WHAT IS A COUPLING BEAM?

Coupling beams are a very important member of a lateral force-resisting system. It couples or you can say combines two independent systems.

Let us say there are two buckets, one completely filled with water and the other is half-filled now you have to level up the amount of water in both the buckets without lifting up the bucket and I will give you a small flexible tube to connect the bucket. What will you do? 

You will connect both the buckets and considering the siphon action you can transfer water from a filled bucket to the half-filled bucket.

Similar to this effect when you have two independent shear walls or concentrically braced frames or anything that is helping you to resist lateral loads and you want to connect them to reduce the overturning effect or increase the overall stiffness of the system then you will use a coupling beam to connect both the systems.

As shown in the image, it is connecting two individual piers of the shear core. Imagine the deformation of the shear wall when a lateral load is applied from left to right and they were not coupled (connected). 

Both piers will move independently without any harmony and this will further complicate the behaviour so to make them a solid core we use the coupling beam to transfer force from one pier to another.

As seen in the image, while deforming the extreme ends of wall piers experience tension and compression. If we couple the system, these tension and compression forces transfer through the coupling beam as a shear force for which the beam is designed. 

The stiffness of the coupling beam plays an important role in adding the stiffness of the system. But can we make a coupling beam very stiff? 

No, because there is one more important role that a coupling plays during an earthquake. It acts as a fuse or a source of energy dissipation. It undergoes cyclic deformations as the wall rock back and forth and resists the seismic force. 

When hysteresis loops of the moment experienced by beam versus rotation also called the cyclic curve, it looks something like as shown in the image.

There are two different types of coupling beams:

1. Conventionally reinforced coupling beam

2. Diagonally reinforced coupling beam

## 1. Conventionally reinforced beam

This is just a regular type of beam with horizontal top and bottom reinforcement and shear ties. This beam is used when the aspect ratio of the beam is large or the beam is pretty long compared to its depth. 

A long beam is a flexible one which means it can form moment hinges at the ends and the failure is ductile. 

Thus the shear reinforcement is generally under control and you can provide a feasible and constructible cross-section of the beam.

## 2. Diagonally reinforced beam

When the beam's aspect ratio is small, say the depth of the beam is very similar to length, then the failure of the beam is shear governed and the beam will see a brittle failure. 

To resist brittle failure, we provide diagonal bars in the coupling beam which will help in resisting shear and will also reduce the amount of shear reinforcement required.

As shown in the image, we would like the core wall to experience a large number of moment forces at the base of the system, but sometimes the core is so big that it does not yield and thus the system becomes inefficient and at that time we can only rely on coupling beams to dissipate all this earthquake energy. 

In a way, they act as the guardian angel of the building. To read more, please go through Professor Wallace's experiments.

DEEP BEAMS & IT'S DESIGN TYPES

 DEEP BEAMS

In most building codes, the conventional approach of shear design of deep

beams are based on some empirical equations in which the nominal shear strength,

Vn, includes two parts: the concrete contribution, Vc, and the steel contribution, Vs.

Separate equations are introduced for both. Though this approach is easy to apply,

it ignores the interaction between Vc and Vs, whereas the strut-and-tie model, STM,

satisfies this goal.

This article explains the design of deep beams, either simply supported, continuous

or corbels, top or bottom-loaded, directly or indirectly supported. 

Let's start with the modelling of simply supported deep beams and continuous deep

beams. Applications to simply supported deep beams are given to cover different

types of models. Bottom loaded deep beams and deep beams with ledge are covered

as well. Deep beams with indirect supports are discussed too. Applications to continuous

deep beams, top or bottom-loaded, are given. The final part of the chapter

is devoted to brackets and corbels, where the modes of failure and modelling of different

corbel problems are discussed. In addition, the detailing of critical nodes is

examined, a step by step design procedure is illustrated, and the assessment of the

web reinforcement of corbels is explained. An example of strength assessment of

double corbel is given at the end.

SIMPLY SUPPORTED DEEP BEAMS

On the basis of the shear span-to-depth ratio, three STMs are considered: Type I,

Type II, and Type III. Types I and II cover deep and short beams, respectively,

and Type III deals with slender beams. In Type I, a direct STM is utilized,

whereas a fan- or arch-action model is used in Type II. The choice between the two

types I and II in some cases is controlled by the shear span-to-depth ratio, a/d, presence

of vertical web reinforcement, and the concrete strength.

CONTINUOUS DEEP BEAMS

In simple deep beams, the region of high shear coincides with the region of low moment. On the other hand, in continuous deep beams, the regions of high shear and high moment coincide and failure usually occurs in these regions. 

Hence, the failure mechanisms of continuous deep beams are different from those of simply supported deep beams. 

Continuous deep beams are divided into two major groups according to their loading conditions: top and bottom loading. 

Top loaded continuous deep beams are commonly used in reinforced concrete buildings, while indirectly loaded or bottom-loaded deep beams are widely used as cross-girders, for example, in concrete

bridges and water tanks. The two groups behave differently under the same applied loads.

CAN A DOUBLY REINCFORCED BEAM BE UNDER-REINFORCED ?

 

To understand the importance and necessity of a doubly reinforced beam, first, we should look at a singly reinforced beam.

A beam when loaded can possibly suffer through two different types of failure:

1. Ductile Failure

2. Brittle Failure

Now, in case of a brittle failure when the beam gets over-stressed, then till the point of over-stressing you will not see any major cracks in the beam, but as the point is passed and suddenly (BAM..!!!) the beam fails. This is no good right? So we always want the beam to fail in a ductile fashion as it will give you more time to see that the beam is over-stressed and it is time that you do some repairs or evacuate the house.

Now how do we make sure that the failure should remain ductile? This can happen only when the tensile strength of steel is less than the compression strength of concrete. This means that when ultimate loads are reached, as the total strength of steel is pretty less than the strength of concrete, steel will try to strain more than what concrete will experience strain in compression. Now we know that steel is ductile and can handle higher strains without any kind of failure. So this is how we get a ductile response of beam. Concrete is all under control while steel is straining itself.

But suppose if I tell you that you cannot use a section greater than say 24" x 24" and you have very high moments to deal with. This high moment will tend to increase the tension steel demand and because of this, a bigger concrete block will be required in compression which will push the neutral axis further down. Now, this is the important part. You may ask yourself that so what if the neutral axis goes further down, I have a whole concrete beam that can take compression. But wait..!!

As the neutral axis starts shifting down, the strains in extreme fibre start to increase and this will be our concern in the case of compression fibre. Concrete is brittle, so at first, it will not show that much impact, but this high value of strain will cause concrete to crushing itself which will lead to ultimate failure and this will be instantaneous. So there you go, you have your answer to why we cannot put more steel than a certain amount.

Now, what decides this limit of steel? Well, it is all an experimental-based approach and to an extent, you can prove it mathematically too, by balancing tension and compressive forces, taking the depth of compression block, then drawing the strains and seeing if the strain in concrete is more than the allowable strain. But if you are designing it, then some codes specify the maximum reinforcement ratio in a beam while some codes specify the maximum possible neutral axis depth that a concrete beam can achieve, if you are under this, then you will see a ductile failure in a beam and you are safe.

Talking about double reinforced beams:

Now as I mentioned before that what if you are limited to a 24" x 24" section and you have a pretty heavy moment and you are exceeding the limits mentioned in the codes, so the only option is to provide compression reinforcement and add some tension steel. Now the extent to which you are adding the compression reinforcement will tell you whether the beam is brittle or ductile.

Suppose the limit on tension reinforcement for a singly reinforced beam is X, and to resist this moment you have to add an additional 0.5X of tension reinforcement. You also decide to add 0.8X of compression reinforcement. So now you have 1.5X of tension reinforcement and 0.8X of compression reinforcement along with the compression stress block. So now what will happen is this 0.8X of compression reinforcement will tend to balance the effect of 0.5X of tension reinforcement. I have added 0.8X of compression reinforcement as the beam does not experience a very high compression strain as it experiences the tension strain. So the compression bars will be under lower stress than their yield point. Thus to balance a fully stressed 0.5X of tension reinforcement I will need a higher amount of compression reinforcement. Now, the concrete block is responsible to resist the X amount of tension reinforcement which is the limit for ductile behaviour. So in this case the doubly reinforced beam will act as a ductile beam and so you can say that it is an under-reinforced section. All good..!!

But suppose you decide to add only 0.4X of compression reinforcement. This will counter a max of 0.4X of tension reinforcement in the worst-case scenario. So now, a plain concrete stress block is responsible to resist 1.1X of tension reinforcement and this is above the limit which will result in brittle failure. So in this case, the beam, even though it is doubly reinforced, will experience a brittle failure which means an over-reinforced section.

To conclude our discussion, not all doubly reinforced sections are under-reinforced. It depends on the trade-off between the amount of compression steel provided as compared to tension steel.