Design of Doubly Reinforced Beam -Working Stress Method

Design of Doubly Reinforced Beam -Working Stress Method

 Design a doubly reinforced beam of section 240X500mm to carry a bending moment of 80kNm.Assume clear cover at top a bottom as 30mm and take m=18.adopt working stress method. Assume the permissible stressed in the concrete and steel are not to exceed 5N/mm2 and 140 N/mm2 . 

Step 1: Design constants.

  Modular ratio, m=18. 

 A Coefficient n σbc.m/(σbc.m + σst) 0.39 

 Lever arm Coefficient, j=1-(n/3) = 0.87 

 Moment of resistance Coefficient Q σbc/2. n. j =0.84 

Step 2: Moment on the beam. M = 80kNm

 M = Qbd2 

D = 500mm, b = 240mm d = 500-30mm = 470mm .

Step 3: Balanced Moment. 

Mbal = Qbd2 = 0.84x240x4702 = 44.53kNm. < M. it can be designed as doubly reinforced section.

 Step 4: Area of Tension steel. 

Ast = Ast1 + Ast2 

Ast1 = Mbal / (σst.j.d) (44.53x106 )/(140x0.87x470) = 777.87mm2 

Use 20mm dia bars ast π/4 (202 ) = 314.15mm2 

No. of bars = Ast/ast = 777.87/314.15 = 2.47 say 3nos. 

Ast2 = (M-Mbal) / (σst.(d-d 1 )) = (80x106 -44.53x106 )/(140x(470-30)) = 575.8mm2 

Use 20mm dia bars ast π/4 (202 ) = 314.15mm2 

No. of bars = Ast/ast = 575.8/314.15 = 1.8 say 2nos. 

 Step 5: Area of Compressionsteel:

 Asc = (M-Mbal) / (σsc.(d-d 1 )) = (80x106 -44.53x106 )/(51.8x(470-30))=1580.65 mm2 

Use 20mm dia bars ast π/4 (202 ) = 314.15mm2 

No. of bars = Ast/ast = 1580.65/314.15 = 5.5 say 6nos. 

 Provide 6#20mm dia bars as compression reinforcement.