Design of Doubly Reinforced Section

The design of the doubly reinforced section is discussed in this article. The basic steps that need to be followed are simply explained for ease of understanding. There are different methods discussed in the literature with the inclusion of different notations. However, all the methods give the same answer though they appeared different in presentation.

1. The value of x/d = 0.5; will be considered for all the calculations : Information.
2. Calculated the Effective Depth (d) based on the cover, assumed link and bar diameters.
3. Calculated the depth to compression bars (d’)
4. Calculate the K = M / ( b d² f_ck ); where the “M” is the applied bending moment, “b” is the width of the beam, “d” is the effective depth and “fck” is characteristic cylinder strength of the concrete.
5. Check K > K’ = 0.167. If this is satisfied, the section need to be design as doubly reinforced or otherwise, it shall be designed as a singly reinforcement section as discussed in a different article.
6. Calculated the d’/d ratio and check whether it is less than 0.171. If this is satisfied, it can be considered as the compression reinforcement has yielded. This expression was derived considering the x/d = 0.45. Further, there are other various methods to check the yielding of compersion reinforcements. It is recommended to do the verification before proceeding with the reinforcement calculations.
7. Calculated area of Compression reinforcement for the equation give in step 8
8. As’ =(K-K’) f_ck b d² / [ 0.87 f_yk (d-d’)]
9. Find the lever arm; Z = d [ 0.5 + √ (0.25 – K / 1.134)] from this equation considering K = K’ = 0.167 or using the equation Z = 0.82d which is derived for balance condition considering x/d = 0.45
10. Check Z < 0.95d, if satisfy, use the same or otherwise use Z = 0.95d
11. Calculated the tension reinfrocement requiment from the equation givein in the Step 12
12. As = [K’ f_ck b d² / 0.87 f_yk Z] + As’
13. Check for minimum reinforcements; A_{s provided} > 0.26 (f_ctm / f_yk )bd but not less than 0.0013bd, where f_ctm is the mean value of axial tensile strength of concrete to be obtained from Table 3.1: Strength and deformation characteristics for concrete of Eurocode 2.
14. Check the Maximum reinforcements; (100 A_{s provided} /A_c) < 4