2. Model and Design
A 3D model of an ordinary moment-resisting RCC (G+3) storey framed building is made with, and without, earthquake loading. The models were designed for India’s highest Seismic Zone-V, with a medium soil profile and a base dimension of 8.44 m × 9.66 m (27’8’’ × 31’8’’). The total height of the building is 14 m (45’11’’) with a 3 m (9’10’’) floor height. Figure 1
and Table 1
show the plan, and preliminary data, respectively for the designed model. The stress-strain relationship of the concrete used is per IS 456 [5
]. Table 2
shows the recommended values for partial safety
material as per BS 8110 [40
], EC 2 [41
] and IS 456 [5
]. In the current study, six model of three multi-storey (i.e., G+3) rigid joint space frame buildings are considered. The cross-sectional dimensions of the structural members are as follows: Beams are two sizes viz., 350 × 450 mm (1’1.8’’ × 1’5.8’’) and 350 × 500 mm (1’1.8’’ × 1’7.7’’), columns are 300 × 300 mm and slab depth is 120 mm (4.7’’). The details of the cross-sectional elevation of the building are shown in Figure 2
a,b. The clear cover of the beam and column are 25 mm, and 40 mm respectively.
The loads on the building that were considered are as follows: Imposed load, including floor finishes, is 2.5 kN/m2
, the outer brick wall load (due to 230 mm) is 13 kN/m, and the inner brick wall load (due to 110 mm) is 6 kN/m Table 1
. This has only given us an insight into the design adopted by various codes. The following load combinations are considered as per the clause 22.214.171.124 mentioned in IS 1893-Part I [6
1.5 (Dead Load + Imposed Load)
1.2 (Dead Load + Imposed Load ± Earthquake Load)
1.5 (Dead Load ± Earthquake Load)
0.9 Dead Load ± 1.5 Earthquake Load
illustrates the values of partial factors of safety for the loadings, and a necessary load combination stipulated by the three codes. From Table 3
, it can be noted that there is a slight difference in the dead load partial safety factor whereas in the case of live load, EC2 [43
] and IS 456 [5
] have the same partial safety factor of 1.5, but BS 8110 [40
] has 1.6. Table 4
shows the design parameter for earthquake loading IS 1893 [6
] considered in the study.
The minimum or maximum amount of percentage of steel reinforcement should not violate the limits stipulated by the codes. Table 5
gives the minimum and maximum percentage of steel reinforcement specified by BS 8110 [40
], EC2 [41
] and IS 456 [5
Static non-linear pushover analysis was performed on the six models to determine their respective performance, and the base shear coefficient (BSC) of all the models was compared. To identify the performance of the buildings, in 1982, the Applied Technology Council (ATC) took the first comprehensive initiative to evaluate the performance of existing buildings. Further, the Federal Emergency Management Agency (FEMA) released a handbook on the seismic evaluation of existing buildings in FEMA-178 [45
] after the ATC report. In 1998, the first standard guideline for analysis, the American Society of Civil Engineers (ASCE) converted FEMA 178 [45
] into FEMA 310 [46
] as an approved national consensus standard document. The guideline suggests that buildings must be evaluated in three phases, i.e., a screening phase, evaluation phase, and a detailed evaluation phase. The procedure used in the evaluation of a building is displacement-based instead of force-based as proposed in ATC-14 [47
]. Now FEMA 178 introduces a displacement-based procedure, which is consistent with the procedures outlined in FEMA 273 [48
In seismic design or the assessment of buildings, modern codes, including the British Code (BS 8110-1997), Euro Code-8 (EC 8), and Indian Code (IS 1893-2002), consider four main methods of structural analysis: Linear static (or simplified modal), linear dynamic (typically multimodal with response spectrum), non-linear static (pushover analysis), and non-linear dynamic.
It has the advantage of providing information on many response characteristics that cannot be obtained from an elastic static or elastic dynamic analysis. Non-linear static analyses is recognized as a practical tool to evaluate the seismic behavior of structures. Tumsek et al. [50
] suggested the use of static analysis, a simplified non-linear method for the seismic assessment of buildings for its retrofitting and strengthening purpose in Slovenia. This method was further refined in the subsequent year [51
], based on the storey-mechanism approach.
Pushover analysis is an approximate analysis method in which the structure is subjected to systematic increasing lateral forces with a vertical distribution until a target displacement is reached. Pushover analysis is a process of systematic elastic analysis, superimposed to plot a force-displacement curve of the overall structure. A two-dimensional (2D) or 3D model that includes load-deformation diagrams of all the elements plotted and gravity loads are applied. A known load distribution pattern is applied as discussed in the aforementioned load combinations. The load increment process continues until the elements yield. The elements are modified as per stiffness, and then loading is applied again so that the additional members will yield. The analysis stops when control node displacement reaches the target displacement, or the structure becomes unstable due to the formation of the mechanisms. Here, the mid-top portion of the building is taken as the control node and the target displacement is predicted to 0.3 m. The top floor displacement is plotted with respect to the base shear to get the pushover curve of the structure.
The various levels of a building’s performance can be obtained from discrete damage states identified from a continuous spectrum of possible damage states viz., O-Operational, IO- Immediate Occupancy, LS- Life Safety and CP- Collapse Prevention
. The structural performance levels based on the roof drifts are the same as those in FEMA 356 [52
]. For the reader’s convenience, this has been reproduced and is shown in Table 6
2.4. Properties of Hinges
This study has been undertaken using a P-M2-M3 hinge, which means that the axial force is in one direction and the biaxial moment is in two mutually perpendicular directions to that of the axial force direction. FEMA-356 [52
] or ACI 318-02 [54
] (Φ=1) is used to define the three-dimensional yield surface of the P-M2-M3 hinges for concrete. The important point to remember is that design forces (Pu, M2, and M3) must lie within the interaction surface. The M2-M3 interaction diagram is drawn for a constant axial load (design force). In the present work, the maximum monitored displacement magnitude of 0.3 m (control displacement) has been adopted at the center of the top storey.
3. Results and Discussion
The amount of steel reinforcement obtained from the design guidelines for all the six models is detailed in Table 7
. It is observed that the model designed for WoEQ detailing with Indian code (MIC
) provides 40.6% and 35.1% more steel than the British (MBC
), and Euro Code (MEC
), respectively. Similarly, WiEQ detailed model provides 65.5% and 43.5% more steel than the British (MBCE
) and Euro code (MECE
). The overall reinforcement for the WoEQ model designed in accordance with the British code contains less steel, and the Indian code has the highest amount of steel of all the codes.
All these structures are safe for their load combinations, and the cross-sectional dimensions of the structural elements (i.e., beam and column) are considered the same in all the models to make them comparable. Further, the comprehensive explanation of obtained results from the non-linear static analysis is described below.
The pushover curve for WoEQ is shown in Figure 3
. At a displacement of 0.07 m, the Indian code reaches a collapse prevention point (CP
) around a base shear of 767 kN. Whereas, the British and Euro code shows a corresponding base shear of 400 kN, and 200 kN, respectively. It is observed that all the models fail suddenly after this point. It can be seen from the plot that at a very small level displacement, all three models follow the same path of the curve, i.e., 197 kN. The base shear of MIC
became almost constant with slight increases for the displacement of 0.065 m and then collapsed. The immediate occupancy (IO
) level and life safety (LS
) level are from 0.02, to 0.05 m, respectively for an almost constant base shear of ~197 kN.
Further, the path followed by MBC
continued and MBC
starts deviating at the base shear level of 350 kN with 0.025 m displacement. There is very less increment in base shear (~50kN) in MBC
over a displacement level of 0.025 m to 0.06 m. Base shear is almost double that of MEC
. The MIC
shows a significant increase in base shear on the same path of the curve, going up to 675 KN of base shear for 0.035 m of displacement and then it increases slowly to the level of 767 KN for a strain level of 0.07 m and then collapses. It shows that the resistance offered by MIC
is much higher than the other two codes viz., MBC
. The sudden failure of all these models is due to the fact that there is no provision for ductility reinforcement in their design. It can also be seen from Table 7
that more steel is provided in MIC
, hence base shear capacity of MIC
is on the higher side. In all the cases, the IO
level ranges from ~0.025m to ~0.06m of the displacement level.
shows the pushover curve for the model design with earthquake loading viz., MBCE, MECE,
, where the curve shows a significant increase in the base shear for the earthquake designed models. The curve shows that all three models followed the same path up to the base shear level of 1250 KN for the displacement of 0.03m, which is six times the base shear achieved in the WoEQ models. At this level, MBCE
starts deviating from the curve path and with a very slight change in the base shear level, it passes through IO
(0.05 m) LS
(0.075 m) and then CP
(0.250 m) and still shows a significant displacement of 0.3 m. Further, MECE
continue on the same curve up to the base shear level of 1800 KN and here MECE,
differs from the path with a very low increase in base shear of 300 KN the displacement level of 0.25 m. Once the base shear crosses the LS
point, there is a very slight increase in base shear whereas displacement is continuous up to CP
. In MICE,
the base shear level at CP
is 2300 KN with a strain level of 0.23 m. All the codal provisions ensure safety in terms of providing additional reinforcement for ductility. It can be seen from both the analyses that there is ~200 % increase in base shear whereas the level increases for CP
up to 228 % in the case where a building is designed with an earthquake provision. The plot shows that the India code performed better than the other codes. Although, the design and detailing is expensive. Further, if we comprise the base shear level by 10%, then the European code saves 43 % of steel. Table 8
shows the load and displacement capacity of a building designed using various codes of practices viz., Indian, British, and Euro.
From Table 8
and the pushover curves of the building for WoEQ Figure 3
and WiEQ Figure 4
loading conditions, it can be said that a building designed in accordance with the Indian code has a reasonably better load, as well as a displacement capacity, before reaching the CP
level. In the case of WoEQ loading, there is an increase in the load capacity of 95% and 279% over the British, and Euro codes, respectively. Whereas, in the case of WiEQ loading, the corresponding increases are about 17%, and 23.42%, respectively. It is observed that for a large displacement capacity without strength and stiffness degradation, the Indian code gives a 19% and 26% increase in displacement capacity, compared to the British, and Euro code, respectively for WoEQ loading. Whereas, for WiEQ loading, the increase is about 11.68% with reference to the Euro code and is almost comparable w.r.t the British code. These characteristics of the Indian code make it a safer design methodology with higher reserve strength and a reasonably good displacement capacity before reaching the collapse prevention (CP
) performance level. The model is compared in terms of base shear and drift ratio. The base shear coefficient (BSC) is the ratio of base shear to the total weight of the model. The drift ratio (%) is the ratio of the top lateral displacement to the height of the model. The allowable limit of the drift ratio in the British code, European code, and Indian Code is 1.5 %, 1.5%, and 1.2 % respectively.
shows the behavior of the building models designed for WoEQ loading. It can be seen that the frame behaved in a linearly elastic manner up to a BSC value of 0.18, 0.10, and 0.33 for the British, Euro, and Indian codes of design. At the BSC value of 0.20, 0.12, and 0.38, there was a sudden drop in the pushover curves of the British, Euro, and Indian models, which indicates the failure of the building, since the model is designed for WoEQ loading, and there is no incorporation of ductility reinforcement in the structural members, which leads to its sudden collapse. Even though all the models failed due to a lack of ductility reinforcement, the model, designed in accordance with the Indian code of practice, resisted the maximum base shear compared to the other codes. It shows that the performance of the MIC
structure of WoEQ is better due to the higher safety factor in the loads, material provided in the building code.
shows the building models designed for WiEQ loading. It can be seen that the frame behaved in a linearly elastic manner up to a BSC value of 0.62, 0.78, and 0.82 for the British, Euro, and Indian codes of design. For a drift ratio value of 0.5 to 1.65, the structures maintained constant BSC values and resisted for a long time, demonstrating non-linearity behavior. The elasto-plastic behavior of the structure was observed with the increase in drift ratio and an increment of BSC from 0.5 to 1.65, which is due to the presence of ductility reinforcement in the building, and the MICE
structure performed well compared to MECE
. The results show that the Indian standard is very conservative in its approach compared to the other two codes.