After the great feedback received from our fellows on the “Step by Step” articles here we go with a new post explaining the method of computation for P-Delta effect using ETABS.
For those who missed the previous articles of ” Step by Step”, I highly recommend to step forward and check it up:
- [Part 1] Step by Step Analysis Procedure of Seismic Loads Based on IBC2012/ASCE7-10
- [Part 2] Step by Step Analysis Procedure of Seismic Loads Based on IBC2012/ASCE7-10
- Step by Step – Deflection Analysis Using CSI SAFE
If you need further information on the Earthquake concept and analysis, I strongly recommend to check our valuable articles at the Earthquake Zone.
First of all, let us brief what is P-Delta effect and why we shall check it. With reference to CSI:
P-Delta effect, also known as geometric nonlinearity, involves the equilibrium and compatibility relationships of a structural system loaded about its deflected configuration. Of particular concern is the application of gravity load on laterally displaced multi-story building structures. This condition magnifies story drift and certain mechanical behaviors while reducing deformation capacity.
P-Delta effect typically involves large external forces upon relatively small displacements. If deformations become sufficiently large as to break from linear compatibility relationships, then Large-Displacement and Large-Deformation analyses become necessary. The two sources of P-Delta effect are illustrated in the Figure below.
Now let’s move forward and have a look on P-delta requirement on ASCE 7-10 §12.8.7:
If we read what is written in the clause above, we can conclude that we may have 3 options:
- θ < 0.1 = P-delta effect is not required to be considered in the analysis.
- θmax < θ < 0.1 = P-delta effect shall be considered in the analysis.
- θ > θmax = The structure is potentially unstable and shall be redesigned.
Here below, We’ll try to clarify how θ shall be calculation when modeling on ETABS.
These are 2 buildings composed of 3 basement, ground floor, 14 upper floors and a roof.
The data that we need to extract from the model is the following:
- h = Story height at level x
- Px = Total vertical design gravity load at level x
- Vx &Vy = Total horizontal shear under seismic load case along X & Y direction respectively at level x
- Ux &Uy= Deflection of center of mass at level x along each principal direction
- Dx &Dy = Story drift between level X & X-1
From display –> Show Tables, We choose to extract Story Data, Diaphragm Center of Mass Displacements & Story Forces to excel sheets.
We will be calculation the factor θ through an excel sheet that you may download it here.
From Story Data excel sheet, we will be able to conduct the stories height “h” and Name.
From Story Forces excel sheet, We get the story force at each level under the service load combination of gravity loads.
After that, We conduct from the same excel sheet (Story Forces) the story force at each level (Vx &Vy) under the seismic load case along each principal direction (X & Y), and our sheet will become like the following:
Now, We need only to conduct the Ux & Uy under each seismic load case along the principal directions (X &Y).
After that, we calculation Dx & Dy, which is the (Ux at level X) – (Ux at level X-1).
Now in order to calculate θ, we still need the Importance factor Ie (§11.5.1) & Deflection Amplification factor Cd (Table 12.2-1).
In our example, We’ll consider Ie= 1 & Cd = 4. Our excel will become like the following:
If you missed to download the excel sheet before, you may download it here.
As you can notice, the maximum value of θ is less than 0.1 , so P-delta effect is not required to be considered in the analysis !
Hopefully we could clarify properly how to check the requirement of P-Delta effect. If you have any question please do not hesitate to drop it by comment below.