According to Witney's theory, the maximum depth of the concrete stress block in a balanced reinforced concrete beam section of depth d is 0.53d.

Explanation:
1. Balanced Reinforced Concrete Beam:
A balanced reinforced concrete beam refers to a beam in which both the concrete and steel reinforcement reach their maximum stress capacity at the same time. In other words, the steel reinforcement is not stressed to its maximum capacity before the concrete reaches its maximum capacity.

2. Whitney's Theory:
Whitney's theory is used to determine the maximum depth of the concrete stress block in a balanced reinforced concrete beam. According to this theory, the depth of the concrete stress block is a function of the tension steel ratio (ρ) and the compressive strength of concrete (fc).

3. Maximum Depth of Concrete Stress Block:
The maximum depth of the concrete stress block is given by the equation:
x = 0.53d

where,
x = depth of the concrete stress block
d = overall depth of the beam

4. Significance of 0.53:
The value 0.53 represents the ratio of the strain in the steel reinforcement at maximum stress to the strain in the extreme compression fiber of the concrete at maximum stress.

5. Derivation:
To derive the equation for the maximum depth of the concrete stress block, various assumptions and calculations are made based on the equilibrium and compatibility of stresses within the beam.

6. Limitations:
It is important to note that Whitney's theory is an approximate method and is based on certain assumptions. It does not consider the distribution of stress within the concrete stress block and assumes a rectangular stress block shape.

7. Practical Application:
The maximum depth of the concrete stress block is a crucial parameter in the design of reinforced concrete beams. It helps determine the amount of steel reinforcement required and ensures the beam is designed to withstand the applied loads and bending moments.

In conclusion, according to Whitney's theory, the maximum depth of the concrete stress block in a balanced reinforced concrete beam section of depth d is 0.53d. This value is derived based on certain assumptions and is used in the design of reinforced concrete beams to ensure structural stability and load-carrying capacity.