Are these the same? if so, why there are two equations given? is there a specific purpose? like, combining the equations for the ease of calculation etc?
Why there are two equations to calculate effective depth for concrete beams?
You show the answer.
As the conditions are changed based on "less than or equal to" a given value or above it.
The referenced Eurocode equations 7.16(a) & 7.16(b) are part of a “simplified” procedure for limiting deflection of reinforced concrete beams to the limits specified in sections 7.4.1(4) and 7.4.1(5) of the code. The applicability of the equations is based on the relative values of the required tension reinforcement ratio p of beams under design loads to a reference reinforcement ratio p0. These two values are used in inequalities for each equation that define which equation is applicable. Another observable difference between the two equations that is that 7.1.6(b) appears to be applicable to doubly-reinforced concrete. There is apparently some confusion among Eurocode users surrounding the use of this procedure.