Design of simply supported Slab Name of work:1 Room size 2 Wall width 3 External Load 4 Lime concrete thickness 4 Concrete mscbc fy PKN 4.00 0.3 2500 0.10 20 7 415 20 10 8 mtr N/m2 m lime weight of concrete Unit weight concrete m Tensile stress Effective cover 130 230 19000 25000 13.3 230 25 mm c/c mm c/c N/m N/m3

x 300

6.00 mm

metre

Grade 2 N/mm N/mm mm mm F mm F2

3

5 Steel 6 Nominal cover 7 Bottom Main reinforcement 8 Distribution reinforcement

N/mm mm

2

300 10 mm f @ 130 mm c/c

4000 mm 8 mm F @ 230 mm c/c

300

179 mm 800 (a) Section 800

Bars A Bars B (b) Bar bending procedure

800 130

800

(D)plan (dotted lines show bentup portion of bars)pk_nandwana@yahoo.co.in

Design of simply supported Slab 1 2 3 4 4 Room size Wall width External load Lime concrete thickness Concrete 4.00 0.30 2500 0.10 M 20 scbc 7 fy x 6.00 mtr mtr N/m2 m Lime concrete wt Unit weight concrete N/mm2 m

= = = =

300 mm3 #### N/m 3 #### N/m 13.3 2 230 N/mm 25 mm

5 Steel 9 Nominal Cover

2 415 N/mm 20 mm

Tensile stess = Effective cover

1 Design Constants:- For HYSD Bars sst = = 230 N/mm2 N/mm3 scbc = = 7

Cocrete M = 20 wt. of concrete

2 = 25000 N/mm

mk= j=1-k/3 R=1/2xc x j x k

= 13.33m*c

m*c+sst = 1 = 0.5 x

=

13.33 13.33 x 0.289 / 7 x

x 7 3

7 +

230

= 0.289 = 0.904

0.90 x

0.289 =

0.913

2 Caculcation of B.M. :The slab will eidently bend over a clear span of Let the over all depth of slab = 4000 / 24 = 167 mm and approximate Effective depth = 167 25 = 142 Hence Effective span = 4.00 + 0.14 = 4.14 Load due to self weight of Slab = 1 x 1.00 x 0.17 Load due to lime concrete finish = 1 x 1.00 x 0.10 Super imposed live load = 1 x 1 x 2500 \ Total load per meter run = 4167 + 1900 + 2500 8567 x 4.14 wl2 Toatl U.D.L. (w) per metre run of slab = = 8 8 WL 8567 x 4.00 V = = 2 2 3 Design of section :taking 1.0 m width for calculation purpose. 18368 x 1000 BM = 0.913 x 1000 Rxb stiffness (or deflection) point of veiw, span / effective depth ratioo kscbc = x 100 For a balance design, percentage reinforcement 2 sst = 0.44 % steel f s = 0.58fy = 0.58 x 415 For Fe = 415 Hence from fig modification factore span span = 20 x 1.3 = 26 Hence d = d 26 keep over all d = 159 + 20 = 179 effective d = 179 Effective depth required = 4 Main Reiforcement :Ast =BM sst x j x D= =

=

4.00 mtr

mm say = 0.14 m m < 4.30 c/c distance x #### = 4167 N/m x #### = 1900 N/m = 2500 N/m N/m = 8567 N/m2

= 18368 = 17133

N-m/m

N-m at the face of supprots

= =

142

mm

20 0.289 x 7 = x 100 x 230 2 241 mm2 1.30 4142 = = 159 mm 26 20 4 = 155 mm = =

18368.00 x 230 x 0.90 x =

This is more than the minimum reinforcement usingpk_nandwana@yahoo.co.in

1000 155 0.12

= x

570

mm2

10 mm f bars

Pitch s = =

3.14xdia2 = 4 x100 1000 x As /A = 1000 x 79 / Hence Provided 10 mm F bar, A =

179 x 1000 = 215 mm2 100 3.14 x 10 x 10 = 79 mm2 4 x 100 570 = 137.7 say = 138 mm 130 mm

Actual provided

79 604 x 100 x = 604 % of reinforcement = = 0.337 % 130 1000 179 It is to be noted that the above pitch is less than 3 time depth of slab = 3 x 179 = 537 mm or 130 < 537 mm Bend every alternative bars at supports . At a distance of L/5 = 4142 / 5 = 800 mm from the edge of supports. which is more than 1 x 604 Ast at supports. = = 302 mm or 0.17 % minimum.12% 2 = 1000

6 Check for devlopment length and shear at supports:The code stipulates that at the simple supports, where reinforcement is confined 1.3xM1 by a compressive reaction, the diameter of the reinforcement be such that + L0 > Ld V where M = 230 x 302 x 0.904 x 155 = 9730552 v = 17133 N Let us assume that nominal cover of = 20 mm is provided at side (end) and the slab has a support of = 300 mm width ls Providing 90 degree bend, =( x' + 3f ) 2 300 =( 20 + 3 x 10 )= 160 mm 2 1.3 xM1 9730552 L0 + = 1.3 x + 160 = 898 mm 17133 V 10 230 f s st x Devlopment length Ld = = = 449 mm 4 tbd 4 x( 1.6 x 0.8 ) Alternatively, Ld = 45 F = 45 x 10 = 450 mm Thus = = 1.3x 898 M1 V > + 450 L0 > Ld

Hence Code requirement are satisfied

Note:the reinforcement should extend by a length equal to Ld/3 449 / 3 = 150 mm = Beyond the face of supports. This suggests that the width of support not be less than 125+25'=150mm . in the present case . The supports width is = 300 mm 17133 V concrete For M 20 tv = = = 0.111 N/mm2 p'= 0.17 % \ tc = 0.18 N/mm2 bxd 1000 x 155 than permissible value of tc this is < = 1.3 x 0.18 = 0.23 N/mm2 Hence safe 7 Distribution reinforcement:Ast = using 8 .12 xb xd 100 mm bars A = =

0.12 x

1000 x 100

179

=

215

mm2

3.14xdia2 3.14 x 8 x 8 = = 50 mm2 4 x100 4 x 100 Pitch s = = 1000 x As /A = 1000 x 50 / 215 = 233.7 say = 234 mm the above pitch is less than 5 time depth of slab and also less than = 450 mm. Hence provided Hence provided = 8 mm bars @ 230 mm c/c. Near the edge of supports, the distribution reinforcement may be provided both at top as well as the bottom. 8 Reinforcement detail shown in drawing

pk_nandwana@yahoo.co.in

Room size 300

4.00

x

Design of simply supported Slab 6.00 metre 4000 mm 8 mm F @ 230 mm c/c 300

10 mm f @ 130 mm c/c

166.6667 mm 800 wall supports (a) Section 800 wall supports

Bars A Bars B (b) Bar bending procedure 10 mm f @ 130 mm c/c 8 mm f @ 230 800 130

mm c/c 800

(D)plan (dotted lines show bentup portion of bars)

VALUES OF DESIGN CONSTANTSGrade of concrete Modular Ratio M-15 18.67 5 93.33 0.4 0.867 0.867 0.714 0.329 0.89 0.732 0.433 0.289 0.904 0.653 0.314 0.253 0.916 0.579 0.23 M-20 13.33 7 93.33 0.4 0.867 1.214 1 0.329 0.89 1.025 0.606 0.289 0.904 0.914 0.44 0.253 0.916 0.811 0.322 M-25 10.98 8.5 93.33 0.4 0.867 1.474 1.214 0.329 0.89 1.244 0.736 0.289 0.904 1.11 0.534 0.253 0.916 0.985 0.391 M-30 9.33 10 93.33 0.4 0.867 1.734 1.429 0.329 0.89 1.464 0.866 0.289 0.904 1.306 0.628 0.253 0.914 1.159 0.46 M-35 8.11 11.5 93.33 0.4 0.867 1.994 1.643 0.329 0.89 1.684 0.997 0.289 0.904 1.502 0.722 0.253 0.916 1.332 0.53 M-40 7.18 13 93.33 0.4 0.867 2.254 1.857 0.329 0.89 1.903 1.127 0.289 0.904 1.698 0.816 0.253 0.916 1.506 0.599 Grade of concrete tbd (N / mm2)

scbc N/mm2 m scbc(a) sst = 140 N/mm2 (Fe 250) (b) sst = 190 N/mm2 (c ) sst = 230 N/mm2 (Fe 415) (d) sst = 275 N/mm2 (Fe 500) kc jc Rc Pc (%) kc jc Rc Pc (%) kc jc Rc Pc (%) kc jc Rc Pc (%)

Permissible shear stress Table tv in concrete (IS : 456-2000)100As bd < 0.15 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.753.00 and above

Permissible shear stress in concrete M-15 M-20 M-25 M-30 0.18 0.18 0.19 0.2 0.22 0.22 0.23 0.23 0.29 0.30 0.31 0.31 0.34 0.35 0.36 0.37 0.37 0.39 0.40 0.41 0.40 0.42 0.44 0.45 0.42 0.45 0.46 0.48 0.44 0.47 0.49 0.50 0.44 0.49 0.51 0.53 0.44 0.51 0.53 0.55 0.44 0.51 0.55 0.57 0.44 0.51 0.56 0.58 0.44 0.51 0.57 0.6

tv N/mm2 M-35 M-40 0.2 0.2 0.23 0.23 0.31 0.32 0.37 0.38 0.42 0.42 0.45 0.46 0.49 0.49 0.52 0.52 0.54 0.55 0.56 0.57 0.58 0.60 0.60 0.62 0.62 0.63

Maximum shear stress tc.max in concrete (IS : 456-2000)Grade of concrete

tc.max

M-15 1.6

M-20 1.8

M-25 1.9

M-30 2.2

M-35 2.3

M-40 2.5

Shear stress tc 100As M-20 bd 0.14 0.17 0.15 0.18 0.16 0.18 0.17 0.18 0.18 0.19 0.19 0.19 0.2 0.19 0.21 0.2 0.22 0.2 0.23 0.2 0.24 0.21 0.25 0.21 0.26 0.21 0.27 0.22 0.28 0.22 0.29 0.22 0.3 0.23 0.31 0.23 0.32 0.24 0.33 0.24 0.34 0.24 0.35 0.25 0.36 0.25 0.37 0.25 0.38 0.26 0.39 0.26 0.4 0.26 0.41 0.27 0.42 0.27 0.43 0.27 0.44 0.28 0.45 0.28 0.46 0.28 0.47 0.29 0.48 0.29 0.49 0.29 0.5 0.30 0.51 0.30 0.52 0.30 0.53 0.30 0.54 0.30 0.55 0.31 0.56 0.31 0.57 0.31 0.58 0.31 0.59 0.31 0.6 0.32 0.61 0.32

Reiforcement % 100As M-20 bd 0.17 0.14 0.18 0.15 0.19 0.18 0.2 0.21 0.21 0.24 0.22 0.27 0.23 0.3 0.24 0.32 0.25 0.35 0.26 0.38 0.27 0.41 0.28 0.44 0.29 0.47 0.30 0.5 0.31 0.55 0.32 0.6 0.33 0.65 0.34 0.7 0.35 0.75 0.36 0.82 0.37 0.88 0.38 0.94 0.39 1.00 0.4 1.08 0.41 1.16 0.42 1.25 0.43 1.33 0.44 1.41 0.45 1.50 0.46 1.63 0.46 1.64 0.47 1.75 0.48 1.88 0.49 2.00 0.50 2.13 0.51 2.25

0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13

0.32 0.32 0.32 0.33 0.33 0.33 0.33 0.33 0.34 0.34 0.34 0.34 0.34 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.36 0.36 0.36 0.36 0.36 0.36 0.37 0.37 0.37 0.37 0.37 0.37 0.38 0.38 0.38 0.38 0.38 0.38 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.4 0.4 0.4 0.4 0.4 0.4

1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64 1.65

0.4 0.4 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.46 0.46 0.46

1.66 1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.90 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17

0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.50 0.50 0.50 0.50 0.50

2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.60 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69

0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51

2.70 2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.80 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.99 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 3.13 3.14 3.15

0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51

Permissible Bond stress Table tbd in concrete (IS : 456-2000)Grade of concreteM-10 -tbd (N / mm2) M-15 0.6 M-20 0.8 M-25 0.9 M-30 1 M-35 1.1 M-40 1.2 M-45 1.3

Development Length in tensionGrade of concrete M 15 M 20 M 25 M 30 M 35 M 40 M 45 M 50 Plain M.S. Bars tbd (N / mm2) 0.6 0.8 0.9 1 1.1 1.2 1.3 1.4 kd = Ld F 58 44 39 35 32 29 27 25 0.96 1.28 1.44 1.6 1.76 1.92 2.08 2.24 H.Y.S.D. Bars tbd (N / mm2) kd = Ld F 60 45 40 36 33 30 28 26

Permissible stress in concrete (IS : 456-2000)Grade of concrete M M M M M M M M M 10 15 20 25 30 35 40 45 50 Permission stress in compression (N/mm 2) Permissible stress in bond (Average) for Bending acbc Direct (acc) plain bars in tention (N/mm2) (N/mm2) 3.0 5.0 7.0 8.5 10.0 11.5 13.0 14.5 16.0 Kg/m2 300 500 700 850 1000 1150 1300 1450 1600 (N/mm2) 2.5 4.0 5.0 6.0 8.0 9.0 10.0 11.0 12.0 Kg/m2 250 400 500 600 800 900 1000 1100 1200 (N/mm2) -0.6 0.8 0.9 1.0 1.1 1.2 1.3 1.4 in kg/m2 -60 80 90 100 110 120 130 140

00)M-50 1.4 fy = 120 fy =145 1.6 1.2 0.8 0.4 fy =190 fy =240 fy = 290

2.0

0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.0