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INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 1, No 2, 2010

© Copyright 2010 All rights reserved Integrated Publishing services Research article ISSN 0976 – 4399

Received on July 2011 published on September 2011 112

Effective truss supporting technique to replace damage column of frame structure building

Hassan. M.K 1 , Alam. M.R 2 , Kaish. A. B. M. A 3 , Zain. M. F.M 4 1 & 4 Dept. of Civil & Structural Engineering, Universiti Kebangsaan Malaysia, Bangi

43600, Selangor, Malaysia 2 & 3 Dept. of Civil Engineering, Chittagong University of Engineering & Technology,

Chittagong4349, Bangladesh [email protected]

ABSTRACT

Truss supporting (TS) is a technique to support a building frame during the replacement of column when its stiffness reduces due to any kind of damage. This paper deals about the effectiveness of TS during replacement of damaged column in a highrise frame structure building. For the case study of the effectiveness of TS, each of six columns was considered as a damaged column at different positions in the ground and first floors. Four types of effective truss supporting models were modelled to transfer the damaged column load to the lower column just below the damaged column. To evaluate the effectiveness of truss supporting model, the numerical analysis of the 2D frame was carried out using finite element software STAAD Pro 2004. Effectiveness of truss supporting model was confirmed by comparing the deflection, axial force, shear force and bending moment of the beam and column within undamaged column condition, damaged column condition and damaged column with truss supporting condition. The analyzed result shows that at truss supporting condition, the deflection, axial force, shear force and bending moment of the beam and column of the 2D frame building were obtained almost same as their design values.

Keywords: Truss Supporting, Numerical Analysis, Damage Column, Column Replacement and Frame Structure.

1. Introduction

For highrise building, column is one of the most important structural elements, which is designed to support the compressive load and bending moment (Taranath, B.S, 1998). When columns of reinforced concrete (RC) frame building damage due to the effect of wind load or earthquake load or any other reasons, it is important to replace the entire damaged columns of the building especially for highrise frame building during further servicing of structure. When a column damages, the beams over it get unsupported and its span will act as a span equal to twice the original beam span. In this condition, a large positive moment is developed at the centre of new beam and also negative moments at the ends of the beam due to the upper column concentrated load and the new beam span. Another major problem is that the load of the damaged column transfers through the nearest columns, causing high axial load on those columns. As a result, bursting of those columns may occur if the load exceeds its carrying capacity. Therefore, total collapse of

Effective truss supporting technique to replace damage column of frame structure building Hassan. M.K et.al.,

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the frame structure building could happen in a minute. To replace a column, propping & supporting techniques are generally used to support the damaged column load (Rehabilitation & Retrofitting Methods, 2002). To prevent the total collapse of the structure during the replacement of damaged column, supporting must be provided because it acts as a load transferring media from upper stories to the lower stories of the building (NEHRP guidelines, 1997). Therefore, supporting system is a crucial part during the replacement of a damaged column for highrise building. In the present paper, the load of the damaged column was transferred to the lower column of the damaged column using a technique called truss supporting (TS).

2. Research Significance

Propping and supporting in a structure is used to relief the over burden stresses and deflections during the retrofitting work of any deteriorated structure (Rehabilitation & Retrofitting Methods, 2002 & NEHRP guidelines, 1997). Props/supports are to be made of built up structural sections (tubular steel) of adequate capacity to be able to resist the total beam reactions from all upper stories. For propping the column at top, bottom or any intermediate column of the stories, props are provided at the below of all beams of all stories (Rehabilitation & Retrofitting Methods, 2002). All props should be at the same position in all stories of building. Sequence of props/supports fixing would be 1234 i.e. from lower to upper most story. And the sequence of props/supports removal would be 4 321 i.e. from topmost story to lower story (Rehabilitation & Retrofitting Methods, 2002). Sometimes only vertical props/supports sitting on some beams and slabs may not be enough. For those cases diagonal bracing should also be considered to transfer the load to the adjacent column [Youssef,M.A et.al., 2007 & Maheri et.al., 1997). In this paper, “truss supporting” was modeled in such way that it was needed only three stories such as damaged column level and above and below of that level. Retrofitting of joint can be done more easily by modeling a suitable truss than propping.

3. Effective Truss Supporting Technique

There are no definite rules of a truss modeling for supporting a frame. Many factors govern in a truss modeling for a frame during the damage column replacement for example such as; types of frame, loading condition, load distribution area of the modeled truss and type of occupancy, etc. So it is important to find out the effective truss supporting model which will be helpful to relief the over burden stresses and strains during the replacement of the damage column of highrise frame structure building. In the present paper, four types of truss model were considered which would be used as effective supporting during the replacement of the damage column of the highrise frame structure building. Because, any one of these four types of truss model is sufficient to replace the any damage column of any floor of the building. The first model which is shown in Figure 1 would be suitable only for the exterior corner column of the ground floor. The second model which is shown in Figure 2 would be suitable for any interior or exterior column of the ground floor except the exterior corner column. The next model which is shown in Figure 3 would be suitable for any exterior corner column of the any middle floor of the building. The last and final model which is shown in Figure 4 would be suitable for any interior or exterior column of the any middle floor of the building. In



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the case studies, these four types of truss model were simulated based on the two types of truss section such as Isection and Lsection for transferring the damage column load to other nearest columns. In this study, Isectional truss element (shown in Figure 1 & Figure 2) was used as a main diagonal element to carry the load and Lsectional truss element was used as a bracing element inside of the main diagonal elements.

Figure 1: Truss modeling for column C11 Figure 2: Truss modeling for column C12

Figure 3: Truss modeling for column C12 Figure 4: Truss modeling for column C12

4. Analytical Considerations

For a parametric study, one interior panel of a reference model of a 25story building of 4 x 5 bays was considered. Floor to floor height of this 2D frame structure building was considered as 350 cm for all stories except the ground floor as 365.7 cm. The building geometry is shown in Figure 5 and Figure 6. An interior frame in the short direction of the building was considered for the analysis since frame in this direction was found to be more vulnerable than other direction.



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Finite element analysis of highrise frame structure building with or without damaged columns and truss supporting was carried out using finite element software STAAD Pro. A total number of six damaged columns such as (C11, C12, C13, C21, C22, C23,) at different locations shown in Figure 5 were taken into consideration for the case study. For each case the frame was analyzed in three different conditions (shown in Figure 8) such as (a) frame without damage column; (b) frame with damaged column and (c) frame with truss supporting at damage column condition.

In all cases of the analysis, the crosssections of beam and column were considered as 25.4 cm x 30.48 cm and 60.96 cm x 30.48 cm, respectively. The young’s modulus of elasticity and density of the concrete and steel materials were considered as 21.72 kN/mm 2 and 200 kN/mm 2 and 2.4 gm/cm 3 and 7.83 gm/cm 3 , respectively. The Poisson’s ratio was set as 0.17 and 0.3 for concrete and steel, respectively. Gravity load such as dead load (1.92 kN/m 2 ), floor finish (1.44 kN/m 2 ) and live load (1.92 kN/m 2 ) and lateral load (wind effect) were considered. Lateral load that was considered in this study is shown in Table 1 and was calculated based on the wind velocity of 210 km/h (kilometer per hour). Twonoded beam elements with three degree of freedom at each node were used to discretize the assumed interior panel. A total number of 225 beam elements were employed to model the panel. Twonoded bar elements were considered to model the truss in this study. At the interface of concrete and truss steel it is assumed that same strain will develop under the load.

Figure 5: Elevation of reference model of an interior panel



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Figure 6: Plan of the reference model

Figure 7: Close view of the column and beam numbering of the actual frame



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Table 1: Wind load at different heights of RC frame structure (unit of height is in meter)

Wind Load Calculation Height Pressure (N/m 2 ) Point Load, kN 3.66 0.127 27.66 6.71 0.138 29.97 9.76 0.157 34.15 12.80 0.172 37.39 15.85 0.185 40.14 18.90 0.196 42.64 21.95 0.207 44.82 25.00 0.216 46.82 28.05 0.225 48.76 31.10 0.232 50.44 34.15 0.24 52.00 37.20 0.247 53.56 40.24 0.254 55.12 43.29 0.26 56.43 46.34 0.266 57.75 49.39 0.272 59.06 52.44 0.278 60.24 55.49 0.283 61.43 58.54 0.287 62.18 61.59 0.294 63.74 64.63 0.299 64.80 67.68 0.304 65.86 70.73 0.308 66.73 73.78 0.312 67.80 76.83 0.317 34.42

5. Results & Discussion

In this study, the effectiveness of truss supporting was determined by comparing bending moment, shear force & deflection of beams and columns of RC frame highrise building under the conditions of damage column with or without truss supporting. In all cases, bending moment, shear force & deflection values were calculated in the local coordinate system. All results was taken directly from STAAD Pro (2004) based on the two types of load combination (LC) such as ‘A’ & ‘B’. Where ‘A’ was the combination of dead load (DL), live load (LL) and wind load (WL) blowing from left to right (1.2 DL +1.0 LL+ 1.6 WL) and ‘B’ was the combination of dead load (DL), live load (LL) and wind load (WL) flowing from right to left (1.2 DL +1.0 LL+ 1.6 WL). The share force and bending moment results of the all beam and column under the three condition of analysis of the frame without damage column condition, frame with damage column condition and frame with truss supporting condition of damage column are summarized in the Table 6 and Table 7 and axial force that obtained in the foundation is shown in the Table 8 and maximum vertical and horizontal deflection results of the frame is shown in the Table 9.



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The beams and columns which are very close to the damaged column were taken into considerations which are shown in the Table 3, Table 4, Table 5 and Table 6. Because when damage develops in the column, the nearest beams and columns of damaged column are normally affected more than the others beams and columns during the load acting on the structure.

From Table 2 it is observed that the shear force, Fy (ydirection) and bending moment, Mz (about zdirection) in beam 10 (beam numbering is shown in Figure 7) at damaged condition of the column C23, are 523.94 kN and 1786.36 kNm, respectively which are greater than the values obtained from undamaged condition of the frame. However, when truss supporting was applied for the replacement of column C23, the shear force and bending moment values of the beam 10 were obtained as 132.17, kN and 139.75, kNm respectively which are less than that of shear force, 523.94 kN and bending moment,1786.36 kNm of the beam 10 of the undamaged frame. Table 6 shows that the shear force and bending moment developed in beams 11, 12, 20 and 21 which are closed to the damaged column for truss supporting condition does not exceed the design shear force and bending moment of those beams at undamaged condition of the frame. This means that beams that are very close to the damaged column are safe if truss support is provided during replacing the damaged column. From Table 3 it is observed that the maximum axial force, Fx and bending moment, Mz developed in column 6 at damaged condition of the column C23, are 7309.34 kN and 5632.90 kNm respectively. At undamaged condition, these values are 5640.75 kN and 1942.83 kNm. And at truss supporting condition, these values are 5632.90 kN and 961.15 kNm. From these results it is clear that the axial force of the column 6 at damage condition of the column C23, is greater than that of undamaged condition. However, it seems that the change of axial force and bending moments obtained in the column 6 at damage condition is 30% and 189% of undamaged condition respectively, but at truss supporting conditions this changing value is 0.1% and 50 % below of the undamaged condition respectively.

Table 2: Shear force (Fy) & bending moment (Mz) of beam under undamaged, damaged & trusssupported conditions of frame

Comparison Among Actual, Damage &Truss Supporting Beam's Result

Without Damage Column, C23

Damage column, C23

Truss Supported column, C23 Beam LC Node

Fy ,kN Mz, kN

m Fy, kN Mz, kN

m Fy, kN Mz, kN

m 6 150.27 380.93 153.13 386.64 75.75 36.16

A 7 318.47 476.23 321.41 481.39 92.54 66.89 6 324.67 494.03 342.01 523.94 132.1

7 139.75

10 B

7 156.51 385.96 173.73 419.54 36.11 36.03



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Table 3: Shear force (Fy) & bending moment (Mz) of column under undamaged, damaged & trusssupported conditions of frame

Comparison Among Actual, Damage &Truss Supporting Column’s Result

Without Damage column, C23

Damage column, C2

3

Truss Supported column, C23

Colum

n

LC Node Fy, kN Mz, kNm Fy, kN Mz, kNm Fy, kN Mz, kN

m 2 3461.59 1942.83 5226.95 1786.36 903.96 24.20

A 7 3418.34 338.37

5185.92 568.13 860.60 168.03

2 5640.75 1942.42 7309.34 1776.84 5632.90 961.15 6

B 7 5596.16 332.39

7268.32 640.31 5589.47 551.27

Table 7 shows the axial force and bending moment of the others columns of the building when column C23 is considered as a damaged column, undamaged column and truss supporting column. From Table 7, it is also seen that when truss supporting is provided for replacing damaged column C23, the axial force and bending moment of the columns such as column 8, 15 and 18 do not exceed the design axial force and bending moment of those column at the actual frame i.e. undamaged column. This means that columns, which are close to the damaged column C23 are also safe when truss supporting is provided for replacing damaged column.

Table 4 shows reaction forces of different footings of the building, when column C11 is considered as damaged column. From the Table 4 it is seen that the maximum reaction force developed in the Footing1 at undamaged condition is found as 8556.9 kN. At damage condition this reaction force is found as 9096.55 kN and in case of truss supporting this force is found as 7732.06 kN. For Footing2, the reaction forces at undamaged, damaged and truss supporting cases are found as 5640.75 kN, 7308.45 kN and 5676.423 kN, respectively. For Footing3, these values are found as 4735.55 kN, 258.18 kN and 4949.59 kN, respectively, and for Footing4 these values are found as 8556.99 kN, 9096.55 Kn and 7732.06 kN, respectively and also for Footing5, these values are found as 8556.9 kN, 9096.55 kN and 7732.06 kN. From these results, it is observed that the reaction forces of the Footing1, Footing2, Footing4 and Footing5 at damage condition of the column C23, are increased and for Footing3, it is decreased because the load which transferred through the damage column are distributed to the nearest columns. But, in the truss supporting condition, the reaction force of the all footings is almost same of the original frame condition because damage column load are transferred to the underneath column of the damage column through the truss supporting. From the summary results of Table 8, it is seen that the maximum reaction force of the footings at damage condition can be reduced by applying the truss supporting during the replacement of damaged column.



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Table 4: Axial load on the foundation

Comparative Result for Axial Load (kN) of the Foundation

Type of model LC Footing 1 Footing2 Footing3 Footing

4 Footing

5 A 1470.21 3461.771 4735.555 5640.75 8556.99 Without damage

column, C 23 B 8556.99 5640.750 4735.555 3461.77 1470.21

A 1001.24 5226.055 258.18 7308.45 9096.55 Damage column, C 23 B 9096.55 7308.450 258.18 5226.05 1001.24

A 750.24 903.947 4949.591 5676.42 7732.06 Truss supported column, C 23 B 7732.06 5676.423 4949.591 903.947 750.24

Table 5 shows the maximum vertical and horizontal deflections of the frame at undamaged, damage and truss supporting condition of the damage column. When frame is analyzed under undamaged condition based on the loading combinations, the maximum vertical and horizontal deflections at the top of the frame were found as 1.99 cm and 61.39 cm. But in the case of damaged condition, the maximum vertical and horizontal deflections are found as 3.68 cm and 61.70 cm respectively. From these results, it is seen that the vertical and horizontal deflections at damaged condition are found higher than that of the undamaged state of frame. However, when truss support was provided for the replacement of the damaged column C23, the maximum vertical and horizontal deflections at the top of the frame were found 2.54 cm and 52.32 cm, which are lower than the damaged state of the frame. The details results of deflection of six studies are shown in the Table 9.

Table 5: Deflection chart for different types of model Type of Model Without

damaged column, C23

Damage column, C23

Truss Supported column, C23

Maximum Vertical Deflection (cm) 1.99 3.68 2.54

Maximum Horizontal Deflection (cm) 61.39 61.70 52.32

5.1 Conclusions

In this paper, truss supporting is proposed to support a frame structure highrise building during replacement of damaged column. To verify the effectiveness of the truss supporting in the replacement of damaged column, numerical analysis of the supported frame structure with different conditions such as undamaged frame, frame with damaged columns and frame with truss supporting at the location of damaged column was carried out using finite element software STAAD Pro 2004. From the analyzed results, it is seen that the maximum moments developed in beams, just above the damaged column,



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exceed the design moment of the same beams found from the analysis of actual frame without any damaged column in the frame.

However, when truss supporting is provided during the replacement of column, the moment of the same beams does not exceed the design moment. Similarly, shear force in the beams, just above the damaged column, found at truss supporting condition does not exceed the design shear force of the actual frame. This means that beams just above the damaged column are safe in terms of bending moment and share force if these types of truss supporting are provided during replacing damaged column. In the case of other structural element such as columns, it is observed that large axial force developed in the columns that are close to the damaged column. If truss supporting is provided, the axial forces of those columns can be minimized (see Table8). Therefore, columns that are close to the damaged column could be made safe by truss supporting. Foundation load could exceed their design load due to self weight of supported truss. However it can be minimized by proper designing of truss member and using of high strength material in making truss member. Maximum horizontal and vertical deflections (see Table9) were found within their allowable limit in the case of “Truss supporting”. Truss Supporting is therefore an effective technique which can be utilized during the damage column replacement of the frame structure building.

Table 6: Shear force (Fy) and bending moment (Mz) of beams under undamaged, damaged and trusssupported conditions of frame.

Comparison Among Actual, Damage &Truss Supporting Beam's Result Without Damage, Column,C23

Damage Column, C23 Truss Supported Column, C23

Beam LC Node

Fy ,kN Mz, kNm Fy ,kN Mz, kN m

Fy ,kN Mz, kNm

6 150.27 380.93 153.13 386.64 75.75 36.16 A 7 318.47 476.23 321.41 481.39 92.54 66.89

6 324.67 494.03 342.01 523.94 132.17 139.75 10 B 7 156.51 385.96 173.73 419.54 36.11 36.03

7 159.19 394.25 150.41 405.26 32.1 12.51 A 8 327.61 496.48 318.69 452.98 2.96 1.36

7 328.81 498.79 272.14 424.84 313.16 291.2 11 B 8 160.53 396.29 103.85 262.92 187.28 99.79

8 160.53 396.29 103.85 262.92 187.28 99.79 A 9 328.81 498.79 272.14 424.84 313.16 291.2

8 327.61 496.48 318.69 452.98 2.96 1.36 12 B 9 159.19 394.25 150.41 405.26 316.56 291.2

9 156.51 385.96 173.73 419.54 36.11 36.03 A 10 324.67 494.03 342.01 523.94 132.17 139.75

9 318.47 476.23 321.41 481.39 92.53 66.89 13 B 10 150.27 380.93 153.13 386.64 75.76 36.3



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11 224.74 517.96 238.52 539.58 48.68 17.27 A 12 393.11 612.31 406.8 640.99 119.61 112.43

11 406.04 643.71 427.18 684.91 99.47 81.84 19 B 12 237.67 534.14 258.89 570.17 68.81 25.69

12 244.8 550.45 37.95 185.03 263.09 162.73 A 13 412.87 652.28 206.23 261.84 298.14 51.12

12 415.28 657.17 630.74 1057.1 69.62 45.41 20 B 13 247.03 554.26 462.41 942.66 104.68 20.94

13 247.03 554.26 462.41 942.66 104.68 20.94 A 14 415.28 657.17 630.74 1057.1 69.62 45.41

13 412.87 652.28 206.23 261.84 298.14 51.12 21 B 14 244.8 550.45 37.95 185.03 263.09 162.73

Table 7: Shear force (Fy) and bending moment (Mz) of columns under undamaged, damaged and trusssupported conditions of frame

Comparison Among Actual, Damage &Truss Supporting Column’s Result Without Damage Column,C23

Damage Column, C23 Truss Supported Column,C23 Column LC Node

Fy ,kN Mz, kNm Fy ,kN Mz, kNm Fy ,kN Mz, kN m

1 1470.16 1847.12 1001.07 1744.21 750.24 12.51 A 6 1513.42 539.31 1044.59 722.83 793.57 148.59 1 8557 1860.58 9098.33 1793.15 7733.54 805.63

5 B

6 8516.86 492.68 9056.41 649.15 7690.15 379.57 2 3461.59 1942.83 5226.95 1786.36 903.96 24.2 A 7 3418.34 338.37 5185.92 568.13 860.6 168.03 2 5640.75 1942.42 7309.34 1776.84 5632.9 961.15

6 B

7 5596.16 332.39 7268.32 640.31 5589.47 551.27 3 4735.55 1950.17 258.18 2279.85 43.34 0 A 8 4690.96 325.46 214.84 715.9 0 0 3 4735.55 1950.17 258.18 2279.85 43.34 0

7` B

8 4690.96 325.46 214.84 715.9 0 0 4 5640.75 1942.42 7309.34 1776.84 5632.72 961.42 A 9 5596.16 332.39 7268.32 640.31 5589.47 551.4 4 3461.59 1942.83 5226.95 1786.36 903.84 23.93

8 B

9 3418.34 338.37 5185.92 568.13 860.52 167.62 5 8557 1860.58 9098.33 1793.15 7733.58 805.9 A 10 8516.86 492.68 9056.41 649.15 7690.15 380.11 5 1470.16 1847.12 1001.07 1744.21 750.24 12.51

9 B

10 1513.42 539.31 1044.59 722.83 793.58 148.46 6 1363.59 920.23 891.37 1109.47 869.3 112.43 A 11 1399.71 84.42 927.58 3.81 905.43 333.07 6 8191.35 986.71 8713.06 1173.09 7558.03 239.81

14 B

11 8155.68 26.1 8677.39 87.96 7522.04 13.46



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7 3259.15 1208.85 5012.46 1454.64 1214.38 222.41 A 12 3223.03 220.24 4976.35 233.56 1178.27 85.92 7 5426.71 1217.28 7167.54 1484.55 4913.38 224.04

15 B

12 5391.04 230.43 7130.09 580.09 4877.35 66.75 8 4525.98 1218.23 0 0 0 0 A 13 4490.3 236.28 0 0 0 0 8 4525.98 1218.23 0 0 0 0

16 B

13 4490.3 236.28 0 0 0 0 9 5426.71 1217.28 7167.54 1484.55 4914.5 225.95 A 14 5391.04 230.43 7130.09 580.09 4878.25 65.93 9 3259.15 1208.85 5012.46 1454.64 1212.7 222.27

17 B

14 3223.03 220.24 4976.35 233.56 1176.58 86.19 10 8191.35 986.71 8713.06 1173.09 7558.07 240.49 A 15 8155.68 26.1 8677.39 87.96 7522.04 14.14 10 1363.59 920.23 891.37 1109.47 869.34 112.29

18 B

15 1399.71 84.42 927.58 3.81 905.46 333.21

Table 8: Axial load or support reaction on the foundation

Comparative Result For Axial Load (kN) of the Foundation

Type of model LC Footing 1

Footing 2 Footing3 Footing

4 Footing5

A 1470.21 3461.77 4735.55 5640.75 8557 Without Damage B 8557 5640.75 4735.55 3461.77 1470.21 A 0 1843.3 4472.47 5778.98 9239.24 Damage column ,

C 11 B 0 14518.8 6006.4 3359.21 4645.48 A 2507.79 5600.62 4748.93 5618.45 8106.63 Truss supported

column, C 11 B 8597.13 1455.14 4561.65 3467.21 943.01 A 706.01 0 5591.7 5016.48 8628.34 Damage Column,

C 11 B 11040.71 0 6595 3367.51 2471.67 A 2719.42 3110.66 4690.96 5591.7 8075.41 Truss supported

column, C 12 B 8632.8 5676.42 2456.83 3425.47 994.02 A 2205.24 5185.92 0 6652.96 8895.89 Damage column,

C 13 B 8895.89 6652.96 0 5185.92 2205.24 A 1010.92 1314.18 4641.91 5359.83 8084.33 Truss supported

column, C 13 B 8084.33 5359.83 4820.28 1314.18 1011.14 A 90.43 1991.56 4485.85 5778.98 11856.72 Damage column,

C 21 B 438.69 15183.2 6965.1 3354.8 462.85 A 5949.32 5596.16 4753.39 5600.62 7821.25 Truss supported

column, C 21 B 8191.35 7584.91 4339.94 3456.64 601.09 A 227.95 239.05 5961.8 5899.38 8561.45 Damage column,

C 22 B 11361.76 275.44 6924.97 3887.52 1558.76



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A 2886.73 2987.19 4659.75 5493.6 7740.98 Truss supported column, C 22 B 8186.89 5729.93 1742.48 3356.8 655.44

A 1001.24 5226.05 258.18 7308.45 9096.55 Damage column, C 23 B 9096.55 7308.45 258.18 5226.05 1001.24

A 750.24 903.95 4949.59 5676.42 7732.06 Truss supported column, C 23 B 7732.06 5676.42 4949.59 903.95 750.24 Max. load at actual condition 8557 5640.75 4735.55 5640.75 8557

Max. load at damage , condition 11361.76 15183.2 6965.1 7308.45 11856.72

Max. load at truss supported condition 8632.8 5729.93 4949.59 5676.42 8106.63

Table 9: Deflection Chart

Maximum Vertical and Horizontal Deflection (cm)

Condition of Frame Vertical deflection (cm) Horizontal deflection (cm)

Without damaged column 1.99 61.39

Damage column , C11 21.95 68.38

Truss supported column, C11 2.16 56.67

Damage column, C12 10.05 134.59






Damage column, C22 5.02 59.49 Truss supported, C22 2.57 52.96 Damage column, C23 3.68 61.7


Max. allowable deflection 1.99 61.39

Deflection at damage condition 21.95 137.64 Deflection at truss supported condition 2.67 56.67



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(a) (b) (c) Figure 8: Variation of deflection along the frame height for gravity load: (a) frame without damage column; (b) frame with damaged column and (c) frame with truss

supporting at damage column condition

(a) (b) (c) Figure 9: Variation of bending moment along the frame height: ((a) frame without

damage column; (b) frame with damaged column and (c) frame with truss supporting at damage column condition



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6. References

1. Taranath, B.S (1998), “Structural Analysis and Design of Tall Buildings”. McGrawHill Book Company, 1988.

2. Chapter 6 (Rehabilitation & Retrofitting Methods), Page: VI1 to VI37) of “Handbook on Repair & Rehabilitation of RCC Buildings”–Central Public Works Department. Govt. of India, Published in 2002.

3. “National Earthquake Hazards Reduction Program (NEHRP) guidelines for the seismic rehabilitation of buildings” (FEMA Publication 273, Published in October 1997.

4. Youssef,M.A., Ghaffarzadehb, H. and Nehdi, M.(2007), “Seismic performance of RC frames with concentric internal steel bracing”, Engineering Structures 29, pp 1561–1568

5. Maheri, M. R., Sahebi, A. (1997), “Use of steel bracing in reinforced concrete flames” Engineering Structures, 19(12), pp 10181024.

effective truss supporting technique to replace damage column of … · 2017-12-12 · effective...

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