Foundation, Concrete and Earthquake Engineering

### Earthquake Induced Torsion and Its Remedies

Center of gravity or center of mass of any object is that point where it can be balanced exactly without subjecting to any rotation. If the plan of building is so arranged that mass of it is distributed evenly, the geometric center of plan will be concurrent with center of gravity.

Earthquake acceleration will yield force based on weight of structure or weight of particular element. Thus lateral force in building is contributed by weight of roof, walls and floors which is applied through center of gravity, generally geometric center of floor plan.If weight exerted by a floor is evenly distributed, the force exerted by horizontal acceleration of all elements of floor is applied though geometric center of floor.

Resisting forces provided by frames (may be moment frames/braced frames), shear walls are developed to counteract this horizontal force. The resultant of resisting forces acts through that point produces a dynamic balance. Torsional forces are generated in a structure when there have no balance between location of resisting components and arrangement of building mass.

In engineering term it is called eccentricity between center of gravity and center of resistance that causes rotation around center of resistance under earthquake ground motion and exerts torsion. This twisting action on structure resists in unexpected and probably harmful stress concentration.

A building, in which, uniformly distributed mass are placed in plan, earthquake resistant components should be placed symmetrically in every directions, so that the seismic acceleration arrived from any direction to push the floors, the structure responds in opposite direction with its balanced stiffness. The ideal arrangement that are discussing can be achieved by planning a symmetrical building having uniform floor column and walls masses; thus rotation can be avoided, only translational force is suffered.

This is why it is suggested to design buildings, in regions where seismic activity is very common, as symmetric as possible considering a simple load path. However, the actual situation is that some degree of rotation of building cannot be avoided and building codes provided suitable treatment for this.

Source of Torsion

Torsion is produced by the eccentricity existing between the center of mass and the center of stiffness. Some of the situations that can give rise to this situation in the building plan are:

Positioning the stiff elements asymmetrically with respect to the center of gravity of the story.
• The placement of large masses asymmetrically with respect to stiffness.
 Figure 1. Torsion
• A combination of the two situations described above.
• Other causes that are not bluntly considered in design of structure; this explicit consideration or uncertainty in assumption comes from stiffness of brick wall or other non-structural members, unsymmetrical yielding of load resisting members etc.

### What is accidental torsion?

The last two causes of torsion i.e. incoherent ground motion and explicit addressing of stiffness or uncertainty in yielding of structural elements are resulted from accidental eccentricity.Building codes have introduced this to account this reasons approximately which requires addition in loading conditions by an amount defined by accidental eccentricity. Regarding the amount we can included that the additional loading required to displace structure by value of accidental eccentricity along both detections (along x axis and y axis of structure).

### Stiffness uncertainty of structure:

Differences between the actual and estimated value of the stiffness of structural element indicate that a structure seems to be symmetric based on plan is asymmetric actually to some uncertain degree which is obviously subjected to torsional vibration even under pure translational motion on ground i.e. when no torsional motion is not exerted by ground incoherence.

Accidental torsion of this type results in an increase in deformation of structural element. These deformations of structural element may be not sensitive to period of uncoupled lateral vibration of the system but may be affected significantly by the ratio of separate periods of uncoupled lateral vibration and torsional vibration. The mean structural deformations are reported to increase by at most 10% for reinforced concrete buildings and 50% for steel building. Such deformations are found even less in wide range of structural system. Increase in deformation due to uncertainty in stiffness calculation is found to be much lower than that specified in UBC (uniform building code) for accidental torsion (also applicable for other building codes).

### Torsion resulted from non-uniform ground motion:

Such ground motion can be arrived at building due to following causes

• When travelling waves exerts excitation to different points on the ground surface with phase lag i.e. throughout the passage of wave, same motion results agitation with phase difference (wave impacting the foundation at finite angle).
• Inconsistency in ground motion, this situation is observed when different points on the ground are subjected to wave of different amplitude and varying phase characteristics as an earthquake of extended source results wave radiating from different ends of source. Thus waves impact foundation

 From different angles
 With different times of incidence
 Some reflection and refraction may also happen around the foundation
 Characteristics of waves may change while they travels through paths (from earthquake source to the foundation) of diverse physical properties.

Such type of accidental torsion may result in increase in deformations and displacement of structural elements of buildings. The mean increase in displacement of structure was found less than five percent for systems (investigation was conducted on 30 buildings subjected to rotation excitations at the base in Californian) having periods of lateral vibration more than 0.5 second.For structures that have period less than 0.5 sec or systems said to be torsionally flexible may suffer significant increase in displacement due to such torsion. As this response is increased and considering complex system parameters, two simple methods are proposed to determine effect of such torsion. They are

• Accidental eccentricity method

• Response spectrum method

The accidental eccentricities computed are much lower than the values specified by codes except for structures that have very long dimensions in plan (b≥50 meter). The response spectrum methods can be used alternatively, which computes response of structure by determining peak response under independent base motion and then combining this peak values applying SRSS value.

### Torsion of building with flexible diaphragms:

Most of the buildings are designed to have floor diaphragms having in-plane rigidity, i.e. they obtain diaphragm action. This action renders resistance to earthquake. But sometimes floors are constructed flexible in their plane mostly due to architectural requirement and such flexibility should be considered in design. It was reported that mean peak displacement of lateral resisting components decrease with in-plane flexibility of floor of the system having initial lateral periods, T>0.4s (considered medium to large).

This value of these components increase as high as 50% for systems having initial periods T < 0.4 s (considered short period). In every case, effect of floor flexibility in its plane is reduced with increase in value of R (response modification factor) and T (initial lateral vibration period).

### Assessment of capacity of asymmetric building:

In last two decades capacity assessment has become matter of great attention, when buildings are required to be repaired and strengthened after some disastrous earthquakes. As before taking any action engineer must have idea about current strength of a building,this assessment is important. To do this one need to know overall behavior of structure and also of it individual components into inelastic state which requires to make detailed models either based on elastic range reducing loads or inelastic range; the last one is preferable. As solving a detailed structural models with dynamic inelastic analysis is considered so advanced that it cannot be used in practical engineering solutions, pushover analysis (based on static limit analyses) are becoming famous.

Torsion has been the cause of major damage to buildings subjected to strong earthquakes, ranging from visible distortion of the structure (and its resultant loss of image and reliability) to structural collapse (see figure 1).

### Corrective Measures

It should be kept in mind that the dividing walls and the facade walls that are attached to the vertical structure are usually very stiff and, therefore, often participate in the structural response to an earthquake and can cause torsion. This is often the case in corner buildings. Quantitatively, an eccentricity between the centers of mass and stiffness is considered significant when it exceeds 10% of the horizontal plane dimensions under study. In such cases, corrective measures should be taken in the structural design of the building. (see figure 2). Torsion may become even more complicated when there are vertical irregularities, such as setbacks. In effect, 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. As with all configuration problems, that of torsion should be addressed starting with the design of space and form of the building. The necessary corrections to the problem of torsion may be summarized as follows:

• Torsion should be considered inevitable due to the nature of the seismic event and the characteristics of the structure. For this reason, the suggestion is to provide buildings with so-called perimetric stiffness, which seeks to brace the structure against any possibility of rotation and distribute torsional resistance among several elements.
 Figure 2. Eccentricity between centers of mass and stiffness increase effects of torsion.

• In order to control torsion, the layout of the structure in plan and elevation must be studied carefully, as well as the presence and need for isolation of the nonstructural partition walls that could structurally intervene during an earthquake. Finally, the objective of these measures should be to provide to the structure the greatest possible symmetry of stiffness with respect to the mass.