Liquid Mass Dampers have been used to stabilize marine vessels or to control a wobbling motion of satellites since 1950, and then was used in structural engineering to reduce lateral displacement. Many experimental and analytical studies have been done to measure the effectiveness of water damper. Some studies use water tanks as Tuned Mass Damper (TMD) based on Water-Structure mass ratio [8] and [9] , while other researches use Tuned Liquid Damper TLD based on wave-structure interaction [10] to reduce lateral displacement of structures. Experimental studies [11] and analytical studies [12] for TLD have been carried out to evaluate the effect of TLD on structure behaviour. The use of TMD and TLD at the same time cannot be done in a developing country because TLD requires maintenance and special equipment to propagate wave sloshing.

Moreover, some researchers discuss the combination of TMD and TLD at the same model and its effect on earthquake response control of buildings [13] considering many parameters such as liquid height, mass, and frequency of water tank. A feasibility study of variable tanks as TMD has been implemented to improve the seismic response of structures during the design stage and select the optimum solution [14] .

It worthy to mention that American code ACI 350.3 [15] and ECP 201-2012 [2] consider a design of tanks to

resist lateral load developing from water structure interaction (impulsive and convective force), i.e., to design water containing tanks itself without considering the effect of tanks at the roof of structures.

This paper presents a study for improvement of an existing school building in Port Said, Egypt. As Egypt is a developing country, the proposed methodology is to use tanks as a TMD. This paper presents an appropriate solution for existing important structures in developing country, and draws attention to improving seismic behaviour of existing structures with low cost using tanks to act in two options; the first is to satisfy the fire fighting requirement of Civil Defence Authority (CDA), second, is to improve the seismic response behaviour of the existing building.

This study has been done considering variation in the mass ratio (water to structure mass ratio μ) in two cases. The first case with one tank at the centre of the roof area, the second case with two tanks on the roof located in a symmetrical position as displayed in Figure 5. Figure 6 shows a graph illustrating the 20 cases considered. For each case, it is considered that the variation of water height with fixation of tank dimensions and fixation of water height and variation of tank sizes. The total number of groups under this study is four groups each group contains five models with different mass ratio μ. Table 3 presents all cases of tank mass damper.

Three-dimensional pushover analysis has been done for 20 models in X and Y direction using SAP 2000 V 17. Then a feasibility study of various water TMDs is studied using pushover analysis. This feasibility study has been done to evaluate which case is the optimum solution to improve the seismic response of the existing building.

Pushover analysis has been used in many researches as a technique to evaluate structures, and discuss nonlinear behaviour of structures such as:

・ Devi and Nandini, (2015) [16] , studied the seismic demand on reinforced concrete structures using pushover analysis. A Comparison between uniform and non-uniform structures has been done. They concluded that structures with a uniform profile in elevation have more lateral load capacity compared to structures with the non-uniform profile in elevation.

・ Oyguc and Boduroglu, (2012) [17] , presented a research paper on seismic capacity of irregular reinforced concrete structure using experimental studies on a prototype building, then compared results with three- dimensional pushover analysis using SAP 2000.

・ Bhatti, and Varum, (2012) [18] , discussed the performance-based nonlinear static pushover analysis for the seismic design of reinforced concrete buildings.

・ Yasrebinia and Pourshrifi (2012) [19] , presented a study for three-dimensional analysis of irregular structures, using four, six and eight stories buildings. Then studied the variation of load pattern, load value and direction effect on results of three-dimensional pushover analysis.

・ Ismaeil, (2014) [20] , performed a pushover analysis to study and evaluate a four-story existing reinforced concrete flat slab building in the Sudan.

・ Pednekar et al., (2015) [21] , Performed three-dimension pushover analysis of reinforced concrete structures. The buildings under study have five, six and seven story. Finally, they compared the results between models.

The analysis using sap 2000 provides the capacity curve, i.e., the force-displacement curve as shown in Figure 7. This figure shows the level of plastic hinges [22] [23] . Besides, the analysis results provide the performance point where the capacity curve of the structure intersects the demand curve of the applied lateral load as shown in Figure 8 ATC-40 [22] .

After reaching the performance point and corresponding T effective, one can indicate the level, number of plastic hinges and corresponding base shear. Table 4 presents the performance level of a building based on the definition of plastic hinges [23] . Figure 8 shows different stages of plastic hinges [22] .

Figure 9 displays force-displacement curve for the building without tanks in X and Y directions, while Figure 10 presents force-displacement curve for the building with tanks in X and Y direction. It is noted that the force-

displacement curve is affected by the variation of mass ratio in the presence of one tank as shown in Figure 10(a) and Figure 10(b), while the force-displacement curve is not affected by variation of the mass ratio in the presence of two tanks as shown in Figure 10(c) and Figure 10(d).

Table 5(a) and Table 5(b) display performance point and number of plastic hinges for building without tanks in X and Y-directions, respectively. While Table 6 presents a comparison between each group (with tanks) con-

sidering performance points and number of plastic hinges in both directions X and Y.

Comparing the results shown in Table 5 and Table 6 it is noticed that; the model with 0.7% mass ratio give the best results as far as the number and type of plastic hinges. This will lead to improving the seismic response of the studied prototype building. This is summarized in Table 7 which displays a comparison between performance points and number of plastic hinges in all cases with μ = 0.7% in both directions X and Y. This confirms that the G2 group with 0.7% mass ratio is the best solution for the seismic improvement of the chosen building.

This study shows that; the use of one tank has a significant effect on improving the seismic response of the

studied building more than the use of two tanks. However Patil et al. [9] found that the use of multiple mass dampers gave better results for the overall displacement of the structure. This can be explained by the fact that; his results have been obtained without considering the nonlinear behaviour of the structure as in this paper.

The results obtained herein agrees with those obtained by Dattatray et al. [8] that show that tanks with 1/2 to 2/3 water depth have better effect more than full tanks, as shown in Table 3.

Besides, the mass ratio of 0.7% that gives best results agrees with the mass ratio of 0.7% to 3% obtained by Dattatray et al. [8] and Tejashri et al. [14] .

It is worthy to mention that; the present study considers the nonlinear behaviour of structure while other previous studies considered the static linear analysis.