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.

 

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

Design of RCC Slab -Limit Stress Method

Design of RCC Slab -Limit Stress Method

Design an interior panel of RC slab 3mX6m size, supported by wall of 300mm thick. Live load on the slab is 2.5kN/m2 .the slab carries 100mm thick lime concrete (density 19kN/m3 ).Use M15 concrete and Fe 415 steel.

Step 1: Type of Slab. ly/lx = 6/3 = 2 = 2.

it has to be designed as two way slab.

 Step 2:Effective depth calculation. 

For Economic consideration adopt shorter span to design the slab.

 d = span/(basic value x modification factor) 

= 3000/(20x0.95) = 270mm

 D = 270 + 20 + 10/2 = 295mm 

Step 3: Effective Span. 

For shorter span: Le = clear span + effective depth

 = 3000 + 270 = 3.27m 

(or) 

 Le =c/c distance b/w supports = 3000 + 2(230/2) =3.23m

Adopt effective span = 3.23m least value.

 For longer span: 

Le = clear span + effective depth = 6000 + 270 = 6.27m

 (or)

 Le =c/c distance b/w supports 

= 6000 + 2(230/2) = 6.23m 

 Adopt effective span = 6.23m least value. 

Step 4: load calculation 

Live load = 2.5kN/m2 

Dead load = 1x1x0.27x25 = 6.75kN/m2 

Dead load = 1x1x0.1x19 = 1.9kN/m2 

Floor Finish = 1kN/m2 

Total load = 12.15kN/m2 

Factored load = 12.15 x 1.5 = 18.225kN/m2 

Step 5: Moment calculation.

 Mx αx . w . lx 0.103x18.225x3.23 = 9.49kNm 

 My αy . w. lx 0.048 x18.225x3.23 = 4.425kNm 

Step 6: Check for effective depth. 

M = Qbd2

 d2 = M/Qb = 9.49/2.76x1 = 149.39mm say 150mm.

 For design consideration adopt d = 150mm. 

Step 7: Area of Steel. 

For longer span: 

Mu = 0.87 fy Ast d (1- (fy ast)/(fck b d)) 

4.425x106 = 087x415xAstx150(1-(415 Ast)/(20x1000x150))

 Ast = 180mm2 

Use 10mm dia bars 

Spacing ,S = ast/Astx1000 = (78.53/300)1000 = 261mm say 260mmc/c 

 Provide 10mm dia @260mm c/c.

 For shorter span: 

Mu = 0.87 fy Ast d (1- (fy ast)/(fck b d))

 9.49x106 = 087x415xAstx150(1-(415 Ast)/(20x1000x150)) 

Ast = 200mm2 Use 10mm dia bars Spacing ,

S = ast/Astx1000 = (78.53/300)1000 = 281mm say 300mmc/c 

 Provide 10mm dia @300mm c/c