beam design acc to sp16

7/27/2019 Beam Design Acc to SP16

1/15

DESIGN OF BEAMS

fy = 415 MPa

ck = 20 MPa

b= 300 mm

D = 500 mm

r Co 25 mm

d = 462.5 mm

d'= 37.5 mm

Mid Span(+ve moment)

Floor embe d(cm) Ref.

1st

34 177.11 24.52 46.25 81.73 0.38 0.108 149.85 180 SP16 Ast provided is for min

35 177.11 22.44 46.25 74.80 0.35 0.099 137.36 180 M n. Re n orcement =

36 177.11 25.48 46.25 84.93 0.40 0.114 158.18 180

37 177.11 22.3 46.25 74.33 0.35 0.099 137.36 180

38 177.11 21.18 46.25 70.60 0.33 0.088 122.10 180

39 177.11 21.14 46.25 70.47 0.33 0.088 122.10 180

41 177.11 50.43 46.25 168.10 0.79 0.232 321.90 321.9

42 177.11 41.76 46.25 139.20 0.65 0.187 259.46 259.5

43 177.11 47.84 46.25 159.47 0.75 0.218 302.48 302.5

44 177.11 32.11 46.25 107.03 0.50 0.143 198.41 198.4

45 177.11 8.95 46.25 29.83 0.14 0.085 117.94 180

46 177.11 35.2 46.25 117.33 0.55 0.158 219.23 219.2

47 177.11 36.63 46.25 122.10 0.57 0.164 227.55 227.6

48 177.11 29.71 46.25 99.03 0.46 0.13 180.38 180.4

49 177.11 32.87 46.25 109.57 0.51 0.145 201.19 201.2

50 177.11 47.88 46.25 159.60 0.75 0.218 302.48 302.5

= 415MPA, fck

= 20MPA, b = 300mm, D = 500mm, d= 462.5mm, Clear. Cover = 25m

Mu,lim

(KNm)u(KNm M

u/b

Mu/

(bd2)(N/mm

2)

pt st

(mm2Ast

provided

Des

ignAidto


2/15

51 177.11 37.34 46.25 124.47 0.58 0.166 230.33 230.3

52 177.11 36.89 46.25 122.97 0.57 0.164 227.55 227.6

53 177.11 36.53 46.25 121.77 0.57 0.164 227.55 227.6

54 177.11 66.9 46.25 223.00 1.04 0.31 430.13 430.1

55 177.11 36.84 46.25 122.80 0.57 0.164 227.55 227.6

56 177.11 72.36 46.25 241.20 1.13 0.337 467.59 467.6

68 177.11 12.530 46.25 41.77 0.20 0.085 117.94 180

378 177.11 41.625 46.25 138.75 0.65 0.187 259.46 259.5

Support(-ve moment)

Floor embeMu(KNm)

d(cm)d'/d Start End St

Start (0) End Start End Start End Pt Pc Pt Pc Ast

1st

34 177.11 140.689 153.83 46.25 2.19 2.40 0.71 0.798 985.125

35 177.11 168.79 168 46.25 2.63 2.62 0.9 0.892 1244.59

36 177.11 213.64 204.53 46.25 3.33 3.19 0.10 0.10 1.13 0.18 1.088 0.139 1569.26

37 177.11 134.15 157.07 46.25 2.09 2.45 0.67 0.819 935.175

38 177.11 152.2 168 46.25 2.37 2.62 0.79 0.892 1090.58

39 177.11 193.78 199.55 46.25 3.02 3.11 0.10 0.10 1.04 0.08 1.063 0.13 1436.06

41 177.11 110.92 99.164 46.25 1.73 1.55 0.54 0.477 749.25

42 177.11 108.94 75.4 46.25 1.70 1.17 0.53 0.349 735.375

43 177.11 94.41 95.6 46.25 1.47 1.49 0.45 0.457 624.375

44 177.11 90.26 82.39 46.25 1.41 1.28 0.43 0.386 596.625

45 177.11 207.9 182.73 46.25 3.24 2.85 0.10 0.10 1.1 0.16 0.983 0.03 1530.41

46 177.11 118.23 127.96 46.25 1.84 1.99 0.96 0.639 1332

47 177.11 194.1 201.21 46.25 3.02 3.14 0.10 0.10 1.04 0.08 1.072 0.13 1436.06

48 177.11 177.65 170.5 46.25 2.77 2.66 0.10 0.96 0 0.91 1329.23

49 177.11 154.62 128.75 46.25 2.41 2.01 0.8 0.644 1112.78

50 177.11 198.2 165.97 46.25 3.09 2.59 0.10 1.06 0.11 0.879 1466.59

IS456

Mu,lim

(KNm)M

u/(bd2)


3/15

51 177.11 152.12 141.48 46.25 2.37 2.20 0.79 0.717 1090.58

52 177.11 153.5 181.35 46.25 2.39 2.83 0.10 0.79 0.977 0.022 1101.68

53 177.11 146.14 174.82 46.25 2.28 2.72 0.75 0.937 1039.24

54 177.11 239.34 251.48 46.25 3.73 3.92 0.10 0.10 1.25 0.31 1.312 0.375 1739.93

55 177.11 234.27 284.350 46.25 3.65 4.43 0.10 0.10 1.23 0.29 1.469 0.54 1706.63

56 177.11 219.45 261.920 46.25 3.42 4.08 0.10 0.10 1.16 0.21 1.362 0.427 1606.73

68 177.11 13.47 29.500 46.25 0.21 0.46 0.08 0.131 111

378 177.11 20.04 19.350 46.25 0.31 0.30 0.09 0.085 124.875

where,

fy = characteristic strength of steel

fck = characteristic cube compressive strength of concrete

b = width of beam section

D = depth of beam section

effective depth of beam section = D - clear cvr - bar d

d' = Nom. Cover + (bar dia)/2

initial bar diameter assumed = 25m

Mu,lim

= ultimate limiting moment = 0.138fck

bd2 (for M2

Mu

= Ultimate moment

pt

= percentage of longitudinal steel reinforcement in t

pc= percentage of longitudinal steel reinforcement in

Ast

= Area of longitudinal steel reinforcement required in tension side

Asc

= Area of longitudinal steel reinforcement required in compression s


4/15

imum reinforcement check0.12% o D


5/15

rt End

Asc Ast Asc

1107.23

1237.65

255.3 1509.6 192.863

1136.36

1237.65

115.163 1474.91 180.375

661.838

484.238

634.088

535.575

215.063 1363.91 41.625

886.613

115.163 1487.4 180.375

2.775 1262.63

893.55

147.075 1219.61


6/15

994.838

1355.59 30.525

1300.09

435.675 1820.4 520.313

399.6 2038.24 749.25

295.538 1889.78 592.463

181.763

117.938


7/15

CALCULATION OF No. Of REINFORCEM

MID SPAN

No. Of Reinforcements Required START

Element No.Tension Side

12mm 12mm 12m 20mm

34 200.00 - 1.77 2.00 985.13 2.00 2.4235 200.00 - 1.77 2.00 1244.59 2.00 3.24

36 200.00 - 1.77 2.00 1569.26 255.30 2.00 4.28

37 200.00 - 1.77 2.00 935.18 2.00 2.26

38 200.00 - 1.77 2.00 1090.58 2.00 2.75

39 200.00 - 1.77 2.00 1436.06 115.16 2.00 3.85

41 321.90 - 2.85 2.00 749.25 2.00 1.66

42 259.46 - 2.29 2.00 735.38 2.00 1.62

43 302.48 - 2.67 2.00 624.38 2.00 1.27

44 198.41 - 1.75 2.00 596.63 2.00 1.18

45 200.00 - 1.77 2.00 1530.41 215.06 2.00 4.1546 219.23 - 1.94 2.00 1332.00 2.00 3.52

47 227.55 - 2.01 2.00 1436.06 115.16 2.00 3.85

48 180.38 - 1.59 2.00 1329.23 2.78 2.00 3.51

49 201.19 -- 1.78 2.00 1112.78 2.00 2.82

50 302.48 - 2.67 2.00 1466.59 147.08 2.00 3.95

51 230.33 - 2.04 2.00 1090.58 2.00 2.75

52 227.55 - 2.01 2.00 1101.68 2.00 2.79

53 227.55 - 2.01 2.00 1039.24 2.00 2.59

54 430.13 - 3.80 2.00 1739.93 435.68 2.00 4.82

55 227.55 - 2.01 2.00 1706.63 399.60 2.00 4.7156 467.59 - 4.13 2.00 1606.73 295.54 2.00 4.39

68 200.00 - 1.77 2.00 111.00 - 0.35

378 259.46 - 2.29 2.00 124.88 - 0.40

Note:Ref. IS 13920 : 1993

Ast,Provided

Asc,Provided

TensionSide

Compression side

Ast,Provided

Asc,Provided

1. (Clause 6.2.1) The top as well as bottom reinforcement shall consist of at least two bars througout th

2. (Clause 6.2.3) The positive steel at a joint face must be at least equal to half the negative steel at t


8/15

NT BARS

END SUPPORTS

END

Tension Side

16mm 12mm 20mm 16mm

2.00 1107.23 2.00 2.80 2.002.00 1237.65 2.00 3.22 2.00

2.00 1509.60 192.86 2.00 4.09 2.00

2.00 1136.36 2.00 2.90 2.00

2.00 1237.65 2.00 3.22 2.00

2.00 1474.91 180.38 2.00 3.97 2.00

2.00 661.84 2.00 1.39 2.00

2.00 484.24 1.00 1.18 2.00

2.00 634.09 2.00 1.30 2.00

2.00 535.58 1.00 1.34 2.00

2.00 1363.91 41.63 2.00 3.62 2.002.00 886.61 2.00 2.10 2.00

2.00 1487.40 180.38 2.00 4.01 2.00

2.00 1262.63 2.00 3.30 2.00

2.00 893.55 2.00 2.12 2.00

2.00 1219.61 2.00 3.16 2.00

2.00 994.84 2.00 2.45 2.00

2.00 1355.59 30.53 2.00 3.59 2.00

2.00 1300.09 2.00 3.42 2.00

3.00 1820.40 520.31 2.00 5.07 3.00

2.00 2038.24 749.25 2.00 5.77 4.002.00 1889.78 592.46 2.00 5.30 3.00

2.00 181.76 - 0.58 2.00

2.00 117.94 - 0.38 2.00

Comp.side

Ast,Provided

Asc,Provided

Comp.Side

e member length.

hat face


9/15

SUMMARY OF No. OF REINFORCEMENT BARS PROVIDED

ElementsMid Span

End Supports

Start End

Tension Compression Tension Compression Tension

12mm 12mm 12mm 20mm 16mm 12mm 20mm

34 2 2 2 3 2 2 3

35 2 2 2 4 2 2 4

36 2 2 2 5 2 2 5

37 2 2 2 3 2 2 3

38 2 2 2 3 2 2 4

39 2 2 2 4 2 2 4

41 3 2 2 2 2 2 2

42 3 2 2 2 2 1 2

43 3 2 2 2 2 2 2

44 2 2 2 2 2 1 245 2 2 2 5 2 2 4

46 2 2 2 4 2 2 3

47 2 2 2 4 2 2 4

48 2 2 2 4 2 2 4

49 2 2 2 3 2 2 3

50 3 2 2 4 2 2 4

51 2 2 2 3 2 2 3

52 2 2 2 3 2 2 3

53 2 2 2 3 2 2 4

54 4 2 2 5 3 2 5

55 2 2 2 5 2 2 6

56 5 2 2 5 2 2 6

68 2 2 - 2 2 - 2

378 3 2 - 2 2 - 2


10/15

Compression

16mm

2

2

2

2

2

2

2

2

2

22

2

2

2

2

2

2

2

2

3

4

3

2

2


11/15

DESIGN OF SHEAR REINFORCEMEN

Beam distance12 mm tensile 20mmTensile Pt% Vu Tuv Tc max Tc

no. bar bar

34.0 0.0 2.0 3 0.842285 113.166 0.815611 2.8 0.5821

34.0 1.7 2.0 0 0.163023 75.19 0.54191 2.8 0.290434.0 3.4 2.0 3 0.842285 127.412 0.918285 2.8 0.5821

35.0 3.4 2.0 4 1.068706 121.482 0.875546 2.8 0.6337

36.0 0.0 2.0 5 1.295127 152.578 1.099661 2.8 0.679

36.0 1.7 2.0 0 0.163023 104.18 0.750847 2.8 0.2904

36.0 3.4 2.0 5 1.295127 158.132 1.13969 2.8 0.679

37.0 0.0 2.0 3 0.842285 108.836 0.784404 2.8 0.5821

37.0 1.9 2.0 0 0.163023 65.206 0.469953 2.8 0.2904

37.0 3.8 2.0 3 0.842285 110.058 0.793211 2.8 0.5821

38.0 0.0 2.0 3 0.842285 103.589 0.746587 2.8 0.5821

38.0 1.9 2.0 0 0.163023 73.617 0.530573 2.8 0.2904

38.0 3.8 2.0 4 1.068706 98.082 0.706897 2.8 0.6337

39.0 0.0 2.0 4 1.068706 140.085 1.009622 2.8 0.6337

39.0 1.9 2.0 0 0.163023 82.241 0.592728 2.8 0.2904

39.0 3.8 2.0 4 1.068706 140.721 1.014205 2.8 0.6337

41.0 0.0 2.0 2 0.615865 95.512 0.688375 2.8 0.517

41.0 2.8 3.0 0 0.244534 15.085 0.108721 2.8 0.3556

41.0 5.5 2.0 2 0.615865 89.743 0.646796 2.8 0.517

42.0 0.0 2.0 2 0.615865 102.894 0.741578 2.8 0.517

42.0 2.3 3.0 0 0.244534 23.931 0.172476 2.8 0.3556

42.0 4.6 1.0 2 0.534353 79.463 0.572706 2.8 0.4909

43.0 0.0 2.0 2 0.615865 69.951 0.504151 2.8 0.517

43.0 2.8 3.0 0 0.244534 27.594 0.198876 2.8 0.3556

43.0 5.5 2.0 2 0.615865 68.927 0.496771 2.8 0.517

44.0 0.0 2.0 2 0.615865 66.16 0.476829 2.8 0.517

44.0 2.3 2.0 0 0.163023 26.516 0.191106 2.8 0.2904

44.0 4.6 1.0 2 0.534353 62.549 0.450804 2.8 0.4909

45.0 0.0 2.0 5 1.295127 220.914 1.592173 2.8 0.679

45.0 2.8 2.0 0 0.163023 53.851 0.388115 2.8 0.2904

45.0 5.5 2.0 4 1.068706 190.747 1.374753 2.8 0.633746.0 0.0 2.0 4 1.068706 82.899 0.59747 2.8 0.6337

46.0 2.3 2.0 0 0.163023 44.96 0.324036 2.8 0.2904

46.0 4.6 2.0 3 0.842285 79.966 0.576332 2.8 0.5821

47.0 0.0 2.0 4 1.068706 128.101 0.92325 2.8 0.6337

47.0 2.5 2.0 0 0.163023 53.851 0.388115 2.8 0.2904

47.0 5.0 2.0 4 1.068706 129.909 0.936281 2.8 0.6337

48.0 0.0 2.0 4 1.068706 100.67 0.72555 2.8 0.6337


12/15

48.0 2.3 2.0 0 0.163023 62.073 0.447373 2.8 0.2904

48.0 4.6 2.0 4 1.068706 106.277 0.76596 2.8 0.6337

49.0 0.0 2.0 3 0.842285 97.633 0.703661 2.8 0.5821

49.0 2.5 2.0 0 0.163023 45.07 0.324829 2.8 0.2904

49.0 5.0 2.0 3 0.842285 72.616 0.523359 2.8 0.5821

50.0 0.0 2.0 4 1.068706 120.194 0.866263 2.8 0.6337

50.0 2.8 3.0 0 0.244534 36.488 0.262977 2.8 0.3356

50.0 5.5 2.0 4 1.068706 100.781 0.72635 2.8 0.6337

51.0 0.0 2.0 4 1.068706 112.644 0.811849 2.8 0.6337

51.0 2.5 3.0 0 0.244534 33.36 0.240432 2.8 0.3356

51.0 5.0 2.0 4 1.068706 103.672 0.747186 2.8 0.6337

52.0 0.0 2.0 3 0.842285 95.015 0.684793 2.8 0.5821

52.0 2.5 2.0 0 0.163023 52.214 0.376317 2.8 0.2904

52.0 5.0 2.0 3 0.842285 96.264 0.693795 2.8 0.5821

53.0 0.0 2.0 3 0.842285 109.851 0.791719 2.8 0.5821

53.0 2.5 2.0 0 0.163023 42.358 0.305283 2.8 0.2904

53.0 5.0 2.0 4 1.068706 115.465 0.83218 2.8 0.6337

54.0 0.0 2.0 5 1.295127 135.342 0.975438 2.8 0.679

54.0 2.8 4.0 0 0.326045 71.768 0.517247 2.8 0.3964

54.0 5.5 2.0 5 1.295127 146.012 1.052339 2.8 0.679

55.0 0.0 2.0 5 1.295127 152.082 1.096086 2.8 0.679

55.0 2.3 2.0 0 0.163023 99.712 0.718645 2.8 0.2904

55.0 4.6 2.0 6 1.521548 168.711 1.215935 2.8 0.7225

56.0 0.0 2.0 5 1.295127 139.229 1.003452 2.8 0.679

56.0 2.5 5.0 0 0.407557 66.197 0.477095 2.8 0.4356

56.0 5.0 2.0 6 1.521548 186.338 1.342977 2.8 0.722568.0 0.0 0.0 2 0.452842 16.674 0.120173 2.8 0.564

68.0 2.5 2.0 0 0.163023 10.879 0.078407 2.8 0.2904

68.0 5.0 0.0 2 0.452842 20.209 0.14565 2.8 0.4573

378.0 0.0 0.0 2 0.452842 76.884 0.554119 2.8 0.4573

378.0 2.5 3.0 0 0.244534 90.33 0.651027 2.8 0.3356

378.0 5.0 0.0 2 0.452842 26.622 0.19187 2.8 0.4573

Note:

2. When TuvTc and Tuv


13/15

Vus 8 mm bar Provided Sv

Spacing

32.39963 518.1251326 300 300

34.897 481.0459352 300 300

46.64563 359.8849839 300 300

33.55613 500.2681329 300 300

58.36675 287.61341 287.61341 280

63.887 262.7617512 262.7617512 260

63.92075 262.6230137 262.6230137 260

28.06963 598.0507399 300 300

24.913 673.8273191 300 300

29.29163 573.1010144 300 300

22.82263 735.5446624 300 300

33.324 503.7528508 300 300

10.15613 1652.900097 300 300

52.15913 321.8432058 300 300

41.948 400.1873748 300 300

52.79513 317.9661001 300 300

23.77825 705.9838298 300 300

0 302.4696 300 300

18.00925 932.1354304 300 300

31.16025 538.7331616 300 300

0 302.4696 300 300

11.35063 1478.954683 300 300

0 302.4696 300 300

0 302.4696 300 300

0 302.4696 300 300

0 302.4696 300 300

0 302.4696 300 300

0 302.4696 300 300

126.7028 132.4916784 132.4916784 130

13.558 1238.166396 300 300

102.8211 163.2646988 163.2646988 1600 302.4696 300 300

4.667 3596.970216 300 300

0 302.4696 300 300

40.17513 417.8471131 300 300

13.558 1238.166396 300 300

41.98313 399.8525598 300 300

12.74413 1317.23912 300 300


14/15

21.78 770.7557392 300 300

18.35113 914.7700754 300 300

16.86663 995.2826959 300 300

4.777 3514.142767 300 300

0 302.4696 300 300

32.26813 520.2366112 300 300

0 302.4696 300 300

12.85513 1305.865171 300 300

24.71813 679.1397001 300 300

0 302.4696 300 300

15.74613 1066.107376 300 300

14.24863 1178.15298 300 300

11.921 1408.192266 300 300

15.49763 1083.202104 300 300

29.08463 577.1798674 300 300

2.065 8129.326877 300 300

27.53913 609.5712918 300 300

41.13075 408.1389228 300 300

16.7675 1001.166542 300 300

51.80075 324.0698252 300 300

57.87075 290.0784939 290.0784939 290

59.419 282.5200693 282.5200693 280

68.46413 245.1949835 245.1949835 240

45.01775 372.89869 300 300

5.7575 2915.685627 300 300

86.09113 194.9917602 194.9917602 1900 302.4696 300 300

0 302.4696 300 300

0 302.4696 300 300

13.43363 1249.62994 300 300

43.7655 383.5683358 300 300

0 302.4696 300 300


15/15

INTERPOLATION

pt pc

x1 4 y1 1.337 0.401

x2 4.1 y2 1.368 0.433

x 4.08 y ?

pt pcy = 1.3618 0.4266

beam design acc to sp16

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