Design of Singly Reinforced Beam -Working Stress Method

Design of Singly Reinforced Beam -WSM
 Design Problems: 

 Design a R.C beam to carry a load of 6 kN/m inclusive of its own weight on an effect span of 6m keep the breath to be 2/3 rd of the effective depth .the permissible stressed in the concrete and steel are not to exceed 5N/mm2 and 140 N/mm2 .take m=18. 

 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 = (w.l2 )/8 = (6x62 )/8 = 27kNm

 M = Qbd2 d 2 = M/Qb = (27x106 )/ (0.84x2/3xd) d = 245mm. 

Step 3: Balanced Moment. Mbal = Qbd2 = 0.84x245x3652 = 27.41kNm. > M. it can be designed as singly reinforced section. 

Step 4: Area of steel. Ast = Mbal / (σst.j.d) 616.72mm2 

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

No. of bars = Ast/ast = 616.72/314.15 = 1.96 say 2nos. 

 Provide 2#20mm dia bars at the tension side.

Design a beam subjected to a bending moment of 40kNm by working stress design. Adopt width of beam equal to half the effective depth. 

 Assume the permissible stressed in the concrete and steel are not to exceed 5N/mm2 and 140 N/mm2 .take m=18. 

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 resistanceCoefficient Q σbc/2. n. j 0.84

 Step 2: Moment on the beam. 

M = 40kNm 

M = Qbd2 

d2= M/Qb 

= (40x106 )/ (0.84x1/2xd) 

 d = 456.2 say 460 mm. 

b = ½ d = 0.5x460 = 230mm 

 Step 3: Balanced Moment. Mbal = Qbd2 

= 0.84x230x4602 = 40.88kNm. > M. it can be designed as singly reinforced section. 

Step 4: Area of steel. Ast = Mbal / (σst.j.d) 

=(40.88x106 )/(140x0.87x460) = 729.64mm2 

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

No. of bars = Ast/ast = 729.64/314.15 = 2.96 say 3nos. 

 Provide 3#20mm dia bars at the tension side. 

Determine the moment of resistance of a singly reinforced beam 160X300mm effective section, if the stress in steel and concrete are not to exceed 140N/mm2 and 5N/mm2 .effective span of the beam is 5m and the beam carries 4 nos of 16mm dia bars. Take m=18.find also the minimum load the bam can carry. Use WSD method.

Step 1: Actual NA. 

b xa2 /2 = m.Ast.(d- xa) 160. xa2 /2 

= 18 X 804.24(300 –xa) Xa = 159.42mm 

Step 2: Critical NA. 

xc σbc.d/(σst/.m + σcbc) 117.39mm < Xa 159.42mm it is Over reinforced Section. 

Step 3: Moment of Resistance 

M =(b. xa/2 .σcbc )(d- xa/3) 

= (160x159.42/2x5)(300-159.42/3)

 = 15.74kNm

 Step 4: Safe load. M = (w.l2 )/8 W = (8 x 15.74)/52 = 5.03 kN/m