A Survey on Structural Plan Density.

By Nan Gao.

In the illustrated essay of 2005 CUREE calendar The Expression of Seismic Design, the author Robert Reitherman discussed the concept of Structural Plan Density. Basically, it is the ratio of the area of vertical structural components to the whole plan area of a building structure. It could be used as a parameter of structural efficiency and reliability. As the figures showed in The Expression of Seismic Design, the plan density of the Temple of Khons in Karnak is over 50%. The famous Taj Mahal in India also has a 50% structural plan density. The plan density of the Parthenon in Athens and the Pantheon in Rome was about 20%. In contrast, the 442 meters high Sears Tower has a plan density of only 2%. From stone to steel, from masonry to bundle-tubes, and from 50% to 2%, this is a phenomenal progress in the field of structural engineering. The overall structural plan density has decreased a lot due to the development of more efficient materials and systems.
Besides the materials and structural systems, the level of plan density is also influenced by the local seismic level, the height of the building, and the architectural design. Typically, structures in high-seismic regions have larger plan density than those in non-seismic regions. Low-rise buildings usually have lower plan density than high-rise buildings. Maybe unnoticed, but the architectural design has a huge impact on structural efficiency, especially in high-rise structures. An irregular architectural plan will cause larger seismic response and thus a higher plan density. Sometimes this impact could be very huge.
What is the overall structural plan density in current Chinese industry? Maybe I could conduct a survey on this topic. As a simple survey, I used the database of my company as my resource. For purpose of comparison, the scope is confined to high-rise concrete structures. All the samples are completed designs in the last 8 years and they are classified as one of these three structural types: moment frame (MF), shearwall (SW), and moment frame-shearwall (MF-SW) or moment frame-corewall (MF-CW).
Plans of moment frame-corewall or moment frame-shearwall structures
Table of moment frame-corewall or moment frame-shearwall structures
Plans of shearwall structures
Table of shearwall structures
Plans of moment frame structures
Table of moment frame structures
We can see the relationship between structural types and plan density. Shearwall structures have relatively high plan density. The range of their plan densities is 5% to 12%. The reason is that all the gravity load and lateral loads are resisted by concrete walls. The whole structure needs a high level of stiffness to maintain reliability.
Moment frame-shearwall structures have a lower plan density, from 7% to 2%. This type of structure is a dual system. Most lateral loads are resisted by the shearwalls. Moment frames resist a small portion of lateral loads. The gravity loads are resisted by the two systems together. The moment frame part could provide more flexible arrangement for architectural design. The efficiency of moment frame-corewall structures is better than the moment frame-shearwall structures, because the arrangement of shearwalls in moment frame-corewall structures is more efficient. The shearwalls in the middle act like a tube. Thus, they could perform better when resisting lateral loads than the dispersed shearwalls in the moment frame-shearwall structures.
Moment frame structures have the lowest plan density and the lowest structural height. They could be used when the height is under 35m or 40m. However, the reliability of this type of structure is not as good as these with shearwalls. Stiffness of moment frames is much smaller. Thus, it may cause larger displacement and more non-structural damage. Also, the beam-column joint is the Achilles’ heel of the moment frame structure. It needs very special treatment and reinforcement.
Structural plan density of different types of structures
Structural plan density in different seismic regions
Also, several samples corroborate the relation between structural efficiency and architectural design. For example, the No. 16 sample has a height of 84.6m and a plan density of 5.99%. As a contrast, the No. 19 sample has a height of 72.8m but a plan density of 11.5%. These two shearwall structures are in the same seismic region and their heights are similar. However, No. 16 sample has a much better structural efficiency since its plan density is about the half of the No. 19 sample. Its rectangle plan shape and its regular arrangement of shearwalls might be the main reasons.
The No.19 sample and the No. 21 sample are from the same project. The plan density of them is more than 10%, much higher than other shearwall structures. Why? A main factor is the irrational design of the architectural plan. This project is a copycat of another design project. The client wanted to build their own buildings exactly the same as that project. However, the original edition is in non-seismic region while their own site is in a high-seismic region. The results are nearly disasters. Thus, their structural efficiency is extremely low.
In conclusion, this simple survey supported the statement of the relationship between structural efficiency and architectural plan. The efficiency can be approximately measured by the parameter of structural plan density. In order to achieve higher structural efficiency and lower cost of investment and material, more rational and regular architectural designs should be recommended.

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