Structural Madness

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 type of failure: 1. Ductile Failure 2. Brittle Failure Image showing significant cracking in tension and still the compression block is not showing any kind of failure. This can lead to ductile failure which is our priority Now, in case of a brittle failure when the beam gets overstressed, then till the point of over-stressing you will not see any major cracks in 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 strength of steel is less than

Urbanization is on it's peak and we, as the resident of that particular city, would like to commute as little as possible to our work on daily basis. So the only option that we do have is to accommodate more and more people into as little area as possible and the only ways we can achieve is to either increase the height or increase the depth of the building. But yes, nobody would like to live underground for the rest of their lives. That narrows down to one option and that is to go tall. But there is a problem.!! Let us say we have about a 10000 sq.ft of land and you are told to design a building. First a 10 story building. You design it quite comfortably for wind as well as seismic you don't see any funny things going on until out building is fairly regular such that it's center of mass and center of rigidity coincides with each other. Now, you are asked to design for 15 story, you still are able to do it but you forces increase and you are looking for sufficient resis