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