Seismic Behavior of Buildings - Explained



What is seismic behavior?


The perimeter design of a building has a significant impact on seismic behavior. The center of mass will not correspond with the center of resistance if there is significant variation in strength and stiffness around the perimeter, and torsional forces will cause the building to rotate around the point of resistance.


An open-front design in buildings like fire stations and garages, where huge doors allow cars to pass through, is a classic example of an imbalanced perimeter.


Seismic behavior of building (Ref:researchgate.net)
Seismic behavior of building (Ref:researchgate.net)

What are the effects of earthquakes on buildings?


Inertia Forces in Buildings:

The ground started to shake during an earthquake. Therefore, a structure resting on it will have motion at the base. Despite the building's base moving with the ground, according to Newton's First Law of Motion, the roof tends to hold in its initial position.


However, because it is attached to the walls and columns, they pull the roof along with them. Similar to when a bus you are standing in suddenly starts, your feet go with it but your upper body tends to stay behind, causing you to fall backward! Inertia is the tendency to maintain one's position after changing it.


The building's roof moves differently from the ground because the walls or columns are flexible 👇
Effect of inertia in a building when shaken at its base (Ref:sksupertmt.com)
Effect of inertia in a building when shaken at its base (Ref:sksupertmt.com)

Impact of Structure Deformations:


The columns encounter forces as a result of the roof's inertia, which is communicated to the ground through the columns. There is another method to understand the forces produced in the columns. The columns move relative to one another when an earthquake shakes them.


Quantity u ( the relative horizontal displacement between the top and bottom of the column) between the roof and the ground is represented in this movement. However, if given the chance, columns would prefer to return to their original, straight vertical posture; in other words, they oppose deformations. The columns do not transmit any horizontal earthquake force through them when they are vertically aligned.


However, when forced to bend, they produce internal forces. Internal forces within columns increase in magnitude in direct proportion to the relative horizontal displacement u between the top and bottom of the column. Additionally, the magnitude of this force increases with the stiffness of the columns (i.e., column size). These internal forces in the columns are known as stiffness forces as a result. In actuality, a column's stiffness force is equal to the stiffness of the column multiplied by the distance between its ends.



Inertia force and relative motion with in a building (Ref:researchgate.net)
Inertia force and relative motion with in a building (Ref:researchgate.net)

Shaking to the horizontal and vertical:


The ground shakes during an earthquake in all three directions, including the two horizontal ones (X and Y, for example) and the vertical one (Z, for example). In addition, the ground shakes erratically back and forth (- and +) along each of the X, Y, and Z directions during an earthquake. All structures are built with the intention of supporting the weight of the earth's gravity, which is represented by an equation


F=M *g

Where,

  • F=force

  • M= mass

  • g=acceleration of gravity acting in a downward vertical direction (-Z).


The term "gravity load" refers to the downward force Mg. The vertical acceleration caused by ground shaking either increases or decreases the acceleration brought on by gravity. Since safety issues are taken into account when designing structures to withstand gravity loads, most structures typically have enough stability to withstand vertical shaking.


However, there is still cause for concern over horizontal shaking in the X and Y directions (both + and - directions of each). In general, structures made to withstand gravity loads might not be able to safely withstand the effects of horizontal earthquake shaking. Therefore, it is essential to guarantee that structures are adequate against the effects of horizontal earthquakes.



Principals direction of a building  (Ref:sjce.ac.in)
Principals direction of a building (Ref:sjce.ac.in)

Methods of Analysis Used in Seismic Design:

Equivalent static analysis:


The dynamic influence of forces must be considered while designing buildings against lateral forces. However, analysis by linear methods that are (Static) comparable to linear static methods is satisfied for simple structures.


Most codes of practice allow the equivalent linear static approach for regular and irregular low- to medium-rise and other buildings. The first stage in the static equivalent approach is to estimate the base shear load, after which the base shear distribution on each story is estimated using IS code formulas. This method is not ideal for tall structures since it is inconvenient to use, and the number of mode forms in tall structures is greater, thus this method should not be utilized.


Response spectrum analysis:

This study is appropriate for structures that have modes other than the fundamental one that has a major impact on the structure's behavior. The response of a multi-degree-of-freedom system is represented by the superposition of modal responses in the response spectrum approach. Each modal response is calculated using spectral analysis of a single degree of freedom system, and then the overall response is computed.


Definition of mode: The deformation that a component would exhibit at its natural frequency of vibration is known as a mode. Structural dynamics makes use of the phrases mode shape and natural vibration form. When a component vibrates at its native frequency, it would deform as described by its mode shape.


Push over-analysis:


In a push-over analysis, the vertical and lateral loads on a structure progressively rise, allowing the displacement and damage of the structure to be studied. This approach also exhibits cyclic behavior and load reversal. The structure is pushed until it reaches its greatest extreme ability to twist, as the name implies.


This method is particularly useful in comprehending the mishaps and splitting of a structure in the event of an earthquake, and it provides a reasonable understanding of the distortion of the structure and the placement of plastic hinges in the structure.


P-Delta analysis:


The P- Delta effect is a non-linear (second-order) phenomenon that occurs in every construction with axial loads on the elements. The genuine effect connected with the magnitude of the applied axial load (P) and the lateral displacement is known as the P D-delta effect (Delta). Because of the deformed shape, it generates additional shear forces and bending moments in the structure. The P-Delta effect is more pronounced in tall structures, and it has a negative impact when deformation is triggered by an earthquake.


P-Delta has two effects:


  • P-BIG delta (P-Δ) - a structure effect

  • P-little delta (P-δ) - a member effect


The member instability effect, also known as the P-δ effect or P-"small-delta," is linked to local deformation relative to the element chord between end nodes. P-δ is usually only important at unreasonably large displacement levels or in particularly thin columns.


The structure instability effect (P-Big delta or Large P-delta) refers to the consequences of vertical loads acting on a laterally displaced structure.



P-δ-Delta effect (Ref:enercalc.com)
P-δ-Delta effect (Ref:enercalc.com)


Useful Links:

  1. https://www.iitk.ac.in/nicee/EQTips/EQTip05.pdf

  2. https://www.sciencedirect.com/topics/engineering/seismic-analysis

  3. https://iopscience.iop.org/article/10.1088/1755-1315/362/1/012119

  4. http://msrblog.com/assign/science/geography/report-on-equivalent-static-force-method-and-time-history-analysis.html

  5. https://www.sksupertmt.com/vol-1-issue-8.html

  6. https://sjce.ac.in/wp-content/uploads/2018/01/EQ2-Earthquake-Effects.pdf