outside the assumed yield lines. The Hillerborg Strip Method is probably a safer and better method for analyzing concrete slabs.

BA

 

[slobo7]

I am attaching two sketches of the problems I would like to learn how to draw the yield lines. I kind of have the intuition when it is about uniform distributed loads, but when it comes to point loads it is not as clear for me. Thanks again!

 

[KootK]

For both cases, I'm going with:

1) Yield lines along both walls and;
2) A yield line from the bottom left running diagonally up through the central point load.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[KootK]

I change my answer for the 3P version: single yield line from the top left corner to the bottom right.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[BAretired]

I agree with KootK. In the 3P version, it is a partial collapse with one point load continuing to be supported.

BA

 

[slobo7]

Thank you both!

 

[BAretired]

It should be recognized that to design the slab, there are two critical yield line patterns for the 3P version. On one diagonal, there is a critical negative moment; on the other there is a critical positive moment. Reinforcing the slab for only one is not sufficient; to prevent collapse, they must both be reinforced.

BA