Effect of Torsion in Seismic Analysis of Buildings  

Seismic analysis of buildings is an essential step in structural design, particularly in regions with significant seismic activity. A building’s structural behavior under seismic loads is strongly influenced by factors such as plan regularity, lateral stiffness, and torsional effects. This article focuses on how torsion impacts structures and how the Towers tool can help accurately assess plan regularity. 

Torsion and Regularity Criteria

Plan regularity is crucial for ensuring an appropriate structural response under seismic loads, as defined in Eurocode 8. Torsion, which arises from offset between the center of rigidity and the center of mass, is one of the most frequent causes of unsatisfactory structural behavior during earthquakes. Such offsets can lead to concentrated stresses and displacements in specific areas of the structure, increasing the risk of premature, unpredictable failures. 

However, practically evaluating regularity criteria is not always straightforward. Even though Eurocode 8 provides clear guidelines, such as the ratio between the torsional radius (ri) and the radius of gyration of the floor mass (Is), architectural constraints and the complexity of calculations often complicate the quest for structurally efficient solutions. 

Challenges in Applying Eurocode 8

Eurocode 8 (EC8) aims to bring objectivity and quantification to structural regularity requirements. Its practical application, however, can be challenging—not so much because of the complexity of the calculations, but because of the number of parameters considered in each verification. 

Studies indicate that most buildings exhibit plan irregularities, often due to inadequate stiffness or structural offset. The criterion set forth in EC8 expression 4.1b is one of the most stringent. If this criterion is not met, the structure is automatically classified as torsionally flexible. 

Practical Case in SAP2000 and Measures to Reduce Torsional Flexibility

In this practical example, using a structural model developed in SAP2000, we show how quick and easy it is to determine the (ri/ls) ratio by using the Towers plugin. 

The structural model represents a reinforced concrete building with specific architectural features that directly affect the distribution of stiffness and mass. With the Towers plugin, we derive ls and ri parameters directly from the structural model’s stiffness and mass properties. 

In this case, the calculated (ri/ls) ratios on each floor do not satisfy the requirement to be greater than or equal to 1, indicating that the building exhibits torsional flexibility. This outcome confirms that there are significant stiffness differences among the vertical elements, largely due to an eccentric core wall in plan. 

Corrective Measures to Minimize Torsional Flexibility

To prevent classifying the building as torsionally flexible and to improve its structural response, several approaches can be taken. One of the most effective solutions is modifying the moment of inertia of the vertical elements, ensuring a more uniform distribution of stiffness throughout the plan. Recommended measures include:

Adjusting Cross-Sections of Vertical Elements:

• Increasing the dimensions of less stiff walls or columns to better balance stiffness distribution in plan.

Changing the Geometry of Central or Perimetral Elements:

• Aligning the inertia values along the direction of analysis by adjusting the geometry of central or perimetral elements.

Adding New Walls Near Facades:

• Increasing stiffness in these areas to offset the stiffness contributions of other, stiffer elements.

Reducing the Eccentricity Between the Center of Mass and the Center of Rigidity:

• Relocating walls to bring the centers of mass and rigidity closer together.

By implementing these adjustments, the (ri/ls) ratio can meet EC8’s requirements, and the building will no longer be classified as torsionally flexible. Beyond minimizing torsional demands, these measures foster a more uniform structural response under seismic events, substantially enhancing safety.