Equilibrium and Compatibility Torsion

I shall directly talk with an example. Imagine a horizontal cantilever slab on a beam. The beam is subjected to torsion. Let us now release the the beam end connections in torsional direction or imagine it like the beam is a wheel and axle system. We see that the slab immediately falls or rotates about the beam axis and hangs on it vertically. It is because the beam is unable to resist the torsion due to slab. This kind of torsion is equilibrium torsion.

Now take a 4 edge discontinuous slab. The edge beams are again subjected to torsion. Once again consider the beams  to be of wheel and axle system i.e all the torsional degree of freedom are released. We see that the end beam rotates for some angle but the beam/slab system doesn't collapse like in previous case. The equilibrium is still maintained. So this kind of torsion when the joints were not released is compatibility torsion.

unfinished(black) bolts vs finished bolts from BC punima

Unfinished(black) bolts vs finished (turned and fitted) bolts from BC punima

Torsion reduction in beams.

It's hidden in clause 11.5.2 in ACI318-08 (presumably the same in 2011 version) if you read between the lines. 

Equations representing stress strain values of steel rebars.

The equations are derived by third order polynomial curve fitting of the data given in SP-16 table  in Indian code.

For Fe 250:
 y = 10802254950x3 - 47811496.7x2 + 74481.40335x + 205.8829164

For Fe 415:
y = 8634745755x3 - 84776621.6x2 + 284712.3995x + 29.42076793

For Fe 500:
y = 7949113254x3 - 89302413.2x2 + 343343.7433x - 20.40632679