# Torsional Sensitivity

When we design a building, in order to achieve code provisions, we are required to meet the Seismic standards in each building code.

This often means that we will need to execute a seismic analysis, so we understand the dynamic behavior of our structure to aid our design decisions.

S-FRAME features various dynamic analysis that are fitting for that purpose, like Response Spectrum Analysis (RSA), Equivalent Static Force Procedure (ESFP) and Time History Analysis.

These different Analysis types are covered in depth on our Seismic Analysis Training Course, when we want to execute an RSA, S-FRAME calculates some factors such as the scale, the base shear, torsional sensitivity, among others, in this article we will discuss what is the Torsional Sensitivity, how does S-FRAME calculate it and where to find the results obtained.

According to the National Building Code of Canada (NBCC)

Torsional Sensitivity, B, may be calculated as:

Where  is the maximum joint displacement for a given floor, and  is the average of the displacements at the extreme points of the structure (at level x) as shown in the image below.

If B > 1.7, the structure is classified as “Torsional Sensitive”

This is illustrated in the following diagram

Please note that the US building code does this calculation differently where storey drifts are used instead.

Let’s look at the lateral deformations in the floor below:

If we average those deformations on a spreadsheet, we find the average to be 0.457”.

The max deflection in that floor is 0.469”.

Using this information, and the formula:

We substitute for the found values and have the next.

S-FRAME calculates and reports this value automatically for each floor.

This may be found in the Floor Forces spreadsheet in the Numerical Results window. It requires the definition of Floor Numbers, from the Geometry Window, in order to report Storey Results.

Note that applying Floor IDs (Storey ID) must be done in sequential order, with no gaps, starting with 0, by S-FRAME’s convention Storey #0 corresponds to Floor 1.

For a building with N floors, the total number of storey would be (N-1).

For example, a 4 storey total for a building with 5 floors.

We can appreciate that the value calculated by S-FRAME’s spreadsheet is the same as the one we obtained manually.

In this particular case, the building cannot be classified as “Torsional Sensitive”