Keywords

1 Introduction

The advancements in the construction of high-rise buildings have led to the implementation of diagrid structures. In the olden times, high-rise buildings were of typical portal frame systems with horizontal beams and vertical columns. Later on, additional bracings were introduced in order to take up the lateral loads more efficiently than that in the conventional building frame systems. The major difference of a diagrid building in comparison with a braced tube building is the absence of vertical columns in the system. With a lower requirement and maximum exploitation of materials, diagrid structures exhibit their effectiveness in contrast to conventional and braced frames.

Diagonal members in diagrid structures act both as inclined columns and as bracing elements, thus carrying both gravity loads as well as lateral forces. With the axial action of diagonal members, it takes up the shear acting on it, thus reducing the shear racking effects. The unique geometric configuration of the system enhances structural stability along with the aesthetic appeal. It provides for a sustainable structure with greater stiffness and structural efficiency. Redundancy in the diagrid design helps in the transfer of load from a failed portion of the structure to another. A diagrid has better ability to redistribute load than a moment frame skyscraper, creating a deserved appeal for the system.

The most commonly used material for the diagrid construction is steel and the system can be applied for various geometric forms. Geometric nonlinearities have led to the evolution of diagrid projects with hyperboloid, aerodynamic, cylindrical, irregular, twisted, tapered, tilted, and free forms, the most challenging among them being “twisted”. Examples for diagrid structures with the common geometric forms are the steel diagrids that can be created using modern 3D modeling software, as the mesh conforming to almost any shape is possible. With the redundancy factor, unusual structures and complex geometries have become possible for the system.

The goal of this paper is to analyze and compare the geometric nonlinearity on diagrid structural systems. The different geometrical shapes considered are building plan sections of square, triangular, and circular. Each shape of the building is analyzed for lateral displacements by varying the cross sections of the members. The different cross-sectional geometries considered are rectangular, circular, hollow circular, and I-section. The study is carried out to obtain the optimal geometries for the building and cross section.

2 Objectives of the Study

The objectives of the study include the following:

  • To analyze the representative models of various geometric forms for optimal construction in terms of strength, stiffness, aesthetic appearance, material requirement, and low cost

  • To study the optimal cross section of diagrid members.

3 Analysis of Diagrid Buildings

Geometrical nonlinear analysis of G+26 story buildings with a plan area of 625 m2 is modeled using PATRAN software and analyzed using NASTRAN software considering the seismic behavior of the structure. Buildings of square, triangular, and circular plans are considered with varying member cross sections of rectangle, circle, hollow, and I-sections.

3.1 Structural Models

Regular structures with the same cross-sectional areas are considered for the analysis. G+26 buildings of 75.75 m height, with a story height of 2.75 m and a footing height of 1.5 m is modeled in PATRAN software.

Plan dimensions of buildings with different geometrical forms are as follows:

  • Square: 25 m × 25 m, shown in Fig. 1

    Fig. 1
    figure 1

    Plan, elevation, and 3D model of square building

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  • Triangle: Side, a = 38 m, shown in Fig. 2

    Fig. 2
    figure 2

    Plan, elevation, and 3D model of triangular building

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  • Circle: Diameter, Φ = 28 m, shown in Fig. 3.

    Fig. 3
    figure 3

    Plan, elevation, and 3D model of circular building

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Member cross sections are modeled for beam cross section to be 80,000 mm2, diagrid cross section to be 90,000 mm2, and footing cross section to be 36,0000 mm2, and are as follows:

  • Rectangle: For beams—200 mm × 400 mm

    For diagrid—300 mm × 300 mm

    For footings—600 mm × 600 mm

  • Circle: For beams—319.154 mm Φ

    For diagrid—338.514 mm Φ

    For footings—677.028 mm Φ

  • Hollow circle: For beams—Φ1 = 382 mm, Φ2 = 210 mm

    For diagrid—Φ1 = 380 mm, Φ2 = 172 mm

    For footings—Φ1 = 720 mm, Φ2 = 245 mm

  • I-section: For beams—Total height, H = 500 mm

    Flange width, W = 300 mm

    Web thickness, tw = 78 mm

    Flange thickness, tf = 92 mm

    • For diagrid—Total height, H = 500 mm

      Flange width, W = 300 mm

      Web thickness, tw = 78 mm

      Flange thickness, tf = 92 mm

    • For footings—Total height, H = 500 mm

      Flange width, W = 300 mm

      Web thickness, tw = 78 mm

      Flange thickness, tf = 92 mm

3.2 Material Properties

Material properties of steel are given as follows:

  • Density of steel = 7800 kg/m3

  • Young’s modulus = 2.1 × 105 N/mm2

  • Poisson’s ratio = 0.3

3.3 Loads and Boundary Conditions

Boundary conditions are provided as fixed at the base.

Dead load value for the roof is given as 1.5 kN/m2 and for all other floors as 4.5 kN/m2.

Live load values for all floors are given as 4 kN/m2.

Earthquake loads are calculated as per IS 1893(Part1):2002.

6 load cases and 13 basic load combinations were considered for the study.

3.4 Analysis Results

Analysis results were taken based on lateral displacement as shown in Figs. 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15.

Fig. 4
figure 4

Maximum lateral displacement obtained for square building with rectangular cross section

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Fig. 5
figure 5

Maximum lateral displacement obtained for square building with circular cross section

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Fig. 6
figure 6

Maximum lateral displacement obtained for square building with hollow circular cross section

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Fig. 7
figure 7

Maximum lateral displacement obtained for square building with I-section

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Fig. 8
figure 8

Maximum lateral displacement obtained for triangular building with rectangular cross section

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Fig. 9
figure 9

Maximum lateral displacement obtained for triangular building with circular cross section

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Fig. 10
figure 10

Maximum lateral displacement obtained for triangular building with hollow circular cross section

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Fig. 11
figure 11

Maximum lateral displacement obtained for triangular building with I-section

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Fig. 12
figure 12

Maximum lateral displacement obtained for cylindrical building with rectangular cross section

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Fig. 13
figure 13

Maximum lateral displacement obtained for cylindrical building with circular cross section

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Fig. 14
figure 14

Maximum lateral displacement obtained for cylindrical building with hollow circular cross section

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Fig. 15
figure 15

Maximum lateral displacement obtained for cylindrical building with I-section

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4 Conclusions

The conclusions obtained are the following:

  • The minimum lateral displacement is obtained for square building and is maximum for triangular building.

  • The maximum displacements are obtained at load case 1.5 (DL+ELZ−) for square and circular buildings and is 1.5 (DL+ELZ) for triangular building.

  • Buildings of members with circular cross section show the minimum displacement and with rectangular cross section shows the maximum displacement.