the effect ---single phasing...  motor oveload protection 
or MCB will trip  and open the circuit.

delta connected winding, one winding burnt off means, its 
open circuited. So the motor will work as open delta system 
and run normaly with non uniform torque.
The max. load that can carry will be reduced to 57.7% of 
full load.
If the motor is connected through a phase faliure relay, 
the relay will trip the total ckt.

In 3phase motor one phase winding is burnt means
>The Motor torque is reduce.
>The motor is overloaded.
>The TPST switch is triped.

a 3 phase motor was running with delta connected, suddenly 
one phase winding got burnt off,this colled as  asingle 
phasing.in this condition motor takes large current from 
suplly.& large current flow in stater winding. so large 
heat produced by stater winding.then burn out motor.

it will run with lesser speed

3 phase motor running delta connection,if one phase got 
burnt means it will work as open delta,it will carry the 
load 57.7 percentage of full load and this is called scott 
connecton.