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Using the matched strong ground motion linear time history analysis is made for flexible and fixed base support conditions of the frames Story 7 (S7) and Story 12 (S12). For all support conditions, the seismic responses are calculated using SAP2000 structural analysis software .
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The drift limitations for perimeter frames both for 6 stories (See Figure 6) and 12 stories (See Figure 7) were not satisfied for some stories when SSI was considered. This is further to be noted that the SBC limits are still relaxed (0/02 h) for satisfying the Interstory drifts as with some codes like Eurocode these limits are quite strict (0/005 h, 0/0075 h and 0/01 h). A comparative study will be useful to see the pros and cons of Eurocode 8 on SCB. Drift checks: 0/02 h = 0/02 × 3500 = 70 mm limiting value.
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In addition, closer examination of spring model of ground motion effects of D and IV on model frames S7 and S12 is different. The smaller ground motion with soil D gives bigger story drift, P-delta effect and Story shear on S7 than S12 while larger ground motion with Soil IV shows the opposite. This indicates bigger earthquake effect more on taller than short building. Because soil IV ground motion (Chinese GB50011-2021) is greater than soil D (Ethiopian ES8-2021), which is related to the design response spectrum of the corresponding seismic codes magnitude.
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Comparison is made in terms of fundamental period of vibration, inter-story drifts and performance for 3, 6 and 12 story frames with and without SSI. These were designed as spatial and perimeter MRFs with a response modification factor of 8 using Saudi Building Codes. In total 12 cases were conducted to see the effect of SSI on such frames. Frames supported on loose granular soil (Site Class D) with moderate seismic zone, compatible to the PGA like Madinah region were considered.
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From Figure 3 and Figure 4 it is evident that SSI influences the overall stiffness of low, medium and high rise MRFs. Although in this case a medium soil was considered under a moderate seismic event. Nevertheless, the effect of SSI can even be more worsen for cases when structures are in high seismicity zones and with more weak and flexible soil which needs to be further investigated.
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The analysis procedures in early 20th century were essentially based on the use of simplified structural models subjected to simplified loading types. For example, for the purpose of structural design, the seismic load was historically idealized as a simple mass-proportional lateral static loading. Later, with the increasing applications of modal analysis and the formulation of the RSA procedure, the role of vibration modes and natural periods in understanding and controlling the seismic demands was recognized. With the advent of computer programs and dynamic analysis solvers in mid-1960s and 1970s, and with the increasing availability of more ground motion records, the use of detailed dynamic analysis procedures based on the direct integration solution of the governing dynamic equations of motion was established. This also started the use of nonlinear modeling for a relatively better structural idealization as compared to the linear elastic models.
Where G is shear modulus of soil defined in Equation 6(e), E is the modulus of elasticity of soil; ν is the Poisson’s ratio of soil. L and B are the length and width of Raft foundation of the whole building, respectively.
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Maximum Induced bending stress in the glass under ULS as shown in Figure 22 (left) is 16/8 Mpa < The allowable bending stress = 50 Mpa. Maximum Induced deflections as shown in Figure 22 (right) in the glass under SLS is 19 mm. Whereas the Acceptance criteria for allowable Deflection under DL + WL = Span/60 equals 2000/60 = 33/3 mm > 22/4 mm. The glass panels are Safe for both ultimate limit states and serviceability limit states. In the following section, mullions and transoms checks are carried out under the adopted acceptance criteria for strength and deflections.
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The reference frames are designed using importance factor 1/0 and considering soil class D with Ss and S1 as 1/07 g and 0/57 g, respectively (See Figure 2). A seismic category for the structure is considered as D from SDS (0/713) and SD1 (0/38) with the assumed site class. In total, 12 cases are analyzed as shown in Table 3 .
Table 6 shows the fundamental period (See Figure 3) and top displacement (See Figure 4) of all the frames with SSI and without SSI. It is obvious that the fundamental period of vibration and the top displacement are higher when SSI was considered.
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Figure 3 shows the same typical residential buildings plan of 15 m × 32 m for both model frames common Architectural plan in China that can be adopted to Ethiopian construction. The plan is adapted from Chinese Seismic and Concrete Design standards and modified for this study purpose. The 2D model frames here after denoted as, S7 and S12 for 7 and 12-story respectively. Figure 4 shows typical transverse frames S7 and S12 story with first story height 4/50 m and others typical Story height of 3/6 m. The frames are considered in the short transfer direction and carry tributary area of floor load shown in Figure 3 for 2D regular frame analysis. The columns and beams of frames are designed according to Ethiopian Concrete Design Standard ES2-2021 that are subjected to design seismic action of PGA = 0/25 g soil type B design response spectrum .
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A linear modal dynamic analysis is developed for the seismic design of the frames. The fundamental period obtained from the codified formulation for 12, 6 and 3 stories are found to be 1/44 sec, 0/83 sec and 0/47 sec, respectively, which is lower than the one obtained by modal analysis (See Table 6); in this circumstance the code specifies that scaling factors for the design forces and drift must be applied. Both scaling factors (forces and drifts) are 85% of the ratio of “the static base shear (Vstatic)” to “the modal base shear (Vb)”.
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The performance is shown in Figure 9, Figure 10 and Figure 11 for 3 stories, 6 stories and 12 stories respectively. The obtained structural capacity curves are plotted in Figure 12, Figure 13 and Figure 14 for 3 stories, 6 stories and 12 stories respectively that shows total base shear (Vb) versus top displacement (Δ). All these curves show reduced stiffness of the frames when SSI was considered.
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On the other hand, for soil IV, 218% and 324% for the corresponding stories in direct method. Furthermore, for soil D spring model the sensitivity coefficient can be 481% and 223% bottom and top stories respectively. On the other hand, for soil IV spring model it is 477% and 256% bottom and top Story.
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The FEMA 356 rules with the IO, LS and CP limit states for hinge rotation have been used in the analysis with the SAP 2000 program. The five points (O, B, C, D and E) as shown in Figure 8 are used to define the hinge rotation behaviour of analysed frame members according to FEMA recommendations. Three more points Immediate Occupancy (IO), Life Safety (LS) and (Collapse Prevention) CP are used to define the acceptance criteria for the hinge. The colours below show different acceptance criteria.
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The glass panel DGU (6 mm + 12 mm (space) + 6 mm = 24 mm) resting on mullions and transoms grid of as shown below is checked for strength and deflection. Conservatively, it is assumed to be without the air gap.
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The various checks related to strength and deformability obtained from the numerical model as shown in Figure 16 have been carried out for glass and Aluminum mullions. The structural elements, glass and brackets been found SAFE according to different acceptance criterion . Maximum Mullion spacing (Maximum Transom Length) is 2 m (See Figure 17 for elevation and Figure 18 for plan), therefore it is considered as worst scenario for the design calculations.
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To investigate the effect of SSI on spatial and perimeter moment resisting frames according to SBC, a case study is conducted on 12, 6 and 3 stories residential building. The building has a rectangular plan measuring 33/0 m by 19/8 m in longitudinal and transversal direction, respectively. Spatial and perimeter frames hereafter are named as “S” and “P”, respectively. The typical floor plan of the building with the indication of spatial and perimeter frame is shown in Figure 1(a), whereas, the elevation of 6 stories frame with the masses calculated from the loads is given in Figure 1(b), the outer columns are named as “col1” and the inner columns as “col2”.
Karavasilis et al. proposed an alternative procedure to estimate the maximum inelastic roof displacement and the maximum inelastic Interstory drift ratio along the height of regular multi-story steel moment resisting frames (MRFs) subjected to pulse-like ground motions based on dimensional response analysis. Malhotra in presented interpretation of the response characteristics of three recorded and one synthetic near-field ground motions and showed that pulse-like ground motions with high peak ground velocity over peak ground acceleration ratio (PGV/PGA) have wide acceleration-sensitive region in their elastic response spectrum. Farouk et al. examined the effect of the superstructure’s rigidity on the contact stress and the differential settlement for plane 2-bay frames. Christopoulos et al. found that the effect of the vertical accelerations of near-fault records on the demand in rotational ductility and on the maximum story deflections of steel moment-resisting frames is negligible, even though a large increase in the maximum axial loads of columns is noted. Makris and Chang found that, although in several occasions near-fault records resemble cycloidal pulses, the response of structures with low to moderate periods is substantially affected by the high-frequency fluctuations that often override the long duration pulse. MacRae et al. found that inelastic demands of medium and longer period oscillators responding to near-fault strike-normal shaking increased for sites close to the fault as the distance along the fault from the epicenter increased. Rao and Jangid , examining sliding systems under near-fault motions found that the resultant sliding base displacement is mainly due to the normal component of the near-fault motion. Mavroeidis and Papageorgiou proposed a simple, yet effective, analytical model for the representation of near-field strong ground motions.
In the present study, the flexible foundation effect is considered to check the influence of SSI on the performance of MRFs. The formulations for springs constraints at the ground surface were used based on FEMA 356 . G is the effective modal mass for the fundamental mode of vibration in the direction under consideration computed to be 20/35 Mpa. In the current case the foundation is considered as rigid rectangular with length (L) equals 3 m and breadth (B) equals 2 m. The embedment depth of the foundation is placed at 3 m. Geotechnical conditions of Al-Madinah region of Saudi Arabia are used in this study. The soil type was selected based on geotechnical investigation report conducted for the construction of one of the academic blocks at the Islamic University of Madinah. The field investigations were carried out in July 2009. The soil strata under consideration are layered, the top 9 m thick layer comprises brown Clayey Sand. The denser underlying layer from 9/0 m to the explored depth of 15 m includes gravels. The groundwater table and the bed rock were not intercepted during exploration. Geometric properties of the foundations imply that the influence zone of the structure transpires only in the top layer of the soil.
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And other response of the model structures S7 and S12 shown in table and graph form. All response comparisons are made with reference to fixed base for both types of flexible base models presented in subsequent sections.
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This study shows both flexible base models give bigger fundamental period of vibration and drift with reduced base shear than fixed base, good agreement with seismic codes provisions and previous studies . Furthermore, this study indicates that the drift, P-Δ effect and Story shear vary along the height of building from bottom to top stories differently. Because P-Delta effect shows the combined effect of the story shear, drift, storey height and story axial load. The spring model gives larger Story drift and second order effect at the bottom stories for both soils D and IV, which is detrimental effect maximized at bottom stories. Conversely, half space direct method gives somewhat reverse to spring model, and gives larger Story drift and P-delta effect in the top stories. This may be the direct method due to higher mode effect for mass participation factor of 90% than spring model.
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Wolf 1985 and many other authors noted that for structures built on strong foundation such as rock during earthquake motion, the force generated in the form of overturning moment and transfers shear will not cause deformation to the base in turn; the stiffness of structure remains constant. For a given control of motion, the seismic response of the structure depends only on the properties of the structure, however for soft soils used as base; the base deformation changes the stiffness of structure during earthquake vibration, which in turn affects its response, known as Soil Structure Interaction (SSI) effect. Even if, SSI has both kinematic and inertia effect on structure; in this study only inertia effect is considered.