Challenge

Project 1_Comparative study of different storey buildings for Seismic forces

SShubham Kumar Singh31 Mar 2023

Aim:

To model the buildings from A to K as per the details given below:

To to carry out a comparative study of these buildings for seismic forces.

Introduction:

Every building has a number of natural frequencies at which it offers minimum resistance to shaking induced by external effects and internal effects.

Each of these natural frequencies and its associated deformation shape of a building constitute a natural mode of oscillation.

The mode of oscillation with smallest natural frequency and largest natural period is called fundamental mode and the associated natural period, T1 is called Fundamental natural period.

Mode shapes of oscillation associated with a natural period of a building is the deformed shape of the building when shaken at the natural period. Hence, a building has as many mode shapes as the number of natural periods.

In this project we need to find out the effects of various parameters on Natural period of the building as well as on the mode shapes of oscillations, details of which are given below:

Factors affecting Natural period of building:
- Effect of stiffness on T: Compare fundamental natural periods of buildings E & F as well as G & H. Why is there a marginal or significant difference in the fundamental natural periods?
- Effect of mass on T: Compare fundamental natural periods of buildings H, J and K. Have the buildings become more flexible or stiff due to change in mass?
- Effect of Building Height on T: How does the fundamental natural periods of Buildings A, B, F and H change with change in building height?
- Effect of Column Orientation on T: How does the fundamental natural periods of Buildings B, C and D change with change in column orientation?

Factors influencing the mode shapes of oscillations:
- Effect of Flexural Stiffness of Structural Elements on mode shapes: Compare fundamental mode shape of Building B in two situations when flexural stiffness of beams relative to that of adjoining columns is very small versus when it is large.
- Effect of Axial Stiffness of Vertical Members on mode shapes: Compare fundamental mode shape of Building H in two situations when axial cross-sectional area of columns is very small versus when it is large.
- Effect of Degree of Fixity at column bases on mode shape: Compare fundamental mode shape of Building B in two situations when base of columns is pinned versus when it is fixed.

Procedure:

Initially open the ETABS software and provide the units, grid and storey informations.

Now, define the material property and section properties.

Now, develop the columns, beams and slabs.
Frame components have been assigned as given below:

Now, we need to assign loads to the frame members and floors.
After assigning all the loads, check the model and run the analysis.
Building A:

Similarly carry out the modelling for other buildings also.
Building B:

Building C:

Building D:

Building E:

Building F:

Building G:

Building H:

Building J:

- Imposed mass 10% larger i.e, Live load = 3.3kN/m2">m2

Building K:

- Imposed mass 20% larger i.e, Live load = 3.6kN/m2">m2

Hence, modelling of the buildings have been completed.
Now, comparison needs to be carried out.

- Effect of stiffness on T: ( considering first three modes)

For buildings E & F:

Building E	Building F
Tx = 1.59s	Tx = 1.635s
Ty = 1.638s	Ty = 1.683s
Tz = 1.434s	Tz = 1.495s

For buildings G & H:

Building G	Building H
Tx = 3.982s	Tx = 4.158s
Ty = 4.154s	Ty = 4.338s
Tz = 3.552s	Tz = 3.773s

In both E & F and G & H, the difference in time period is very less.

In building E & F, the total mass of the structure varies as the column size varies in Building E whereas in building F the column size is uniform. Similarly, in building G & H also both the buildings are 25 storey buildings but their masses varies due to the variation in column sizes.

Building E and G has comparatively lesser mass compared to the building F and H respectively, and as such the time period of the E and G is also less than that of F and H respectively.

Now, considering the stiffness of the structures, in both the structures the columns are arranged in a regular manner and hence the there wont be much shift in the centre of stiffness from centre of mass. Hence, the small difference in time period of the two buildings are mainly due to the difference in their masses.

T = (2π)⋅mk">(2π)⋅√mk

. Hence, T∝m12">T∝m12 and T∝1k">T∝1√k

- Effect of mass on T : ( comparing H, J and K buildings)

Building H	Building J	Building K
Tx = 4.158s	Tx = 4.166s	Tx = 4.174s
Ty = 4.338s	Ty = 4.346s	Ty = 4.354s
Tz = 3.773s	Tz = 3.778s	Tz = 3.784s

All the three buildings have same storey height and column sizes, but the mass imposed on it varies.

Here, the variation of time period in the three buildings is very minimal in the range 0.008 and this variation is due to the variation in the mass imposed on it which adds to the total mass of the building. Since the time period is directly proportional to mass, the variation in time period is given as K>J>H.

- Effect of building height on T: ( Comparing buildings A,B,F and H)

Building A (2 storey)	Building B (5 Storey)	Building F (10 Storey)	Building H (25 Storey)
Tx = 0.439s	Tx = 0.988s	Tx = 1.635s	Tx = 4.158s
Ty = 0.447s	Ty = 1.009s	Ty = 1.683s	Ty = 4.338s
Tz = 0.397s	Tz = 0.89s	Tz = 1.495s	Tz = 3.773s

From the above table it is clear that, with the increase in height the time period of the building increases.

This is because as the height increases the stiffness of the building decreases, as stiffness is inversely proportional to height of the structure and as the stiffness decreases the time perios of the building increases as T∝1k">T∝1√k

- Effect of column orientation on T: ( Comparing buildings B, C and D)

In Building B, all the columns are square i.e 400mmx400mm, hence, the entire stiffness of the building will be equal in both X and Y direction.

Building B (Column 400x400)

Tx = 0.988s

Ty = 1.009s

Tz = 0.89s

In Building C the longer edge of the column is arranged in X direction as shown in the figure below. Hence, the stiffness will be more in X direction compared to y direction. So, the time period will be lesser in X direction and it will be more in Y direction. That is the reason that for this building the time period in X direction is the least.

Building C (Column 550x300)

Tx = 0.837s

Ty = 1.041s

Tz = 0.757s

In building D, the longer edge of the column is arranged in Y direction as shown below and as such the stiffness of the structure in the Y direction is higher compared to X direction. So, the time period of the structure will be lesser in the Y direction than in X direction.

Building D (Column 300x550)

Tx = 0.916s

Ty = 1.109s

Tz = 0.869s

-Effect of flexural stiffness of structural elements on mode shapes:

Comparing the fundamental mode shapes of the building B in two situations:

1. For the original building B.

2. For the building B with flexural stiffness very small compared to the original building.

So, for this we need to develop another model B with lesser flexural stiffness of beam. In this model the moment of inertia about the 2 and 3 axis is changed to 0.1.

Original building B	Modified building B1
Tx = 0.988s	Tx = 1.768s
Ty = 1.009s	Ty = 1.791s
Tz = 0.89s	Tz = 1.696s

From table, it is clear that the time period of the building has been increased. As the flexural stiffness of the beam is reduced, the building becomes more flexible and the time period is increased hence maintaining the inverse proportionality between time period and stiffness.

- Effect of Axial stiffness of vertical members on mode shapes:

Comparing the mode shape of building H in two situation:

1. Original building H

2. When axial cross sectional area of the column is reduced by a factor of 0.1.

So, for this we need to develop another model H with smaller axial cross section of column.

Original building H	Modified building H1
Tx = 4.158s	Tx = 5.412s
Ty = 4.338s	Ty = 6.145s
Tz = 3.773s	Tz = 3.82s

Here also, as the axial stiffness of column is reduced, the time period of the building is increased.

- Effect of Degree of fixidity at column bases on mode shape:

Comparing the mode shape of building B in two situation:

1. Original building B i.e when the base is pinned

2. Another model of the building B, when the base of the column is fixed.

Original building B	Modified building B2
Tx = 0.988s	Tx = 0.967s
Ty = 1.009s	Ty = 0.987s
Tz = 0.89s	Tz = 0.87s

From the table we can understand that, as the support is changed to fixed support the time period of the building is reduced.

Results:

All the 10 model from A to K has been analysed and comparison study is also carried out with regarding to the time period of the structure.

To model the buildings from A to K as per the details given below:

To to carry out a comparative study of these buildings for seismic forces.