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STREN GTH EN IN G OF REIN FORCED CONCRETE

BUILDINGS ON STILTS WITH MASON RY IN FILL

FOR EARH QUAKE FORCES

A number of buildings are able to withstand moderate earthquak es eventhough not designed for

eartquak e forces. Quite often this is because of latent strength of masonry infill which is normallyignored in design. H owever in case of buildings on stilts , in stilt portion this latent strength is not

available, hence remain vulnerable. Feasibility of strengthenining this vulnerable portion is cheked

through a solved example for a case of six storied building. Calculations are based on 1984

version of Indian standard code of earthquak e resistant design 1.Same ex ercise with 2002 version

of the code is not attempted as it arbitrarily imposes a load factor of 2.5 for buildings on stilts.

While reporting on the extent of damage caused by major earthquakes, many authors have notedthat , among RC buildings, buildings on stilts have suffered maximum damage. In a article onfailure of multistorey buildings in Ahmedabad during Gujrat earthquake (January 26, 2001) DrAshok K Jain has noted that during past 75 years or so, different earthquakes all over the world

have repeatedly shown that a frame with a soft ground storey is the most vulnerable structuralsystem in a earthquake zone1. In a paper on lessons of Gujrat earthquake, Padamshree Dr A.S.Arya has noted that most damaged buildings were built on stilts2.

Causes of building failurePossible causes of building failure during earthquake are extensively covered in literature 1,2.

Following are the possible causes specifically related to buildings on stilt,

a.L ack of strength contribution from infill walls. - Walls provide considerable reserve strength tobuildings during earthquake. That is why many buildings , even though not designed forearthquake forces, survive moderate earthquakes. In many cases of failures of buildings on

stilt, it has been noted that upper stories , with walls, remain intact even after the failure.

b.A bsence of plinth beams -. This is due to misconception that plinth beams are to be providedonly if walls are to be supported. Absence of plinth leaves ground floor columns laterally

unsupported and foundations unconnected to each other.

Solved example

Following are the design parameters assumed for solved example (Fig 1 ),a. Building is in seismic zone III3b. Importance factor3 =1.0

c. Soil-foundation system factor3 = 1.2d. Performance factor3 =1.6e. Concrete grade of building = M15f. Building is originally designed for vertical loads only.

g. Column sizes are worked out assuming 3% vertical steel has been originally provided.h. Walls are strong enough to resist earthquake loads in portion above stilt.

i. Spacing of frames = 4mj. All bays , except at ground storey, have 230mm thick masonry infill.k. Safe bearing capacity of soil = 15 t/ m2

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.l. As built drawings of building are not availablem.Yield strength of reinforcing bars : 415 N/ mm2,

Calculations are done in following steps,1.Required sizes of columns and foundations are worked out, considering only vertical loads.2.Building frame is analized for earthquake forces on STAAD. Results are given in annexure I

member nos and node numbers are given in Fig 3. and 4 .Walls are modelled as strut and tie ofsize 150x150mm cross section.Deflected view of frame and bending moment diagram is

shown in fig 5 and 6.3.Sizes worked out in step 1, are checked for earthquake forces worked out in step 2. Wherever

required , extent of strengthening is worked out. Portion of frame proposed to be strengthenedis shown in Fig 2.

Vertical load on each internal column,

Live load = 0.3 t/ m2 x 4m x 4m x 7 = 33.6 MTSize of bay No. of floors

including roof

Wall load = 0.23m x 2 t/ m3 x 3.5m x 6 x 8m = 77.2 MTThickness Density Height No of Length of wallof wall stories on each column

Slab load =( 0.12m x 2.5 t/ m3 + 0.1 t/ m2 ) x 4m x 4 m x 7 = 44.8 MTThickness Density Flooring Size of bay No. of floorsof slab including roof__________

=155.6 MT_________________

Working out column size,

Try 0.23m x 0.65m column size,Referring to chart 334,

Pu 155.6 x 1.5------------- = ------------------------ = 1.04

fckb d 1500 x 0.23 x 0.65

where,Pu = Ultimate axial load on column,fck = Characteristic strength of concrete.b = Width of column

d = Depth of columnFrom the chart,

p/ fck = 0.2 (corresponding to 0 moment)hence , p = 0.2 x 15 n/ mm2 =3%where,

p = % vertical steelPercentage steel required matches with assumed steel . Hence size of column considered is ok.



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Checking foundations,Size required for vertical loads,

P/ SBC =155.6/ 15 = 3.22m x 3.22mwhere,P =Column loadSBC =Safe bearing capacity

Column load under seismic condition,Live loads( 1/ 4 of normal case) = 33.6/ 4 = 8.4 MTWall loads (same as in normal case) = 77.2 MTSlab load (same as in normal case) = 44.8 MT

Due to earthquake loads (Refer Annexure I ,for member no. 5) = 30.75MT

=161.15 MTColumn moment(Refer Annexure I, for member no.2 ) =11.7 t-m

161.15 6 x 11.7Soil pressure under seismic condition = +

3.22 x 3.22 3.22 x 3.222

= 15.6 + 2.1 =17.7 t/ m2Soil pressure permitted under seismic condition = 15 x 1.25 = 18.75

>17.9

Therefore foundations don't require strengthening.

Strengthening of columns,

Vertical load 'P'( same as for foundation ) =161.15 MT

Moment 'M'( same as for foundation ) = 11.7 t-m

Pu 161.15 x 1.2------------- = ------------------------ = 0.86

fckb d 1500 x 0.23 x 0.65

Mu 11.7 x 1.2

------------- = ------------------------ = 0.27fckb d

2 1500 x 0.65x 0.232

Referring to chart 334,

p/ fckexceeds 0.2 ( the value corresponding to steel provided in existing columns).Therefore column needs to be strengthened by increasing its size,Try 75mm guniting all around. For the new column size,

Pu 161.15 x 1.2------------- = ------------------------ = 0.43

fckb d 1500 x 0.38 x 0.8

Mu 11.7 x 1.2------------- = ------------------------ = 0.081

fckb d

2

1500 x 0.8x 0.38

2

New cover ( d')= 40 (existing cover) + 75(guniting) = 115mmd'/ D = 115/ 380 = 0.3



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Referring to chart 324 for d'/ D = 0.1p/ fck = 0.06

Referring to chart 344 for d'/ D = 0.2p/ fck = 0.07

Extrapolating, for d'/ D = 0.27,(0.3-0.1) x (0.06 -0.05)

p/ fck = 0.06 +(0.2 -0.1)

=0.06 + 0.02 =0.08hence, p = .08 x 15 =1.2%

Total vertical steel required = 1.2 x 38 x 80 / 100 = 36.5 cm2Steel already provided = 3 x 23 x 65 / 100 = 44.85 cm2Hence additional reinforcement is not required.

Strengthening of first floor beams,

Additional beams are provided on either side of existing beams to resist extra bending momentsand shear due to earthquake loads, Fig 7. From Annexure I,

Bending moments due to earthquake loads( for member number 9) = 5.9 t-m,

Providing 100mm wide x 420mm deep beam on either side of floor beams,Bending moment per beam(M), =5.9/ 2 = 2.95 t-m

Mu 2.95 x 1.2

------------- = ------------------------ =190b d2 0.1x 0.422

From Table 14,Percentage steel required (p t) = 0.64Hence, area of tension steel required = 0.64 x 10 x 42/ 100 =2 68cm2

Provided 1-20mm dia. bar at top and bottom

Shear ( V, for member number 9) = 2.82 t

Vu = 2.82 x 1.2 = 3.4 tShear capacity of concrete from table 614= 55 t/ m2

Shear capacity of both beams = 52 x 0.2 x 0.4 = 4.16 t> 3.4 t

Hence provided only nominal stirrups i.e 8mm dia @ 300mm c/ c

Dowels for shear transfer,Providing 2-20mm dia dowels,

Capacity of 2-20mm dia bars in axial tension = 2 x 3.142 x 4.15 / 1.15Area in cm2 Yield strength partial safety

of bars in t/ cm2 factor for steel=22.6 t

Capacity for shear by shear friction theory = 22.6 x 0.3 = 6.8 t > 3.2 hence ok

Design of plinth beams

From Annexure I, bending moment(M) due to earthquakeloads( for member number 128) = 7.1 t-mTry 230mm (width) x 500 mm (depth) beam,



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Mu 7.1 x 1.2------------- = ------------------------ =167

b d2 0.23 x 0.472

From Table 14,Percentage steel required (p t) = 0.55Hence, area of tension steel required = 0.55 x 23 x 47/ 100 =5.9cm2

Provided 2-20mm dia. bar at top and bottom, Fig 8.

Shear ( V, for member number 124 and 126) = 3.2 tVu = 3.44 x 1.2 = 4.1 t

Shear capacity of concrete from table 614= 45 t/ m2

Shear capacity of both beams = 45 x 0.23 x 0.47 = 4.86 t> 4.1 t

Hence provided only nominal stirrups i.e 8mm dia @ 300mm c/ c

Dowels for shear transfer5,Providing 2-20mm dia dowels,Capacity of 2-20mm dia bars in axial tension = 2 x 3.142 x 4.15 / 1.15

Area in cm2 Yield strength partial safety

of bars in t/ cm2 factor for steel=22.6 t

Capacity for shear by shear friction theory = 22.6 x 0.3 = 6.8 t > 4.1 hence ok

Conclusions and observations

1.Strength of brick walls may be taken into account while strengthening RC building forearthquakes.

2.Strengthening of foundations may not be required for RC buildings up to six stories.3.Existing reinforcement in columns may be adequate for earthquake forces for buildings

up to six stories. However size may have to be increased.4.Anchoring of beam reinforcement in to columns should preferably be done after

guniting/ jacketing of columns. Thereby strengthening the columns, before holes aredrilled for anchoring

References

1. Jain, A. K. Failure of multistorey buildings in Ahmedabad: Lessons to relearn, T he IndianConcrete Journal, December 2001, Vol 75, No. 12.

2. Arya, A.S. Lessons of Kachchha Earthquake of January 26, 2001, Seminar on Seismic A ssessmentand R etrofitting of Buildings, Mumbai February 16,2002.

3. -----------Indian Standard Criteria for E arthquak e Resistant Design of Structures, Bureau of IndianStandards, .IS : 1893 (1984), New Delhi, India.4. -----------D esign A ids for Reinforced Concrete to IS :456-1978, SP-16(S&T) 1980, Bureau of Indian

standards, New Delhi, India.5. -----------Building code requirements for structural concrete (318-02) and commentary (318R-02), American

Concrete Institute , Detroit



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ANNEXURE - I : ANALYSIS RESULTS FOR EARTHQUAKE FORCES* *

* STAAD.Pro *

* Version 2002 Bld 1001 *

* Proprietary Program of *

* Research Engineers, Intl. *

* Date= NOV 2, 2002 *

* Time= 14:53:35 *

* ** USER ID: BMCPL *

****************************************************

1. STAAD PLANE STILT

2. START JOB INFORMATION

3. ENGINEER DATE 19-OCT-02

4. END JOB INFORMATION

5. INPUT WIDTH 79

6. UNIT METER MTON

7. JOINT COORDINATES

8. 1 0 0 0; 2 4 0 0; 3 8 0 0; 4 12 0 0; 5 16 0 0; 6 0 5.5 0; 7 4 5.5 0; 8 8 5.5 0

9. 9 12 5.5 0; 10 16 5.5 0; 11 0 9 0; 12 4 9 0; 13 8 9 0; 14 12 9 0; 15 16 9 0

10. 16 0 12.5 0; 17 4 12.5 0; 18 8 12.5 0; 19 12 12.5 0; 20 16 12.5 0; 21 0 16 0

11. 22 4 16 0; 23 8 16 0; 24 12 16 0; 25 16 16 0; 26 0 19.5 0; 27 4 19.5 0

12. 28 8 19.5 0; 29 12 19.5 0; 30 16 19.5 0; 31 0 23 0 ; 32 4 23 0; 33 8 23 0

13. 34 12 23 0; 35 16 23 0; 36 0 26.5 0; 37 4 26.5 0; 38 8 26.5 0; 39 12 26.5 0

14. 40 16 26.5 0; 41 0 2 0; 42 4 2 0; 43 8 2 0; 44 12 2 0; 45 16 2 0

15. MEMBER INCIDENCES

16. 1 1 41; 2 2 42; 3 3 43; 4 4 44; 5 5 45; 6 6 7; 7 7 8; 8 8 9; 9 9 10; 18 6 11

17. 19 7 12; 20 8 13; 21 9 14; 22 10 15; 23 11 12; 24 12 13; 25 13 14; 26 14 15

18. 27 6 12; 28 7 13; 29 8 14; 30 9 15; 31 7 11; 32 8 12; 33 9 13; 34 10 14

19. 35 11 16; 36 12 17; 37 13 18; 38 14 19; 39 15 20; 40 16 17; 41 17 18; 42 18 19

20. 43 19 20; 44 11 17; 45 12 18; 46 13 19; 47 14 20; 48 12 16; 49 13 17; 50 14 18

21. 51 15 19; 52 16 21; 53 17 22; 54 18 23; 55 19 24; 56 20 25; 57 21 22; 58 22 23

22. 59 23 24; 60 24 25; 61 16 22; 62 17 23; 63 1 8 24; 64 19 25; 65 17 21; 66 18 22

23. 67 19 23; 68 20 24; 69 21 26; 70 22 27; 71 23 28; 72 24 29; 73 25 30; 74 26 27

24. 75 27 28; 76 28 29; 77 29 30; 78 21 27; 79 22 28; 80 23 29; 81 24 30; 82 22 26

25. 83 23 27; 84 24 28; 85 25 29; 86 26 31; 87 27 32; 88 28 33; 89 29 34; 90 30 35

26. 91 31 32; 92 32 33; 93 33 34; 94 34 35; 95 26 32; 96 27 33; 97 28 34; 98 29 35

27. 99 27 31; 100 28 32; 101 29 33; 102 30 34; 103 31 36; 104 32 37; 105 33 38

28. 106 34 39; 107 35 40; 108 36 37; 109 3 7 38; 110 38 39; 111 39 40; 112 31 37

29. 113 32 38; 114 33 39; 115 34 40; 116 32 36; 117 33 37; 118 34 38; 119 35 39

30. 120 41 6; 121 42 7; 122 41 42; 123 43 8; 124 42 43; 125 44 9; 126 43 4431. 127 45 10; 128 44 45

32. MEMBER PROPERTY INDIAN

33. 1 TO 5 18 TO 22 35 TO 39 52 TO 56 69 TO 73 86 TO 90 103 TO 107 120 121 123 -

34. 125 127 PRIS YD 0.65 ZD 0.23

35. 27 TO 34 44 TO 51 61 TO 68 78 TO 85 95 TO 102 112 TO 119 PRIS YD 0.15 ZD 0.15

36. 6 TO 9 23 TO 26 40 TO 43 57 TO 60 74 TO 77 91 TO 94 108 TO 111 122 124 126 -

37. 128 PRIS YD 0.5 ZD 0.23

38. UNIT METER KN

39. CONSTANTS

40. E 2.17185E+007 MEMB 1 TO 9 18 TO 128

41. POISSON 0.17 MEMB 1 TO 9 18 TO 128

42. DENSITY 23.5616 MEMB 1 TO 9 18 TO 128

43. ALPHA 5.5E-006 MEMB 1 TO 9 18 TO 128

44. MEMBER COMPRESSION

45. 27 TO 34 44 TO 51 61 TO 68 78 TO 85 95 TO 102 112 TO 119

46. UNIT METER MTON47. SUPPORTS

48. 1 TO 5 FIXED

49. *MEMBER TRUSS

50. *27 TO 34 44 TO 51 61 TO 68 78 TO 85 95 TO 102 112 TO 119

51. CUT OFF MODE SHAPE 3

52. DEFINE 1893 LOAD

53. ZONE 0.04 I 1 K 1.6 B 1.2

54. JOINT WEIGHT

55. 11 TO 35 WEIGHT 6.44

56. 6 TO 10 36 TO 40 WEIGHT 3.22

57. MEMBER WEIGHT

58. 23 TO 26 40 TO 43 57 TO 60 74 TO 77 91 TO 94 UNI 1.4

59. 6 TO 9 108 TO 111 UNI 0.7

60. 23 TO 26 40 TO 43 57 TO 60 74 TO 77 91 TO 94 108 TO 111 UNI 1.6

61. 6 TO 9 23 TO 26 40 TO 43 57 TO 60 74 TO 77 91 TO 94 UNI 0.3



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62. 108 TO 111 UNI 0.15

63. LOAD 1 SEISMIC

64. 1893 LOAD X 1.165

65. PERFORM ANALYSIS

*********************************************************

* *

* TIME PERIOD FOR X 1893 LOADING = 0.76857 SEC *

* FACTOR C PER 1893= 0.644, LOAD FACTOR= 1.165 *

* FACTOR V PER 1893= 0.0495 X 512.40 *

* *

*********************************************************

**NOTE-Tension/Compression converged after 2 iterations, Case= 1

66. PRINT ANALYSIS RESULTS

ANALYSIS RESULTS

SUPPORT REACTIONS -UNIT MTON METE STRUCTURE TYPE = PLANE

JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z

1 1 -4.78 -30.75 0.00 0.00 0.00 10.52

2 1 -6.78 -7.54 0.00 0.00 0.00 11.67

3 1 -6.66 0.04 0.00 0.00 0.00 11.63

4 1 -6.73 7.52 0.00 0.0 0 0.00 11.70

5 1 -4.59 30.74 0.00 0.00 0.00 10.53

MEMBER END FORCES STRUCTURE TYPE = PLANE

ALL UNITS ARE -- MTON METE

MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z

1 1 1 -30.75 4.78 0.00 0.00 0.00 10.5241 30.75 -4.78 0.00 0.00 0.00 -0.97

2 1 2 -7.54 6.78 0.00 0.00 0.00 11.67

42 7.54 -6.78 0.00 0.00 0.00 1.90

3 1 3 0.04 6.66 0.00 0.00 0.00 11.63

43 -0.04 -6.66 0.00 0.00 0.00 1.69

4 1 4 7.52 6.73 0.00 0.00 0.00 11.70

44 -7.52 -6.73 0.00 0.00 0.00 1.75

5 1 5 30.74 4.59 0.00 0.00 0.00 10.53

45 -30.74 -4.59 0.00 0.00 0.00 -1.35

6 1 6 -5.54 -2.67 0.00 0.00 0.00 -5.53

7 5.54 2.67 0.00 0.00 0.00 -5.16

7 1 7 -5.55 -2.64 0.00 0.00 0.00 -5.26

8 5.55 2.64 0.00 0.00 0.00 -5.29

8 1 8 -4.11 -2.68 0.00 0.00 0.00 -5.35

9 4.11 2.68 0.00 0.00 0.00 -5.37

9 1 9 -2.31 -2.82 0.00 0.00 0.00 -5.41

10 2.31 2.82 0.00 0.00 0.00 -5.8718 1 6 -24.73 -0.84 0.00 0.00 0.00 -3.17

11 24.73 0.84 0.00 0.00 0.00 0.22

19 1 7 -13.36 0.02 0.00 0.00 0.00 -1.31

12 13.36 -0.02 0.00 0.00 0.00 1.37

20 1 8 -6.82 0.06 0.00 0.0 0 0.00 -1.31

13 6.82 -0.06 0.00 0.00 0.00 1.52

21 1 9 0.51 0.04 0.00 0.00 0.00 -1.33

14 -0.51 -0.04 0.00 0.00 0.00 1 .45

22 1 10 17.36 -0.82 0.00 0.00 0.00 -3.30

15 -17.36 0.82 0.00 0.00 0.00 0.41

23 1 11 -4.65 -0.82 0.00 0.00 0.00 -1.68

12 4.65 0.82 0.00 0.00 0.00 -1.60

24 1 12 -6.24 -0.99 0.00 0.00 0.00 -2.00

13 6.24 0.99 0.00 0.00 0.00 -1.97

25 1 13 -6.75 -1.00 0.00 0.00 0.00 -1.97

14 6.75 1.00 0.00 0.00 0.00 -2.0226 1 14 -6.94 -0.79 0.00 0.00 0.00 -1.53

15 6.94 0.79 0.00 0.00 0.00 -1.62

27 1 6 0.00 0.00 0.00 0.00 0.00 0.00

12 0.00 0.00 0.00 0.00 0.00 0.00

28 1 7 0.00 0.00 0.00 0.00 0.00 0.00

13 0.00 0.00 0.00 0.00 0.00 0.00

29 1 8 0.00 0.00 0.00 0.00 0.00 0.00

14 0.00 0.00 0.00 0.00 0.00 0.00

30 1 9 0.00 0.00 0.00 0.00 0.00 0.00

15 0.00 0.00 0.00 0.00 0.00 0.00

31 1 7 8.52 0.00 0.00 0.00 0.00 0.00

11 -8.52 0.00 0.00 0.00 0.00 0.00

32 1 8 10.53 0.00 0.00 0.00 0.00 0.00

12 -10.53 0.00 0.00 0.00 0.00 0.00

33 1 9 11.20 0.00 0.00 0.00 0.00 0.00

13 -11.20 0.00 0.00 0.00 0.00 0.00

34 1 10 10.81 0.00 0.00 0.00 0.00 0.00

14 -10.81 0.00 0.00 0.00 0.00 0.00

35 1 11 -18.30 0.73 0.00 0.00 0.00 1.46

16 18.30 -0.73 0.00 0.00 0.00 1.08



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MEMBER LOAD JT AXIAL SHEAR -Y SHEAR-Z TORSION MOM-Y MOM-Z

36 1 12 -10.49 1.22 0.00 0.00 0.00 2.23

17 10.49 -1.22 0.00 0.00 0.00 2.04

37 1 13 -5.00 1.32 0.00 0.00 0.00 2.42

18 5.00 -1.32 0.00 0.00 0.00 2.21

38 1 14 1.70 1.15 0.00 0.00 0.00 2.09

19 -1.70 -1.15 0.00 0.00 0.00 1.94

39 1 15 11.93 0.62 0.00 0.00 0.00 1.21

20 -11.93 -0.62 0.00 0.00 0.00 0.94

40 1 16 -4.68 -0.90 0.00 0.00 0.00 -1.89

17 4.68 0.90 0.00 0.00 0.00 -1.73

41 1 17 -6.02 -1.05 0.00 0.00 0.00 -2.1218 6.02 1.05 0.00 0.00 0.00 -2.09

42 1 18 -6.13 -1.03 0.00 0.00 0.00 -2.06

19 6.13 1.03 0.00 0.00 0.00 -2.08

43 1 19 -4.94 -0.81 0.00 0.00 0.00 -1.55

20 4.94 0.81 0.00 0.00 0.00 -1.68

44 1 11 0.00 0.00 0.00 0.00 0.00 0.00

17 0.00 0.00 0.00 0.00 0.00 0.00

45 1 12 0.00 0.00 0.00 0.00 0.00 0.00

18 0.00 0.00 0.00 0.00 0.00 0.00

46 1 13 0.00 0.00 0.00 0.00 0.00 0.00

19 0.00 0.00 0.00 0.00 0.00 0.00

47 1 14 0.00 0.00 0.00 0.00 0.00 0.00

20 0.00 0.00 0.00 0.00 0.00 0.00

48 1 12 6.43 0.00 0.00 0.00 0.00 0.00

16 -6.43 0.00 0.00 0.00 0.00 0.00

49 1 13 8.45 0.00 0.00 0.00 0.00 0.0017 -8.45 0.00 0.00 0.00 0.00 0.00

50 1 14 8.68 0.00 0.00 0.00 0.00 0.00

18 -8.68 0.00 0.00 0.00 0.00 0.00

51 1 15 7.05 0.00 0.00 0.00 0.00 0.00

19 -7.05 0.00 0.00 0.00 0.00 0.00

52 1 16 -13.16 0.51 0.00 0.00 0.00 0.81

21 13.16 -0.51 0.00 0.00 0.00 0.98

53 1 17 -8.81 1.06 0.00 0.00 0.00 1.81

22 8.81 -1.06 0.00 0.00 0.00 1.91

54 1 18 -4.57 1.14 0.00 0.00 0.00 1.94

23 4.57 -1.14 0.00 0.00 0.00 2.06

55 1 19 0.79 1.00 0.00 0.00 0.00 1.69

24 -0.79 -1.00 0.00 0.00 0.00 1.80

56 1 20 7.00 0.47 0.00 0.00 0.00 0.74

25 -7.00 -0.47 0.00 0.00 0.00 0.90

57 1 21 -4.04 -0.78 0.00 0.00 0.00 -1.63

22 4.04 0.78 0.00 0.00 0.00 -1.5058 1 22 -5.32 -0.94 0.00 0.00 0.00 -1.91

23 5.32 0.94 0.00 0.00 0.00 -1.87

59 1 23 -5.38 -0.91 0.00 0.00 0.00 -1.81

24 5.38 0.91 0.00 0.00 0.00 -1.84

60 1 24 -4.18 -0.67 0.00 0.00 0.00 -1.28

25 4.18 0.67 0.00 0.00 0.00 -1.40

61 1 16 0.00 0.00 0.00 0.00 0.00 0.00

22 0.00 0.00 0 .00 0.00 0.00 0.00

62 1 17 0.00 0.00 0.00 0.00 0.00 0.00

23 0.00 0.00 0.00 0.00 0.00 0.00

63 1 18 0.00 0.00 0.00 0.00 0.00 0.00

24 0.00 0.00 0.00 0.00 0.00 0.00

64 1 19 0.00 0.00 0.00 0.00 0.00 0.00

25 0.00 0.00 0.00 0.00 0.00 0.00

65 1 17 6.12 0.00 0.00 0.00 0.00 0.00

21 -6.12 0.00 0.00 0.00 0.00 0.0066 1 18 8.01 0.00 0.00 0.00 0.00 0.00

22 -8.01 0.00 0.00 0.00 0.00 0.00

67 1 19 8.08 0.00 0.00 0.00 0.00 0.00

23 -8.08 0.00 0.00 0.00 0.00 0.00

68 1 20 6.26 0.00 0.00 0.00 0.00 0.00

24 -6.26 0.00 0.00 0.00 0.00 0.00

69 1 21 -8.35 0.45 0.00 0.00 0.00 0.66

26 8.35 -0.45 0.00 0.00 0.00 0.93

70 1 22 -6.83 0.92 0.00 0.00 0.00 1.49

27 6.83 -0.92 0.00 0.00 0.00 1.73

71 1 23 -3.87 1.00 0.00 0.00 0.00 1.62

28 3.87 -1.00 0.00 0.00 0.00 1.86

72 1 24 0.17 0.83 0.00 0.00 0.00 1.33

29 -0.17 -0.83 0.00 0.00 0.00 1.57

73 1 25 3.14 0.38 0.00 0.00 0.00 0.50

30 -3.14 -0.38 0.00 0.00 0.00 0.82

74 1 26 -3.14 -0.62 0.00 0.00 0.00 -1.30

27 3.14 0.62 0.00 0.00 0.00 -1.18

75 1 27 -4.30 -0.78 0.00 0.00 0.00 -1.57

28 4.30 0.78 0.00 0.00 0.00 -1.54



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76 1 28 -4.30 -0.73 0.00 0.00 0.00 -1.45

29 4.30 0.73 0.00 0.00 0.00 -1.48

77 1 29 -3.03 -0.48 0.00 0.00 0.00 -0.91

30 3.03 0.48 0.00 0.00 0.00 -1.00

78 1 21 0.00 0.00 0.00 0.00 0.00 0.00

27 0.00 0.00 0.00 0.00 0.00 0.00

79 1 22 0.00 0.00 0.00 0.00 0.00 0.00

28 0.00 0.00 0.00 0.00 0.00 0.00

80 1 23 0.00 0.00 0.00 0.00 0.00 0.00

29 0.00 0.00 0.00 0.00 0.00 0.00

81 1 24 0.00 0.00 0.00 0.00 0.00 0.0030 0.00 0.00 0.00 0.00 0.00 0.00

82 1 22 5.26 0.00 0.00 0.00 0.00 0.00

26 -5.26 0.00 0.00 0.00 0.00 0.00

83 1 23 6.96 0.00 0.00 0.00 0.00 0.00

27 -6.96 0.00 0.00 0.00 0.00 0.00

84 1 24 6.84 0.00 0.00 0.00 0.00 0.00

28 -6.84 0.00 0.00 0.00 0.00 0.00

85 1 25 4.85 0.00 0.00 0.00 0.00 0.00

29 -4.85 0.00 0.00 0.00 0.00 0.00

86 1 26 -4.26 0.35 0.00 0.00 0.00 0.37

31 4.26 -0.35 0.00 0.00 0.00 0.87

87 1 27 -4.64 0.70 0.00 0.00 0.00 1.02

32 4.64 -0.70 0.00 0.00 0.00 1.42

88 1 28 -2.91 0.76 0.00 0.00 0.00 1.13

33 2.91 -0.76 0.00 0.00 0.00 1.52

89 1 29 -0.20 0.58 0.00 0.00 0.00 0.8234 0.20 -0.58 0.00 0.00 0.00 1.22

90 1 30 0.71 0.25 0.00 0.00 0.00 0.18

35 -0.71 -0.25 0.00 0.00 0.00 0.69

91 1 31 -1.92 -0.37 0.00 0.00 0.00 -0.77

32 1.92 0.37 0.00 0.00 0.00 -0.69

92 1 32 -2.96 -0.53 0.00 0.00 0.00 -1.08

33 2.96 0.53 0.00 0.00 0.00 -1.05

93 1 33 -2.82 -0.48 0.00 0.00 0.00 -0.95

34 2.82 0.48 0.00 0.00 0.00 -0.97

94 1 34 -1.53 -0.21 0.00 0.00 0.00 -0.39

35 1.53 0.21 0.00 0.00 0.00 -0.44

95 1 26 0.00 0.00 0.00 0.00 0.00 0.00

32 0.00 0.00 0.00 0.00 0.00 0.00

96 1 27 0.00 0.00 0.00 0.00 0.00 0.00

33 0.00 0 .00 0.00 0.00 0.00 0.00

97 1 28 0.00 0.00 0.00 0.00 0.00 0.00

34 0.00 0.00 0.00 0.00 0.00 0.0098 1 29 0.00 0.00 0.00 0.00 0.00 0.00

35 0.00 0.00 0.00 0.00 0.00 0.00

99 1 27 3.86 0.00 0.00 0.00 0.00 0.00

31 -3.86 0.00 0.00 0.00 0.00 0.00

100 1 28 5.32 0.00 0.00 0.00 0.00 0.00

32 -5.32 0.00 0.00 0.00 0.00 0.00

101 1 29 5.02 0.00 0.00 0.00 0.00 0.00

33 -5.02 0.00 0.00 0.00 0.00 0.00

102 1 30 2.97 0.00 0.00 0.00 0.00 0.00

34 -2.97 0.00 0.00 0.00 0.00 0.00

103 1 31 -1.35 0.06 0.00 0.00 0.00 -0.09

36 1.35 -0.06 0.00 0.00 0.00 0.32

104 1 32 -2.19 0.33 0.00 0.00 0.00 0.36

37 2.19 -0.33 0.00 0.00 0.00 0.79

105 1 33 -1.71 0.41 0.00 0.00 0.00 0.48

38 1.71 -0.41 0.00 0.00 0.00 0.95106 1 34 -0.27 0.18 0.00 0.00 0.00 0.14

39 0.27 -0.18 0.00 0.00 0.00 0.50

107 1 35 0.02 -0.05 0.00 0.00 0.00 -0.25

40 -0.02 0.05 0.00 0.00 0.00 0.06

108 1 36 -0.40 -0.14 0.00 0.00 0.00 -0.32

37 0.40 0.14 0.00 0.00 0.00 -0.23

109 1 37 -1.37 -0.27 0.00 0.00 0.00 -0.57

38 1.37 0.27 0.00 0.00 0.00 -0.52

110 1 38 -2.08 -0.23 0.00 0.00 0.00 -0.42

39 2.08 0.23 0.00 0.00 0.00 -0.50

111 1 39 -1.11 -0.02 0.00 0.00 0.00 0.00

40 1.11 0.02 0.00 0.00 0.00 -0.06

112 1 31 0.00 0.00 0.00 0.00 0.00 0.00

37 0.00 0.00 0.00 0.00 0.0 0 0.00

113 1 32 0.00 0.00 0.00 0.00 0.00 0.00

38 0.00 0.00 0.00 0.00 0.00 0.00

114 1 33 0.00 0.00 0.00 0.00 0.00 0.00

39 0.00 0.00 0.00 0.00 0.00 0.00

115 1 34 0.00 0.00 0.00 0.00 0.00 0.00

40 0.00 0.00 0.00 0.00 0.00 0.00



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116 1 32 1.85 0.00 0.00 0.00 0.00 0.00

36 -1.85 0.00 0.00 0.00 0.00 0.00

117 1 33 3.11 0.00 0.00 0.00 0.00 0.00

37 -3.11 0.00 0.00 0.00 0.00 0.00

118 1 34 2.66 0.00 0.00 0.00 0.00 0.00

38 -2.66 0.00 0.00 0.00 0.00 0.00

119 1 35 0.73 0.00 0.00 0.00 0.00 0.00

39 -0.73 0.00 0.00 0.00 0.00 0.00

120 1 41 -27.41 4.73 0.00 0.00 0.00 7.85

6 27.41 -4.73 0.00 0.00 0.00 8.70

121 1 42 -7.71 6.48 0.00 0.00 0.00 10.947 7.71 -6.48 0.00 0.00 0.00 11.74

122 1 41 -0.05 -3.34 0.00 0.00 0.00 -6.88

42 0.05 3.34 0.00 0.00 0.00 -6.49

123 1 43 0.07 6.59 0.00 0.00 0.00 11.12

8 -0.07 -6.59 0.00 0.00 0.00 11.95

124 1 42 -0.35 -3.18 0.00 0.00 0.00 -6.34

43 0.35 3.18 0.00 0.00 0.00 -6.38

125 1 44 7.74 6.70 0.00 0.00 0.00 11.34

9 -7.74 -6.70 0.00 0.00 0.00 12.11

126 1 43 -0.42 -3.21 0.00 0.00 0.00 -6.42

44 0.42 3.21 0.00 0.00 0.00 -6.43

127 1 45 27.30 5.03 0.00 0.00 0.00 8.45

10 -27.30 -5.03 0.00 0.00 0.00 9.16

128 1 44 -0.44 -3.44 0.00 0.00 0.00 -6.66

45 0.44 3.44 0.00 0.00 0.00 -7.10

************** END OF LATEST ANALYSIS RESULT **************

67. FINISH



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Fig. 1 Frame of building in solved example



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Fig 2 Portion of frame to be strengthened



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Fig 3 Member Numbers



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Fig 4 Node numbers



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Fig 5 Deflected shape of the frame



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Fig 6 Bending moment diagram



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Fig 7 Strengthening of first floor beams



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Fig 8 Proposed plinth beam

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