Initial Assumptions

Model Detail

Finite element models of tall buildings can range from simple stick models to three dimensional models that closely resemble the prototype. Stick models typically comprise a single vertical beam element that models the vertical distribution of stiffness. Uniform mass properties can be specified for the beam element, or it can be subdivided into multiple segments with lumped masses and rotational masses assigned to the nodes, which model the mass inertia and mass moment of inertia respectively. These lumped masses and rotational masses typically represent the influence of the floor plates, which often contain a significant portion of the total mass.

In order to facilitate the updating process, the level of detail used to create the finite element model for this research was relatively high. Latitude tower comprises a complex structural arrangement compared with more typical tall buildings. The structure below level 16 is relatively simple, with reinforced concrete core walls,

columns, and floor plates. Above level 16, complexities arise due to column transfers between levels 16 to 20, the extended floor plates at level 20 and above, and the outrigger bracing at the plant room between levels 34 and 36. Furthermore, the non-sequential construction method also adds complexities due to the demolition of structural elements at lower levels while construction of upper levels progressed.

Considering the preceding discussion, a three dimensional finite element model of Latitude tower was generated. The model was constructed according to the geometry and dimensions described in Section 3.2. Few simplifying assumptions were used to reduce the geometric complexity of the model. The goal was to create a model that closely resembled the actual geometry of the structure. This would allow fine tuning of mass and stiffness properties during the updating process.

The shear walls and floor slabs were modelled using plate elements that allow both in-plane and out-of plane actions. The in-plane rigidity of the floor slabs was the only source of rigid diaphragm action — no other elements, in addition to the floor slab plates, were used to model the rigid diaphragm action of the floor plates.

The columns, braces, and trusses were modelled using beam elements, with appropri-ate action releases assigned at the beam ends. No structural elements were included to model the facade, as it was deemed to have little influence on the structural stiffness.

Mass Distribution

Due to the level of detail used in the model, most of the structural mass was modelled via the structural elements. The exception was the steel beams supporting the floor slabs, which were excluded from the model. These beams are designed as simply supported members, and the lack of moment actions at the connection to columns means these beams will not contribute to the lateral stiffness of the structure. The mass of these beams was included via the addition of equivalent non-structural mass uniformly distributed over the floor plate area.

The mass of the facade was modelled by a non-structural mass applied around the perimeter of each floor plate. The weight of the facade was estimated to be 0.5 kPa, and for a typical level with a floor height of 3.765 m, this results in a uniformly distributed load of 192 kg/m applied to the edge of the floor plates. The mass of the fire stairs located on the western facade was also included as a non-structural mass.

Table 5.12 lists the standard dead loads (SDL) and live loads (LL) applied to the model. In the Australian design standard on structural design actions [150], these two loads are known as permanent actions and imposed actions respectively.

The SDL represents the mass associated with fittings and finishes, such as floor coverings and false ceilings. The LL represents the mass from the intended use and occupancy of the structure. For models of the structure during construction, the

SDL LL

Floor Type (kPa) (kPa)

Plant 2.5 7.5

Office 1.1 1.5

Lobby 1.5 4.0

Retail 1.5 2.0

Parking 0.2 2.5

Table 5.12: Standard dead loads and live loads used in the finite element modelling.

f_c⁰ E_c

(MPa) (MPa)

Core Walls Typical 50 34800

L34–L36 80 39600

Columns L1–L36 80 39600

L36–L41 60 36500

L41–L55 40 32800

Floor Slabs Typical 40 32800

Table 5.13: Concrete properties for the initial finite element model.

SDL values were only applied to levels included in the fit-out, and LL were only applied to occupied levels.

Material Properties

The characteristic compressive strength of concrete at 28 days (f_c⁰) that was specified on the structural drawings for various structural elements are listed in Table 5.13.

The table includes the modulus of elasticity (E_c) for the specified concrete. These values were sourced from the Australian design code for concrete structures [152].

The core walls also included minor sections of masonry infill. These sections were modelled with a modulus of elasticity of 25 000 MPa.

Shear Wall Link Beams

It is typical that some walls within a reinforced concrete core have large openings at each floor level for doors, elevators, and services. The vertical alignment of the openings tends to divide the wall into separate wall segments that are connected via short beams. These beams link the walls, such that the effective depth of the wall section is increased to a value between the individual wall sections and the total wall

section when no openings are present. The modelling of the link beams will have a significant influence on the stiffness of the structure.

For the modelling of Latitude tower, all link beams were modelled with dimen-sions specified on the structural drawings. No reduction in the effective stiffness of the link beams was modelled since the excitation levels experienced over the life of the structure are significantly less than the lateral loads for the serviceability case, and are therefore unlikely to be cracked.

Boundary Conditions

A description of the foundations is included in Section 3.2.2. Pad footings were used for wall and column foundations, and the underlying ground material is high class Sydney sandstone. In this configuration it is unlikely that significant compres-sion of the underlying ground material under cyclical loading will occur, and the influence on the dynamic characteristics will be negligible [48]. For this reason, the nodal restraints at the base of the structure were assumed to be fixed in the three translational directions. For the below ground levels above the base, a sufficient gap between the structure and the surrounding soil is typically required to prevent forces from rock heave. No other restraints were applied to the model.

Non-structural Elements

The intended use of the tower was for commercial offices, and therefore very few internal partitions were constructed. Any stiffness associated with non-structural elements was not included in the finite element model.