1. Structure II Course Code: ARCH 209 Dr. Aeid A. Abdulrazeg
By :Dr. Aeid A. Abdulrazeg

2. Doubly-reinforced Sections
When the applied design bending moment exceeds the concrete capacity (i.e bd2fcu) compression reinforcement is required.
Consider the rectangular beam shown in Figure in which the neutral axis depth is equal to d/2 and both tension (As) and compression (As′) reinforcement are present:

3. As is the area of tension reinforcement,
As′ is the area of compression reinforcement,
Ft is the force in the tensile reinforcement,
Fc is the compression force in the concrete,
Fcs is the force in the compression reinforcement,
ζcs is the strain in the compression reinforcement,
b, d, fcu and ζs are as before.

4. The force in the compression reinforcement is dependent on the stress and consequently the strain ζcs. In order to ensure that this is greater than or equal to the yield stress, the ratio of (d′ / x) is limited to 0.37 as shown in Figure below:

5. At the yield with Fy =460 N/mm2, the stress strain
ζsc = ζst =
as specified in the code

6. Area of compression reinforcement
Area of tension reinforcement

7. Example 1
The rectangular beam shown in Figure is required to resist an ultimate design bending moment of 340 kN.m. Using the data given, determine the required areas of main reinforcing steel..