ANALYSIS AND RESULTS

First the analysis is carried out with initial designed details for all columns and beams as shown in figure 2 and 3. The pushover curve obtained for initial design condition is shown in figure 5 with 1% steel. For the initial condition, the ultimate strength of the frame is 211.15 kN at a displacement of 16.5 cm. and ductility at ultimate strength is 5.8. At the end of the pushover analysis, all bottom storey columns have failed and strength carrying capacity dropped to 20% of ultimate strength and reached to point E(figure 4). To increase the performance of the frame, the two failed end columns of bottom storey, 1 and 16 are strengthened by increasing longitudinal reinforcement from 1% to 2.6% in 6 steps, and pushover analysis is repeated for each case. When the reinforcement is increased by 30%, the ultimate strength of the frame is dropped by 6% and ductility increase by 10%. The structure attained unstable state at a displacement of 22 cm which is less than the initial state of structure. So increase of 30% of longitudinal reinforcement is not shown good performance of the frame when compared to the initial condition. When reinforcement is increase to 67%, the strength increased is only 1.4% but the ductility is increased by 17% at ultimate strength. For this case, the frame attained

Effect of a Member on Global Performance of a Structure — A Case Study on 5 Storey RC Frame

unstable state at a displacement of 32 cm which is more than the initial condition. When the reinforcement is increased 100%, i.e provided twice of the initial design value, strength is increased only 5% and the structure attained unstable state at a displacement of 21cm which is less than the initial condition. When steel increased further as 2.3% and 2.6%, very little increase in strength and ductility is observed, but the structure attained unstable state at ultimate strength itself. Results shows that by increasing the longitudinal reinforcement from 1%

to 2.67%, the increase in strength is only about 10%, because the strength mainly depends on c/s area and grade of concrete. Table 1 represents the strength, ductility and stiffness variation of the structure with increase of reinforcement.

Fig. 5: Behavior of the structure under variation of longitudinal reinforcement of columns 1 and 16 Figure 6. represents the pushover curves with variation of the shear reinforcement spacing of failed bottom storey columns 1 and 16. The curve with 225 mm spacing is the initial design spacing curve. The spacing is reduced from 225 mm to 75 mm in six steps. When the spacing reduced to 200 mm, ultimate strength is reduced by 8% and further decrease of spacing has no effect on strength.

Other than the initial design spacing, for all the cases, the structure attained unstable state at a displacement of 22cm. For initial designed spacing, 225 mm the structure

yielded at 2.9 cm but when the spacing of two columns is reduced to 200mm, the structure yielded at 2.5cm. From the results it is observed that shear reinforcement spacing of two bottom storey columns is not increasing the overall strength of the frame and it is not showing good performance of the frame. The reason for this is that when these two columns are strengthened in shear capacity and flexure capacity, other weaker members are failed and overall strength is reduced and unstable state is reached at lesser displacement. Ductility of the structure is calculated as the ratio of ultimate displacement to yield displacement, as the yield displacement is reduced the ductility is increased for lesser spacing of shear reinforcement. Shear reinforcement spacing is not effected the initial stiffness of the frame. Table 2 represents the variation of strength, stiffness and ductility of the frame with variation of shear reinforcement spacing.

Fig. 6: Behavior of the structure under variation of shear reinforcement of columns 1 and 16

Figure 7 shows the behavior of the frame for different cross sections of columns, 1 and 16. For every increased step of cross section area, the stiffness of the frame is increased. When the c/s area of two columns is increased by 33% i.e 400x400mm, the ultimate strength is dropped slightly and structure attained unstable situation at a

0 50 100 150 200 250 300 350

Base shear Vs Roof displacement for c/s 300x400

steel 1%

Base shear Vs Roof displacement for c/s 300x400 with 1% steel

225 c/c

Table 1: Effect of longitudinal reinforcement of two columns

Effect of longitudinal reinforcement of end columns(300X400) of ground storey on strength and ductility of frame steel used

Proceedings of the National Conference on Advances in Civil Engineering and Infrastructure Development

displacement of 22cm, which shows the poor performance when compared with initial designed case i.e 300x400mm cross section. When the column sizes increased to 500x500mm, the structure shows good performance.

Ductility of the frame is increased upto 500x500mm cross section area, behind this, when the area changed to 500x600mm, ductility is reduced and the structure attained unstable state at smaller displacement. This shows that by increasing the area of the member, increases the strength and stiffness, but it not compulsory that gives good performance to the structure. Results shown that there is a limit to increase the c/s area of the members, if the c/s area is increased without proper assessment may lead to the sudden failure of the structure.

Table 3 shows the variation of strength, ductility and stiffness of the frame.

Fig. 7: Behavior of the structure under variation of cross section of columns 1 and 16

Pushover analysis is performed for individual column for all the conditions as mentioned in Figure 5, Figure6 and Figure 7. The column is modeled in SAP2000, considering the end conditions as in the frame of bottom storey columns. Bottom end of the column is fixed and top end translation and rotation is released in x and y directions and restrained in z direction as shown in figure 8. Figure 9 shows the behavior of frame and column for different percentage of longitudinal reinforcement. When the pushover analysis is performed for column alone, there is no changes in strength or displacement for change of longitudinal reinforcement, because the strength depends on c/s area and grade of concrete. But in the frame, there is little variation because of frame action i.e redistribution of the forces among all the members if one member is failed. In case of column alone, concrete is failed well before the reinforcement is yielded. The ultimate strength of column with 1% steel is 130 kN, when the same columns are existing in the frame with 1%

reinforcement, the ultimate strength of the frame is 211.15

Fig. 8: Column model in SAP2000

0 50 100 150 200 250 300 350

Base shear Vs Roof displacement for c/s 300x400 with 1% steel

300X400 400X400 400X500 500X500 500X600

Table 2: Effect of shear reinforcement spacing of two columns

Effect of shear reinforcement of end columns(300X400) of ground storey on strength and ductility of frame lateral ties size

and spacing Ultimate

strength(kN) Stiffness of frame (kN/m)

Table 3: Effect of c/s area of the two columns

Effect of C/S area of end columns with 1% of longitudinal reinforcement of ground storey on strength and ductility of frame

C/S area Ultimate

strength(kN) Stiffness of frame

(kN/m) Ductility at

Effect of a Member on Global Performance of a Structure — A Case Study on 5 Storey RC Frame

Fig. 9: Comparison of Behavior of frame and Behavior of column with variation of longitudinal reinforcement

Fig. 10: Comparison of Behavior of frame and Behavior of column with variation of shear reinforcement spacing

Fig. 11: Behavior of frame Behavior of column with cross section variation

0 50 100 150 200 250 300 350

0 50 100 150 200 250

Displacement(mm)

Base shear(kN)

Base shear Vs Roof displacement for c/s 300x400

steel 1%

steel 1.3%

steel 1.67%

steel 2.0%

steel 2.3%

steel 2.6%

0 50 100 150 200 250 300

0 50 100 150 200 250

Displacement(mm)

Base shear(kN)

Base shear Vs Roof displacement for c/s 300x400 with 1% steel

225 c/c 200 c/c 175 c/c 150 c/c 100 c/c 75 c/c

0 50 100 150 200 250 300 350

0 50 100 150 200 250 300

Displacement(mm)

Base shear(kN)

Base shear Vs Roof displacement for c/s 300x400 with 1% steel

300X400 400X400 400X500 500X500 500X600

Proceedings of the National Conference on Advances in Civil Engineering and Infrastructure Development kN. The results shows that there is lot of difference in the

behavior of column alone and the frame when the same column exists in the frame.

Figure 10 represents the behavior of the frame and column alone for different shear reinforcement. The ultimate strength of column is constant, it is not changed with shear reinforcement spacing, because the strength depends on c/s area and grade of concrete. The frame carries higher strength and resist higher displacements compared to column alone.

Figure 11 represents the behavior of frame and column for different cross sections of column. When the cross section is increased for column, the strength carrying capacity of the column is higher than the frame though the same column is used in the frame at bottom storey. When the column 500x500mm is used, for column alone the ultimate strength is 360 kN, but, when the same column exists in the frame the ultimate strength of the frame is 260 kN. The results shows that the behavior of column alone is not comparable with the behavior of the frame when the same column exists in the frame.

CONCLUSIONS

Static pushover analysis is an attempt to understand the real nonlinear strength of the structure. The non linear behavior of a structure depends on strength and deformation capacity of each member. The effect of two end columns on overall nonlinear behavior of a 2D frame have been studied and the main conclusions can be drawn as follows:

1. The increase of longitudinal reinforcement is not showing much effect on strength and ductility of frame. 34% increase of reinforcement increases only 5%of ultimate strength and about 10% of ductility at ultimate strength. Increase of longitudinal reinforcement behind 1.67% shown early unstable situation of the structure. It has no effect on stiffness.

2. Decrease of shear reinforcement spacing not shown any effect on strength but ductility is increased at ultimate strength and at 80% of ultimate strength by 10%. but, when the spacing is reduced behind 200 mm there is no effect on strength and ductility, it is constant. it has no effect on stiffness.

3. Increase of c/s area of two end columns of bottom storey increased the stiffness of the frame and strength of the frame. But the ductility increased to certain limit and after further increase of c/s area it has decreased.

4. The individual column performance is completely different with the frame performance, when same column exists in the frame.

REFERENCES

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Methods to Improve Infilled Frame Ductility. Journal of Structural Engineering, Vol. 137, No. 6, June 1, 2011.

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[10] K.A. Cashell, A.Y. Elghazouli, B.A. Izzuddin.

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[11] Qingxiang Wang, Guofan Zhao, Liyan Lin. Ductility of high strength reinforced concrete columns. Nuclear Engineering and Design 156 (1995) 75-81.

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[13] C. G. Trezos. Reliability considerations on the confinement of R C columns for ductility. Soil Dynamics and Earthquake Engineering 16 (1997).

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Proceedings of the National Conference on Advances in Civil Engineering and Infrastructure Development (ACEID-2014), Vasavi College of Engineering, Hyderabad, A.P. 6 - 7 February, 2014. pp.97-102.