Project 1_Comparative study of different storey buildings for Seismic forces

COMPARATIVE STUDY OF DIFFERENT STOREY BUILDINGS FOR SEISMIC FORCES

AIM:

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

• 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 constitutes a natural mode of oscillation.

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

Mode shapes of oscillation associated with a natural period of a building are 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 the Natural period of the building as well as on the modes and shapes of oscillations, details of which are given below:

• Factors affecting the 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 do the fundamental natural periods of Buildings A, B, F and H change with change in building height?
• Effect of Column Orientation on T: How do the fundamental natural periods of Buildings 8, C and D change with change in column orientation?

• Factors influencing the modes and shapes of oscillations:
• Effect of Flexural Stiffness of Structural Elements on mode shapes: Compare the fundamental mode shape of Building 8 in two situations when the 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 the fundamental mode shape of building in two situations when the 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 the base of columns is pinned versus when it is fixed.

PROCEDURE:

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

Now, define the material property and section properties.

Now, develop the columns, beams and slabs. Frame components have been assigned.

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 I:

Imposed mass 10% larger i.e., Live load= 3.3kN/m 2

• Building K:

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

Hence, modelling of the buildings has been completed.

Now, a comparison needs to be carried out.

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

For buildings E & F:

Building E Building F

Ty = 1.731s Ty = 1.735s

Tx= 1.676s Tx= 1.678s

R1 = 1.47s R1 = 1.488s

For buildings G & H:

Building G Building H

Ty = 4.529s Ty= 4.294s

Tx = 4.33s Tx = 4.107s

R1= 3.383s R1 = 3.273s

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

In buildings, 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, both the buildings are 25 storey buildings but their masses vary due to the variation in column sizes.

Building E and G have comparatively lesser mass compared to the buildings F and H respectively, and as such the time period of 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 there won’t be much shift in the centre of stiffness from the centre of mass. Hence, the small difference in the time period of the two buildings is mainly due to the difference in their masses.

`T=(2pi)*sqrt(m/k)`. Hence `T prop m^(1/2)` and `T prop 1/sqrtk`

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

Building H Building J Building K

Ty= 4.294s Ty= 4.529s Ty= 4.548s

Tx= 4.107s Tx= 4.33s Tx= 4.348s

R1= 3.273s R1= 3.383s R1= 3.395s

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

Here, the variation of the time period in the three buildings is very minimal 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 the time period is given as K > J > H.

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

Building A(2 storeys) Building B(5 Storey) Building F(10 Storey) Building H(25 Storey)

Ty= 0.5s Ty= 1.036s Ty= 1.735s Ty= 4.294s

Tx= 0.488s Tx= 1.01s Tx= 1.678s Tx= 4.107s

R1= 0.444s R1= 0.912s R1= 1.488s R1= 3.273s

From the above table, it is clear that with an 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 the height of the structure and as the stiffness decreases the time period of the building increases as `T prop 1/sqrtk`

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

In Building B, all the columns are square i.e 400 mm x400 mm, hence, the entire stiffness of the building will be equal in both X and Y directions.

Building B (Column 400 x 400)

Ty= 1.036s

Tx= 1.01s

R1= 0.912s

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

Building C (Column 550 x 300)

Ty= 1.145s

Tx= 0.929s

R1= 0.926s

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

Building D (Column 300 x 550)

Ty= 1.12s

Tx= 0.953s

R1= 0.899s

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 building B the flexural stiffness is very small compared to the original building.

So, for this, we need to develop another model B with lesser flexural stiffness of the beam. In this model, the moment of inertia about the 2 and 3 axes is changed to 0.01.

Original building B Modified building B1

Ty= 1.036s Ty= 7.721s

Tx= 1.01s Tx= 7.483s

R1= 0.912s R1= 4.54s

From the 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 B in two situations:

1. Original building B
2. When an axial cross-sectional area of the column is reduced by a factor of 0.01

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

Original building B Modified building B2

Ty= 1.036s Ty= 1.649s

Tx= 1.01s Tx= 1.441s

R1= 0.912s R1= 0.933s

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

Effect of Degree of fixity at column based on mode shape:

Comparing the mode shape of building in two situations:

1. Original building B i.e. when the base is pinned
2. Another model of building B, when the base of the column is fixed.

Original building B Modified building B3

Ty= 1.036s Ty= 0.941s

Tx= 1.01s Tx= 0.919s

R1= 0.912s R1= 0.828s

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 models from A to K have been analysed and a comparison of the study is also carried out regarding the time period of the structure. The results of each drawing drawn in ETABS are attached.