continued

The acceptable inelastic deformation was then determined from the strength degradation "backbone" curve to ensure that there was sufficient residual strength to support the gravity loads after a severe earthquake event.

Having established the inelastic global structure and local member deformation acceptance limits, the next step was to carry out nonlinear numerical seismic response simulation of the entire 3D building subjected to level 2 and level 3 design earthquakes. Both the nonlinear static pushover analysis method and the nonlinear dynamic time history analysis method were used to determine the seismic deformation demands in terms of the maximum inelastic inter-story drifts and the maximum inelastic member deformation.

These deformation demands were compared against the structure's deformation capacities story-by-story and member-by-member to verify the seismic performance of the entire building. All global and local seismic deformation demands were shown to be within their respective acceptance limits, demonstrating that the building achieves the quantitative and hence qualitative performance objectives when subjected to level 2 or level 3 earthquakes.

Foundation Design

The design of the foundations required that the applied superstructure loads be redistributed across the pilecap (raft) so as to engage enough piles to provide adequate strength and stiffness. To validate the load spread to the pile group, a complex iterative analysis process was used adopting a nonlinear soil model.

The superstructure loads were applied to a discrete model of the piled raft system. Several hundred directional load case combinations were automated in a spreadsheet controlling GSRaft, iterative nonlinear soil-structure interaction analysis software.

This procedure iteratively changed the input data in response to the analysis results to model the redistribution of load between piles when their safe working load was reached. The analysis was then repeated until the results converged and all piles were within the allowable capacities. The envelope of these several-hundred analyses was then used to design the reinforcement in the raft itself.

Connections

The force from the braces and edge beams must be transferred through and into the column sections with minimal disruption to the stresses already present in the column. The connection is formed by replacing the flanges of the steel column with large "butterfly" plates, which pass through the face of the column and then connect with the braces and the edge beams. To simplify the detailing and construction of the concrete around the steel section, no connection is made to the web of the column.

The joints are required to behave with the braces, beams, and columns as "strong joint/ weak component." The connections must resist the maximum probable load delivered to them from the braces with minimal yielding and a relatively low degree of stress concentration. High stress concentrations could lead to brittle fracture at the welds under cyclic seismic loading, a common cause of failure in connections observed after the 1994 Northridge earthquake in Los Angeles.

Two connections, representing the typical and the largest cases, were modeled from the original AutoCAD drawings using MSC/NASTRAN, a heavy-duty finite element analysis package. The models were analyzed, subjected to the full range of forces that can be developed before the braces buckle or yield — assuming the maximum probable material properties — to evaluate the stress magnitude and degree of stress concentration in the joints.

The shape of the butterfly plate was then adapted by smoothing out corners and notches until potential regions of yielding were minimized and the degree of stress concentration reduced to levels typically permitted in civil and mechanical engineering practice. CAD files of the resulting geometry of the joints were exported from the finite element models and used for further drawing production.

The structural design of CCTV posed many other technical challenges to the large international team which delivered the design through global collaboration, transcending time zones, physical distance, cultures, cost centers, and even the SARS outbreak. In the end, the team delivered a complex design on time and won approval from the Chinese construction ministry's expert panel.

A longer version of this article first appeared in The Arup Journal, 2/2005, and is excerpted here with permission.

Discuss this article in the Architecture Forum...

Models illustrating the development of the CCTV headquarters' facade pattern, designed by Rem Koolhaas, engineered by Arup. Image: © OMA Brace stresses for a uniform grid. Image: Arup Unfolded view of the structure showing areas to densify or rarefy the mesh. Image: Arup Nonlinear finite element simulation model showing local buckling of a typical steel brace. Image: Arup GSRaft model of the piled foundation. Image: Arup The von Mises stress distribution of a large connection plate under the most unfavorable loading combination. Image: Arup   Click on thumbnail images to view full-size pictures.