Problems of configuration in the ground plan

The problems referred to below have to do with the horizontal layout of the structure in relation to the form and distribution of the architectural space.

Length

The length of a building determines its structural response in a manner that is not easy to determine by usual methods of analysis. Since ground movement consists of a transmission of waves, which occurs with a velocity that depends on the mass and stiffness of the supporting soil, the excitation that takes place at one point of support of the building at one time differs from the excitation at another time, the difference being greater as the length of the building is greater in the direction of the waves. Short buildings adjust more easily to the waves and receive a similar excitation at all supports, unlike long buildings.

Figure 24. Simple and complex shapes in plan and elevation

From Arnold, Christopher and Reitherman, Robert, Building Configuration and Seismic Design (John Wiley & Sons, New York: 1982, p. 232). Reprinted with permission of John Wiley & Sons.

Long buildings are also more sensitive to the torsional components of ground movements because the differences in the transverse and longitudinal movements of supporting terrain, on which this rotation depends, are greater

The usual solution to the problem of excessive building length is to partition the building into blocks by inserting joints in such a way that each of the sections can be considered as short. These joints should be designed to permit adequate movement of each block without danger of pounding, as described further on.

Flexibility

The flexibility of a structure under seismic loads may be defined as its ability to resist large lateral deformations between the floors, known as drifts. The leading causes are the distance between the support elements (clear spaces or clearances), their vertical clearance, and their stiffness. The degree of flexibility can determine:

· Damages to the nonstructural elements attached to contiguous levels.
· Instability of the flexible floor or floors, or of the building in general.

Lack of redundancy

Seismic-resistant design takes into account the possibility of damage to elements during the most intense earthquakes. From this standpoint, the design of the structure should ensure that resistance to seismic forces does not depend largely or totally on a limited number of elements, since their failure could result in partial or total collapse immediately after the earthquake because of the weakness of the remaining elements. The aim should be to distribute the resistance to seismic forces among as many elements as possible (14).

The problem of lack of redundancy is usually linked to the problem of flexibility, since fewer elements in a given area implies the presence of large gaps between supports and, accordingly, less lateral stiffness of the structure.

Torsion

Torsion has been the cause of major damage to buildings subjected to strong earthquakes, damage that ranges from the sometimes visible warping of the structure (and its resultant loss of image and reliability) to structural collapse.

Torsion takes place because of the eccentricity of the center of mass in relation to stiffness. The three major situations that can give rise to this situation in plan are:

· The positioning of the stiffest structure asymmetrically with respect to the center of gravity of the floor.

· The placement of large masses asymmetrically with respect to stiffness.

· A combination of the two situations described above.

It should be borne in mind that the dividing walls and the facade walls that are attached to the vertical structure are usually very stiff and, accordingly, as long as their resistance is greater than the stress of the earthquake, they participate in the structural response to such stress and torsion can result, as commonly occurs in corner buildings.

If height is also considered, the situation with respect to torsion may become even more complicated when there are vertical irregularities, such as setbacks. The upper part of the building transmits an eccentric shear to the lower part, which causes downward torsion of the transition level regardless of the structural symmetry or asymmetry of the upper and lower floors.

Quantitatively, eccentricity between mass and rigidity may be considered large when it exceeds 10% of the dimension in the plan under study. In such cases corrective measures should be taken in the structural layout of the building.

As with all problems of configuration, the problem of torsion should be addressed starting in the spatial and formal design stage. The necessary correctives to the problem of torsion may be summarized as follows:

· Torsion should be considered unavoidable because of the nature of the phenomenon and the characteristics of the structure. For this reason, it is suggested that buildings be provided with what is known as "perimetric stiffness" which is aimed at bracing the structure against any possibility of gyration and distributing torsional resistance among several elements in accordance with the need for redundancy.

· In order to control elastic torsion, careful attention should be paid to the layout of the structure in plan and in elevation, in addition to the presence of and need for isolation of the partition wall that could be structurally involved during an earthquake, as will be discussed later on. The objective at all times should be the greatest possible symmetry between stiffness and mass.

Flexibility of the diaphragm

Flexible behavior of the floor diaphragm implies greater lateral deformations, which are in principle detrimental to the nonstructural elements attached at contiguous levels. Additionally, the assembly work of the vertical structure by the diaphragm is deficient, and consequently there is greater stress on some elements and less on others.

There are several reasons why this type of flexible stress may occur, as follows:

· Flexibility of the material of the diaphragm. Among the usual building materials wood presents the greatest disadvantages in this regard.

· Aspect ratio of the diaphragm. Since this is a matter of flexural stress, the larger the length/width ratio of the diaphragm or of a segment of it, the greater its lateral deformations may be. In general, diaphragms with aspect ratios greater than 5 may be considered flexible.

· Rigidity of the vertical structure. The flexibility of the diaphragm should be also be judged in accordance with the plan distribution of the stiffness of the vertical structure. In the extreme case of a long diaphragm in which all elements are of equal stiffness, better performance of the diaphragm may be expected than when there are major differences in this respect.

· Openings in the diaphragm. Large openings in the diaphragm for purposes of illumination, ventilation, and visual connections between floors cause flexible areas to appear within the diaphragm that impede the stiff assembly of the vertical structures.

There are many solutions to the problem of flexibility of the diaphragm, depending on its cause. In principle, for large structures, such as hospitals, building floors with flexible materials such as wood should be avoided. Second, as is the case with the effects of length, buildings with a large plan aspect ratio should be segmented by means of joints. Third, very large differences in stiffness between the elements of the vertical structure should be avoided. Finally, large openings in the diaphragm should be studied carefully in order to provide for stiffening or, if this is not possible, segmentation of the building into blocks should be considered.

Concentration of plan stress

This problem arises in buildings known as complex plans and is very common in hospital buildings. The definition of such a plan is one in which the line joining any two sufficiently distant points of the plan lies largely outside the plan. This occurs when the plan is composed of wings of significant size oriented in different directions (H. U. L shapes, etc.). In them, every wing can be likened to a cantilever built into the remaining body of the building, a site at which it would be subjected to smaller lateral deformations than in the rest of the wing. For this reason large stresses appear in the transition area, where damage frequently occurs to nonstructural elements, to the vertical structure, and even to the diaphragm.

In this case the solution ordinarily adopted is to install seismic separation joints, such as those mentioned in the case of long buildings. These joints enable each block to move on its own without being tied to the rest of the building, thus breaking the pattern of cantilever stress on each wing. The joints must obviously be wide enough to allow the movement of each block without pounding (15).