The correct answer is $\boxed{\text{B. 233 cm}}$.
The breadth of the flange is the distance from the top of the beam to the bottom of the flange. The clear cover is the distance from the top of the beam to the bottom of the tensile steel. The width of the beam is the distance from one side of the beam to the other.
The breadth of the flange is equal to the width of the beam plus twice the clear cover plus the depth of the beam. In this case, the width of the beam is 20 cm, the clear cover is 13 cm, and the depth of the beam is 23 cm. Therefore, the breadth of the flange is $20 + 2 \times 13 + 23 = 233$ cm.
Option A is incorrect because it is the width of the hall. Option C is incorrect because it is the distance between the adjoining beams. Option D is incorrect because it is the depth of the beam.