How to reinforce long shear walls? 2

[ugoveri]

Imagine that you have a shear wall with 0.25 x 9.00 meters, that somehow was needed with this geometry! How do I calculate the reiforcement! Is it still valid the theory that the section remain plain, and perpendicular to it's axis?

In a smaller shear wall, for example, 0.25x2.00 or 0.25x3.00, my code (Portugal) proposes that we consider two virtual columns with the following dimensions b x H2=min (2b; H/10) being b the widht and H the height, and that you concentrate the longitudinal reinforcement for the major bending in this virtual columns. The distance to the centre of the rebars in tension would be d=H - H2/2 so the reduced moment would come m = Msd/(b.d^2.fcd) being fcd the concrete design compression resistance.

But in a bigger shear wall is still the same? Is it ok to calculate the longitudinal reinforcement of the shear wall, as if it was a single element?

 

[GraemeL]

I recommend that you get hold of a copy of "Reinforced Concrete Structures" by Park and Paulay, published by Wiley. Chapter 12 deals with shear walls.

How you design your wall depends on the height to length ratio. Squat shear walls are designed differently to tall walls (that have an aspect ratio > 1.5-2.0). So it is not just the thickness and length that is important, you need to consider the aspect ratio of the wall and reinforce accordingly.

Generally squat walls act in shear and you have to consider the diagonal compression struts in the wall and reinforce these to stablise them. Tall walls act flexurally and you reinforce them similar to a beam plus reinforce the central portion so shear can be transferred across any construction joint and into the foundations. But Park and Paulay are the gurus, so read and wonder.

 

[faisal25]

I am designing a 15 storey apartment building; for my graduation project at the university. I used the 3 stair cases and the elevators shafts as the R.C shear walls
1. I would like to know if I should divide the basic shear force between the R.C shear walls and the framing system.
2. Can you provide me with simplified equations to use in the design of shear walls for flexural instead of the strain compatibility equations.

 

[rlflower]

To Faisal25:

It is diffucult to explain our projects in this format, isn't it?

Please elaborate on what you mean when you said "divide the basic shear force between the RC walls and framing system".

As far as flexural analysis of the shear wall, have you thought of turning your "free-body diagram" 90 degrees? Since it is a fee-body, it does not matter whether you consider it as a shear wall or... perhaps a beam.

Treat the shear wall as if it were a fixed-end/ cantilevered end beam, or as a fixed-end/ fixed-end beam undergoing translation.

 

[faisal25]

Thank you rlflower,

I meant by “divide the basic shear force between the R.C shear walls and the framing system”; is there is a need to share the lateral load resistance between the shear wall and the framing system. In order to determine the design forces on columns and beams from lateral load.

Or it’s ok to use the same basic shear used in the design of the shear wall and distribute it over the height of the structure when designing the framing system component.

 

[rlflower]

OK, a little more clarity:

Are you saying that you have a concrete frame in line with - and attached to - a series of concrete shear panels?

Assuming this is the case, I would think that the dominant system should be designed for the entire lateral force. I am assuming that the dominant lateral force system in this case is the concrete frame system. The shear panels that comprise the stairwell would be considered as a sub-system that is intended only for the stability of the stairwell and not attributing to the lateral stability of the main structure. A subsequent analysis should then be made to determine the detrimental effects upon the shear panels (if any) due to the drift and distortion of the frame system. Ideally, this sub-structure should be rendered entirely structurally separate from the main structure. Keep in mind the structural intent to ensure the safety of pedestians using the stairway during a seismic event.

I am basing this approach upon what I have seen in parking garages in Southern California. I do not know what your building code says about the feasibility of a concrete frame for an inhabitable structure; give some thought of what it would feel like on the top floor when the building drifts due to wind or seismic activity.

 

[GraemeL]

I would be tempted to look at your problem another way.

I am writing this in an 8 storey building whose lateral load resisting system comprises of a central core that houses two lift shafts and two stair wells. The rectangular box gives four shear walls with one side punctured at each floor by the doors to the stair wells and lifts. Around the perimeter are columns and beams only taking their share of the gravity load.

If you have a mix of shear walls and moment resisting frames, you can determine the load for each system by considering their relative stiffness's. However, the two systems have a different deflection response to lateral load and a shear wall can oppose a moment-resisting frame at upper floors. For more detailed information, see either:

"Interaction of shear walls and frames", Khan & Sbarounis, Journal of the Structural Division, ASCE Vol 90 ST3 June 1964.

"Design of Combined Frames and Shear Walls", Advanced Engineering Bulletin No. 14, Portland Cement Association, 1965.

ACI Committee 442, "Response of Buildings to Lateral Forces", Journal ACI, Vol. 68 No. 2 February 1971, pp 81-106.

Being at a university, you should have access to one of these.

 

[faisal25]

Thank you all for your help;
Since I think the second approach is more feasible (to design each of the framing system and the shear panels for their share of the load).
But how is analysis of the framing system + shear walls will be carried, is their a software to this kind of analysis.

 

[jedge]

faisal25

I agree with GraemeL. The relative stiffnes of the shear walls and moment frames should determine how lateral loads are distributed to the individual elements. On a recent 18 story concrete structure in a 140 mph wind zone, I utilized RISA 3D to model the structure and found load distribution between moment frames and shears walls that was consistent with the 1965 PCA Bulletin that was recommended by Graemel. Basically, the relative stiffness of the elevator and stair cores far out weighed the moment frames. Since I had rigid diaphragms to distribute the loads, I was basically able to design the shear walls to resist all of the lateral loads and let the moment frames carry only gravity loads.

The trouble with using this sort of finite element analysis program for concrete analysis is that you must make some assumptions about the effective moment of inertia of the individual elements. After you get design moments for these elements, you must confirm that your assumed moment of inertias are appropriate.

 

[rlflower]

My comment here has to do with the common difference between the thought process of engineering persued in a University environment versus the thought process of engineering in the "real world."

With all due respect to those of you in engineering programs at our respected universities, field experience is what directs the changes in the building code far more than does mathematical analysis.

Field experience shows us what happens when engineers believe their numbers more than mother nature. The numbers hide our blindness to real problems with the way we tend to construct our buildings.

Based upon my 14 years as an engineer, and based upon what I have seen as a result of the 1994 Northridge earthquake, I have to disagree with your decision to assume that systems with different rigidity will "share" the load.

Pay attention to rigidity! The more rigid elements will be the first elements to attempt to resist the lateral drift - all on their own - before the less rigid - albeit stronger - elements are even engaged. If the more rigid elements do not have the capacity to resist ALL the lateral force, then they will fail - then the less rigid elements are engaged.

Every engineer - me included - needs field experience to challenge and correct our thought process. After the next disater strikes, I challenge each one of you to get out and look at the damage with your own eyes. It is a lesson well learned, and you will never forget it.

 

[faisal25]

In order to determine the dominate system we need to determine the more rigid of the two systems (walls or the framing system) But when we can make that call; when one of the system is two or three times as rigid as the other system?
Or if the difference in rigidity is small we design the two systems to the same load!
Why not to design the two systems for the complete force

 

[kayah]

Each element in the structural system will resist a "share" of the lateral load, but the amount of the load that each element attracts will be proportional to its stiffness (assuming rigid diaphragm etc).
As a shear wall is (generally) much stiffer than a rigid frame, the contribution of the rigid frame will be very small. So small that the contribution is usually taken to be zero. Therefore you are left with the shear wall system resisting all of the lateral loads. If the walls are not strong enough they will fail before the capacity of the frame is engaged as outlined above. It might help to think of the relative displacement of the wall vs. frame (again proportional to the stiffness)
If the relative stiffness of the wall:frame is indeed 3:1, then the loads carried by each can be proportioned accordingly (ie the frame will take 1/4 of the load). Same goes for walls of different sizes(different stiffnesses).
Also pay attention to the centre of stiffness & torsional effects.

 

[jheidt2543]

rlflower's comments are at the heart of most engineering problems, field experiance. When I graduated from engineering school I could design a building's structure, but I couldn't build one. Our designs must be buildable! How many times have you seen plans with details so complex or cobbled up that they couldn't be built in the field? Our designs must be buildable!

Also, rlflower's comments raise the question of whether it is advisable to mix structural systems. My intuition would tell me that if you use a moment frame or a shear wall shaft, stick with it throughout the design. It is not a question of whether it can be done by mixing systems, it is a question of design consistantcy. Why mix systems and have to try to figure out a complex load path? Avoid possible, keep it simple and consistant.

All this is even more complicated when you consider how theoretical our building codes are becoming. Yes, they have to accomadate a lot of situations, but just take the new ACI 318-02 code Appendix D for anchor bolts. There are four (4) different values for phi depending on certain conditions. Why? Is there REALLY that much difference between .60, .65, .70 and .75 when considering an anchor bolt? (I think these are correct, I don't have the code next to me right now, it is under my pillow so I can dream about it! But you get the idea.)

 

[kayah]

I agree with you there jheidt2543.

 

[rlflower]

The idea of mixing systems is not commonly accepted. By that, I mean you have to "sell" the idea to the plan-check engineer - who represents the local jurisdiction, and is not about to stick his neck out.

The basic philosophy that permeates structural engineering today is: "keep it simple." You just can't fool mother nature - she always takes the path of least resistance. She doesn't always follow our theories. She hasn't attended our universities. However, she is consistant. Field experience teaches us of her unfailingly consistant behaviour as she encounters our various structures. Our structures respond differently to her consistant behaviour simply because each engineer thinks and designs differently. And if any engineer thinks he or she can out-fox mother nature, that engineer will in due time be taught a very valuable lesson in the "school of hard knocks."

So, that being said, the plan checker is going to ask you to keep it simple. He will not tell you how to build your lateral system, but he will ask for a clearly and easily definable lateral system.

I guess I am saying that, by comparrison to the real world, I haven't learned much in my college days. But, it was a start in the right direction. The Dean of my college once said, "The most valuable lesson you learn in college is to learn how to learn." College introduces you to the disipline of learning - the real world is where you really learn.