Analysis and Design concept of doubly reinforced beam section

Analysis and Design concept of doubly                  reinforced beam section 

Design Steps

Step 1: Find Mu-limit and At1

𝑀𝑢−𝑙𝑖𝑚𝑖𝑡−𝑐𝑜𝑛𝑐𝑟𝑒𝑡𝑒 = 0.36𝑓𝑐𝑘𝑏𝑥𝑚(𝑑 −0,42𝑥𝑚)

Use 𝐶1 = 𝑇1 to find At1 where 𝐶1 = 𝑜. 36𝑓𝑐𝑘𝑏𝑥𝑚 and 𝑇1 = 0.87𝑓𝑦𝐴𝑡1

At1 = Area of tension steel corresponding to a balanced singly reinforced beam

Step 2: Check for doubly reinforced section and find Asc

If (𝑀𝑢 − 𝑀𝑢𝑙𝑖𝑚𝑖𝑡) > 0, 𝑡ℎ𝑒𝑛 𝑔𝑜 𝑓𝑜𝑟 𝑑𝑜𝑢𝑏𝑙𝑦 𝑟𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑒𝑑 𝑠𝑒𝑐𝑡𝑖𝑜𝑛

Use 𝑀𝑢 − 𝑀𝑢−𝑙𝑖𝑚𝑖𝑡 = (𝜎𝑠𝑐 − 𝜎𝑐𝑐)𝐴𝑠𝑐(𝑑 − 𝑑′) to find Asc

Step 3: Find At2𝐶2 = 𝑇2

(𝜎𝑠𝑐 − 𝜎𝑐𝑐)𝐴𝑠𝑐 = 0.87𝑓𝑦𝐴𝑡2

Step 4: Find At 𝐴𝑡 = 𝐴𝑡1 + 𝐴𝑡2

Step 5: Check for minimum reinforcement

𝐴𝑏𝑑 =

0.85

𝑓𝑦

Step 6: Check for maximum reinforcement

𝐴𝑚𝑎𝑥 = 0.04𝑏𝐷

Step 7: Detailing of reinforcement