Three groups of archetype buildings (Fig. 1) are considered to represent a wide range of applications, from low- to high-rise diagrid buildings. Such groups refer to different diagonals’ angles θ of the triangular module, i.e., 50°, 60°, 70°; for each group, four aspect ratios H/B, i.e., 0.5, 1, 3, 5, and the same square plan 53 x 53 m are selected (Fig. 2a) [25, 26]. The number of storeys and the height of the buildings are shown in Fig. (1). The triangular modules with the relevant diagonal length and module height are provided in Fig. (2b), showing that the number of storeys of the module is equal to 2, 3, and 4, respectively, for θ equal to 50°, 60°, and 70°. The material used for the diagrid is S275 steel (f_yk = 275 MPa, f_tk = 430 MPa). The dead and live gravity loads are 5 kN/m² and 3 kN/m², respectively. The design seismic action is derived according to Eurocode 8, as specified in the following subsection. Both linear dynamic and nonlinear static analyses are carried out on the archetypes’ 3D FE models using the software SAP2000 [27].

Fig. (1). Archetype diagrid buildings.

Fig. (2). Archetype diagrid buildings: (a) floor plan; (b) diagrid’s triangular modules.

Fig. (3). (a) Critical zones; (b) axial forces in the module members; (c) diagonals DCRave; (d) diagonals’ cross sections.

Fig. (4). (a) Constitutive law of plastic hinges (IO = Immediate Occupancy, LS = Life Safety, CP = Collapse Prevention); (b) seismic performance factors.

Fig. (5). DCR in diagonal members of web façade for H/B = 3 and each angle θ.

For the evaluation of the design seismic action, the design acceleration response spectrum prescribed by Eurocode 8 [28] is assumed, characterized by 10% exceedance probability in 50 years, for high seismicity zone (a_g = 0.35 g), soil type B (S = 1.2; T_B = 0.15 s; T_C = 0.5 s; T_D = 2 s), and damping ratio equal to 0.05. The behaviour factor q is assumed equal to 3, according to Kim and Lee [8].

The main results of the elastic analysis are provided in Fig. (3), by considering the axial forces due to the combined effect of compression gravity loads and shear and bending moment induced by the lateral actions. By considering the “web” building façades, i.e., the façades parallel to the applied lateral action (Fig. 3b), the location of the most stressed diagonals (depicted in red) is shown in Fig. (3a). As the building becomes taller, the bending mode governs more than the shear mode. Therefore, for low-rise buildings, the most stressed elements are all the diagonals at the base, while for high-rise buildings, they are the corner diagonals. The average values of the Demand to Capacity Ratio, DCR_ave, and the minimum and maximum cross-sections of the diagonals are provided in Fig. (3c and d), respectively.

In order to evaluate the overstrength and ductility of the diagrid buildings subjected to seismic actions, pushover analyses are carried out by assigning axial plastic hinges to the diagonals according to the model proposed by ASCE 41-13 [29] for diagonals of concentric brace frames (Fig. 4a). For this purpose, two seismic performance factors are introduced and depicted in Fig. (4b) for each group of archetypes, i.e., the ductility µ_T and the overstrength factor Ω, given by Eq. 1:

(1)

Where δ_y,eff, δ_u, and V_max, are the effective yield drift, the ultimate roof drift, and the maximum base shear, obtained from the pushover curve linearized according to the methodology of FEMA P695 [30]; V is the design base shear. From the results of the pushover analyses, it can be stated that the diagrid systems are characterized by great overstrength and poor global ductility, which are in line with the outcomes provided in the current literature [7-12] (see §1).

For a better insight into the seismic performance of the diagrid systems, more detailed results are provided in Figs. (5 and 6), by assuming H/B = 3 and varying the diagonal’s angle. By observing the distribution of the DCR along the height of the building obtained from the elastic analysis (Fig. 5), it is shown that the diagonals at the base corner are the most stressed elements for each diagonal’s angle. In addition, the pushover curves, depicted in Fig. (6a), highlight the poor redistribution capacity of the diagrid systems, for example, by observing the sequence of plastic hinges for θ = 60° (Fig. 6b) with maximum plastic deformation demands concentrated in the corner zone. The crucial role of the corner diagonals with respect to the other members is therefore evident, both in the elastic range, in terms of internal force distribution, and in the plastic range, in terms of deformation demand.

Fig. (6). (a) Pushover curves for H/B = 3 by varying θ; (b) sequence of plastic hinges for H/B = 3 and θ = 60°.

Fig. (7). (a) Shear links at the nodes of diagrid structures, (b) BRB application in diagrid structures.

Fig. (8). Mega-frame configurations.

The concept behind megastructures was initially formulated by Fazlur Khan based on three static requirements [40-42]: (1) to transfer as much as possible, if not all, the compression gravity load into the mega-columns, thus stabilizing the building structure against overturning moments caused by lateral loads; (2) to position the mega-columns at the planned perimeter, thus maximizing the bending stiffness of the building; (3) to interconnect the columns with a stiff shear resisting structural system, thus forcing the columns to work as an integrated system. These three requirements give rise to mega-frame structures, having the form of a multi-story portal placed on the exterior of a building. The exterior mega-frame consists of mega-columns arranged in the corners of the building, connected by mega-beams every 10-15 storeys; each interior substructure spans 10-15 storeys between two mega-beams. The mega-beams, at least one story deep, also act as transfer trusses, supporting the columns of the interior substructures and transferring the relevant gravitational load to the exterior mega-columns. Some megastructure configurations are shown in Fig. (8) [43]. In particular, the vertical and horizontal mega-elements of the diagonalized façades are rigidly connected to each other and very stiff in their plane. Hence, an equivalent cantilever beam is obtained, having the same efficacy as a tubular system.

A seminal study by Fazlur Khan provides the mega-frame concept applied to the Chicago World Trade Center project, a tower of 170 storeys, 655 m high, 706,000 m² of gross floor area. Although never built, this project has had great importance in the evolution of the structural systems of tall buildings. Fazlur Khan [41] proposed to go from a multi-column tube to a square tower with four giant corner mega-columns. Hence, the moment of inertia and the effective section modulus of the new configuration increase, consequently improving the structural efficiency. Approximately every 20 floors, exterior and interior transfer trusses carry the gravity loads into the four mega-columns that are also utilized as service cores for the building.

In order to show the proposed strategy, a case study is selected from the groups of archetypes described in the previous Section 2.1, i.e., the 39-storey building with H/B = 3 and θ = 60°, 154 m tall (Figs. 1, 2 and 9a).

The design seismic action is estimated by assuming the same design spectrum adopted in Section 2.1. Based on the results of the response spectrum analyses (RSA) performed on the 3D FEM model of the DiaGriD structure (DGD) (Fig. 9b), the cross-sections derived for the different members are shown in Table 1. Then, two MegaStructure (MS) solutions, appointed as MS1 and MS2, are define using diagrid densification. The MS FEM model of the two variants is shown in Fig. (9c), while the cross-sections adopted for the structural members are provided in Table 1. In particular, the MS1 and MS2 models are both obtained by increasing the density of diagonals at corner areas and at four horizontal levels, which subdivide the building into four zones, the first three of 9 storeys, while the top one of 12 storeys. In the MS1 solution, the cross-sections of diagonals and beams are the same as in the DGD model. In the MS2 solution, instead, the cross-sections utilised for the members at levels 19-27 in the DGD model are adopted throughout the structure.

The accuracy of the structural sizing in terms of stiffness and strength of the proposed structural solutions MS1 and MS2 has been verified by carrying out response spectrum analyses. For the sake of brevity, only the main analysis results are reported in Fig. (10) and compared to the DGD model, in terms of: fundamental period, T₁; base shear, derived from the RSA and normalized to the overall weight of the structure, V_b/W; maximum DCR of the diagonals; top displacement, D_top; lateral drifts along the height.

The two-degree-of-freedom (2DOF) model of the MSCS is depicted in Fig. (11), where m, k, and c denote mass, stiffness, and damping coefficients, respectively, and subscripts “1” and “2” refer to the primary system, respectively, i.e., the megastructure, and to the absorber, i.e., the secondary substructures.

Fig. (10). RSA results: (a) fundamental period T1, normalised base shear Vb/W, DCR, top displacement Dtop, (b) drifts.

Fig. (11). 2-DOF model of the MSCS configuration.

The equations of motion of the system under seismic excitation are written in the matrix form (Eq. 2):

(2)

Where: M, C, K refer, respectively, to the (2x2) mass, damping and stiffness matrices; x = {x₁ x₂}^T is the vector (2x1) of relative displacements of the structure with respect to the ground; I = {1 1}^T is the vector that multiplies the ground acceleration ẍ_g.

The natural frequencies and damping ratios of megastructure and substructure are defined as follows (Eq. 3):

(3)

with the damping ratio of the substructure ξ₂ defined as a function of ω₁. The mass ratio and frequency ratio are represented by the following parameters (Eq. 4):

(4)

By modelling the earthquake excitation as a white noise input, Feng and Mita [13] impose the minimization of the variance of the displacement of the first degree of freedom, with respect to two design variables, i.e., the frequency ratio β and the damping ratio ξ₂, whose optimal values are provided in closed form in Eq. (5). It is worth noticing that in the expression of the optimal damping ratio ξ_2opt, the frequency ratio β is not explicitly expressed as the optimal value, thus allowing for selecting an appropriate value for β within practical design ranges.

(5)

The mass m₁, stiffness k₁, and damping coefficient c₁ for the SDOF MS model depicted in Fig. (12b) are evaluated from the corresponding properties of the reference 3D FEM MS model, provided in Table 2, by recalling that m₁ is the total mass of the MS configuration, appointed as M_tot in Table 2, while k₁ is equal to ω₁²m₁ and c₁ is calculated as 2ξ₁ω₁m₁.

For the 2DOF MSCS models (Fig. 12c), the total mass M_tot is distributed between the megastructure and substructure, as a function of mass ratio μ, i.e., m₁ = M_tot/(1+μ), m₂ = μm₁. Once defined the value of m₁, the period T₁ (and the frequency ω₁) of the first DOF, representing the exterior mega-frame, is assumed equal to the MS model counterpart, therefore: k₁ = ω₁²m₁ and c₁ = 2ξ₁ω₁m₁. The stiffness k₂ and the damping coefficient c₂ of the second DOF, representing the secondary substructures, are evaluated starting from the optimal parameters β_opt and ξ_2opt, i.e., k₂ = ω₂²m₂ and c₂ = 2ξ_2optω₁m₂, with ω₂ = β_optω₁. In particular, assuming a mass ratio equal to 1, the optimal values of the parameters are: β_opt = 0.35 and ξ_2opt = 0.15 (Table 3). Hence, the period values of the substructure T₂ are obtained, i.e., 4.59 s and 4.91 s for the MS1 and MS2 models, respectively (Table 3). It is worth observing that such period and damping values, T₂ and ξ₂, can be easily obtained by means of a seismic isolation system at the base of each substructure.

Fig. (12). Models: (a) 3D FEM MS, (b) SDOF MS, (c) 2DOF MSCS, (d) 4DOF MS, (e) 4+4 DOF MSCS.

In the four-degree-of-freedom megastructure model (Fig. 12d), appointed as 4DOF MS, the i-th mass, stiffness, and damping coefficients of the megastructure are denoted by m_1i,_MS, k_1i,_MS, and c_1i,_MS (with i = 1, …, 4). The i-th mass is equal to the product of the total number of floors in the i-th mega-frame segment, n_fr,i, and the floor mass, M_floor, i.e., m_1i,_MS = n_fr,i·M_floor. The stiffness coefficients k_1i,MS of the four degrees of freedom of the mega-frame are evaluated according to the procedure of Connor and Laflamme [50], by assuming a stiffness distribution corresponding to the fundamental modal shape of the 3D FEM model. For the damping factors, the same value of the MS configurations is assumed, namely ξ₁ = 0.05.

With reference to the 4+4 DOF MSCS model, the i-th mass, stiffness, and damping coefficients of the megastructure are appointed as m_1i, k_1i, c_1i, while the substructure counterparts are appointed as m_2i, k_2i, c_2i. For the sake of simplicity, all substructures are assumed equal. The i-th mass of the 4DOF MS model is distributed between megastructure and substructure as a function of the mass ratio μ. The i-th mass of the megastructure is m_1i = m_1i,_MS/(1+μ), while the mass of the i-th substructure is m_2i = μm₁/n_frame, with m₁ = Σ_im_1i. The i-th stiffness of the megastructure and substructure are derived assuming that the periods (and circular frequencies) are equal to the counterparts of the 2DOF MSCS model (T₁ and T₂, ω₁ and ω₂, provided in Table 3). It follows that: k_1i = k_1i,_MS/(1+μ) and k_2i = ω₂²m_2i.

Fig. (13). Mode shapes: (a) SDOF MS, (b) 2DOF MSCS (1st and 2nd modes), (c) 4DOF MS (1st – 4th modes).

Modal analyses are carried out on the four models (SDOF and 4DOF MS, 2DOF and 4+4 DOF MSCS). Since the damping values of the megastructure and substructures are different, respectively equal to 0.05 and 0.15 (Table 3), the MSCS is characterized by non-proportional damping. In particular, a viscous system that is not classically or non-proportional damped exhibits complex natural modes and does not satisfy the Caughey and O 'Kelly identity: CM^-1K = KM^-1C [51]. Therefore, non-diagonal elements in the C-matrix cannot be neglected. Hence, in order to decouple the equations of motion, the state-space formulation is developed.

By considering the undamped system, the modal shapes of the SDOF MS, 2DOF MSCS, 4DOF MS, 4+4 DOF MSCS models, obtained using SAP2000 software [27], are shown in Figs. (13a-c and 14), respectively. The corresponding values of periods and participating masses are given in Tables 4 and 5. Looking at the periods and the participating masses of the SDOF MS and 2DOF MSCS models (Table 4), it should be observed that the first mode of the MSCS model is the mode of the substructure, while the second mode represents the mode of the megastructure. For μ=1, although the total mass is divided equally between the two structural parts, a participating mass of the fundamental mode greater than 0.50 is activated, equal to 0.62.

By observing the periods and participating masses of the 4DOF MS and 4+4DOF MSCS models (Table 5), as well as the relevant vibration modes (Figs. 13c and 14), it should be pointed out that the first four modes of the MSCS model are the substructure modes, while the subsequent four modes are the megastructure modes. The comparison between the SDOF and MDOF MS models shows a perfect agreement of the fundamental period. Similarly, the first and fifth periods of the MDOF MSCS model are close to the first and second periods of the 2DOF MSCS model (MSCS1: 4.87 s vs. 4.92 s, 1.53 s vs. 1.52 s; MSCS2: 5.22 s vs. 5.25 s, 1.64 s vs. 1.63 s). This correspondence is also observed in terms of participating mass. Indeed, the sum of the first four modal participating masses of the 4+4DOF MSCS model is approximately equal to the first participating mass of the 2DOF model (MSCS1: 0.59 vs. 0.62; MSCS2: 0.60 vs. 0.62). The sum of the participating masses of the next four modes is approximately equal to the second participating mass of the 2DOF model (MSCS1: 0.41 vs 0.38; MSCS2: 0.40 vs 0.38).

As regards the non-classically damped system, modal analyses are only carried out on the 2DOF MSCS model. The periods and damping ratios, derived from the complex modal analysis, of models MSCS1 and MSCS2 are given in Table 6. The following observations can be made. The values of damping are the same for the two models since for both models, a mass ratio μ equal to 1 is assumed. Since the first vibration mode mainly involves the substructure and the second mode mainly involves the megastructure, by combining the two structural parts, a reduction is obtained for the damping in the first mode (from 0.15 to 0.124) and an increase in the second mode (from 0.05 to 0.107). The comparison between the Tables 4 and 6 suggests that the periods derived from classical and complex modal analyses are almost coincident.

Fig. (14). Mode shapes, model 4+4 DOF MSCS: (a) 1st mode – (h) 8th mode.

Fig. (15). Response spectra of three spectrum-compatible ground motions.

Time-history analyses are carried out by adopting a set of three spectrum-compatible ground motions, defined using SeismoMatch software [52], which selects accelerograms by matching their average response spectrum to a reference elastic spectrum (here, the one prescribed by Eurocode 8 [28]). In Fig. (15), the acceleration spectra with the relative PGA values are reported, as well as the average and the reference spectra.

The time history analyses are carried out by assigning the damping ratio as a function of the periods, according to the following considerations. Recalling that the first vibration modes are the modes of the substructures, while the next ones mainly involve the megastructure (Fig. 14), and considering the values of complex modal damping provided in Table 6, then the damping ratio of 0.124 is assigned to the first four modes, while the damping ratio of 0.107 is assumed for the following ones.

The results of the time-history analyses are provided in terms of top displacement and acceleration and base shear. With reference to the peak values of these response parameters, three performance indexes are introduced for a preliminary estimation of the effectiveness of the MSCS:

1. d_top, the ratio between the top displacements of the controlled and uncontrolled structures, d_top=d_top,MSCS/d_top,MS.

2. a_top, the ratio between the top absolute accelerations of the controlled and uncontrolled structures, a_top=a_top,MSCS/a_top,MS.

3. v, the ratio between the base shear forces of the controlled and uncontrolled structures, v=V_b,MSCS/V_b,MS.

The values of the top displacement and acceleration ratios for each accelerogram and MDOF model, as well as the average value, are shown in Fig. (16a and b), respectively. Similarly, base shear ratio values are reported in Fig. (17a and b) for MS and MSCS models 1 and 2, respectively. The results provided in Fig. (17), in terms of base shear ratio v, obtained by adopting both pairs of SDOF MS – 2DOF MSC and MDOF MS – MDOF MSC models confirm the accuracy of the simplified models in the first design phase. In fact, a close correspondence between the simplified 2DOF or SDOF models and the respective MDOF models is registered, with scatters in terms of average values of 1% and 7%, for solutions 1 and 2, respectively.

Fig. (16). MDOF MS e MSCS models: (a) top displacement ratio dtop, (b) top acceleration ratio atop.

Fig. (17). Base shear ratio v (a) MS1 and MSCS1; (b) MS2 and MSCS2.

Fig. (18). Base shear - Imperial Valley ground motion: (a) models MS1 and MSC1, (b) models MS2 and MSCS2.

From the results depicted in Figs. (16 and 17), it should be emphasized that the passive control of the megastructure induced by the substructures results in a dramatic reduction of the seismic response. In fact, in the MSCS1 configuration, the displacement and acceleration ratios are approximately equal to 60%, and the base shear ratio is about 30%. In the MSCS2 model, the displacement and acceleration ratios are equal to 65%, and the base shear ratio is about 30%.

Moreover, as an example, the base shear time histories of the controlled and uncontrolled configurations (models MDOF 1 and 2) for the Imperial Valley ground motion are compared, as shown in Fig. (18a and b). The plots confirm that the passive control of the megastructure using the substructures’ mass damping effect results in a substantial reduction of the overall seismic response.

Although the results of these dynamic analyses refer to a single case study and MSCS configurations derived from the same optimal values of design parameters, they are representative of more general applications. These outcomes, in fact, are in line with the previous studies [53, 54], in which different structural solutions are considered by varying the building’s fundamental period, i.e., going from very rigid (e.g., stiff diagrid structures or diagonalized mega-frame) to more flexible structural systems (e.g., moment-resisting frames or frame tubes). Then, by adopting 2DOF and MDOF lumped mass models, the dynamic behaviour of MSCS configurations is evaluated by varying all design parameters (μ, T₂, ξ₂) in a wide range. The effect of the distribution of moving secondary substructures is also investigated [54].

The MSCS concept starts from the mega-frame structural typology, composed of primary mega- columns and mega-girders, which resists both gravity and lateral loads due to the frame action, and a number of secondary substructures, 10-15 storeys tall, that are placed between two mega-beams and are only designed for their gravity loads. The substructures, indeed, rely on the mega-frame stiffness and strength due to the floor diaphragm action. In the case of the MSCS, instead, a detachment between exterior mega-frame and interior substructures is required for allowing the relative motion, which also requires a physical separation in the floor slab. Therefore, the secondary structures should possess adequate lateral strength and stiffness, necessary to absorb internal force demand and maintain drifts within the serviceability limit. In general terms, the engineering solutions that guarantee the expected behaviour and the construction feasibility of the MSCS should account for the following issues:

1. The “physical” detachment of the parts of the building that must work as substructures from the megastructure, and the subdivision of the building mass between megastructure and substructure.

2. The relative motion between substructures and megastructures.

3. The stiffness and the damping of the substructures, defined by the optimal value derived from optimization procedures [13, 53, 54] or parametric analyses [53, 54].

The disconnection between the main and secondary structures requires a joint (gap) in each floor slab, whose position depends on the percentage of the tributary mass of primary and secondary structures, which, in turn, should be compatible with construction aspects and functional requirements. The size of the gap should be larger than the maximum relative displacement predicted by the analyses. With reference to the design of the substructures, it is necessary to define a structural system which bears the floors’ weight and possesses adequate lateral stiffness. In Section 3.3, seismic isolation system at the base of the substructures is the strategy preliminarily suggested for dividing the design process of the substructure into two independent parts, each related to a specific function: (1) the design of the isolation system, aimed at tuning the substructure mass at the optimal frequency, and making it works as a tuned mass damper; (2) the design of the structural system, aimed at ensuring safety and serviceability of the substructures, as inhabited parts of the building. As a result of the analyses carried out by the authors in other studies [53, 54], an additional option emerges to design the substructure without taking into account the optimal frequency value, since, due to the large mass ratio, the response of the megastructure is highly reduced in the whole range of typical isolation periods.

Concerning the damping associated with substructures, which is essential for mitigating the displacement of the substructure and avoiding the occurrence of collision with the exterior mega-frame, different strategies can be considered, namely:

1. Installing dampers between the megastructure and the substructure [16].

2. Inserting a tuned-inerter-damper between the megastructure and the substructure [24].

3. Including dampers in the substructures [22].

4. Adopting an isolation system at the base of the substructures made either of high damping rubber bearings, or by coupling isolators and viscous (or hysteretic) dampers.

Another engineering aspect that must be properly addressed in order to make the MSC configuration feasible concerns the floor structural system at the transfer levels. Its role is fundamental, and its design is challenging: it should span the large bay between the corner mega-columns (say, 20-30 m, or more), bear the gravity load of the upper substructure (10-15 storeys tall), and transfer this load to the mega-columns. Therefore, the design solutions should account for very long and heavily loaded free spans. A system made of two-ways mega-truss girders seems a very good candidate. Finally, from a functional and architectural point of view, it should be recalled that both the classical typology of mega-frame and the innovative MSCS usually assume that the mega-columns, which are the only vertical continuous structures, are located at the building corners. For this reason, it is implicitly assumed that the vertical transportation system (elevators, escalators, as well as staircases) is concentrated in the corner locations, thus implying that the classical core-centred floor plan should be rearranged in a solution with split corner cores.

As an example, two MSCS engineering solutions, based on the concept of mass damping, are briefly described.

The first structural solution is proposed by several papers [14-16, 18, 23] and is obtained first from the Tokyo City Hall, an emblematic mega-frame, 144 m tall, composed of steel truss mega-columns and mega-girders that subdivide the building into three mega-zones, each of 48 m. In the MSCS solution, a gap of 0.5 m separates the external mega-frame to two or three interior substructures. The bases of such substructures are fixed to the mega-beams structures of the mega- frame at the transfer floors. Viscous or friction dampers are utilized, either between the exterior and interior structures or within the substructures according to different arrangements. Additional columns are introduced between the mega-beams and the upper floors of the substructures by means of slip supporting joints in order to realize intermediate supports for the mega-beams.

The second structural solution is proposed by Martinez-Paneda and Elghazouli [21]. An exterior mega-frame, 250 m tall, is composed of four reinforced concrete corner mega-columns and steel mega-trusses that subdivide the building into five interior blocks. Each block is vertically stacked and overhangs alternately in the two plan orthogonal directions. The structural system of the interior blocks is a simple frame with hinged beams; thus, it leans on the mega-columns for lateral stability by means of the diaphragm action of the composite steel-concrete floor. A sliding joint is provided between the substructures floor and the core at each level, with a spring and a viscous damper connecting the two structural parts, in order to allow the relative motions between the exterior mega-frame and the interior blocks.

As discussed in Section 3.1, the mega-frame (Fig. 10c) consists of four continuous corner mega- columns and four mega-beams, each three storeys depth. Consequently, the mega-frame is made up of four blocks, with the first three ones 9 storeys tall and the last one of 12 storeys. In order to realize the controlled mega-substructure, it is planned to use the mega-columns as service cores and disconnect the substructure slabs by means of a joint at each floor (Fig. 19a-c). The continuity of the service cores along the building height gives rise to a cruciform floor plan for the substructure slabs (Fig. 19b and d); the columns of the substructures are connected at their bases to the mega- beams by means of the seismic isolation system. Finally, the mega-floors are made up of a two-way truss beam system (Fig. 19a, c, e).

Fig. (19). a) Façade, (b) Aection A-A’, (c) Section B-B’, (d) Typical substructure’s floors, (e) Typical mega-girder system.