Project 1_Comparative study of different storey buildings for Seismic forces

AIM:
Objective of the project is to model and comparison of result between the models (A-K). And to investigate the models based on the time period in modal behaviour for various effects given below,

• Effect of stiffness on Time period.
• Effect of mass on Time period.
• Effect of Building height on Time period.
• Effect of column orientation on Time period.
• Effect of Flexural stiffness of Structural Elements on mode shapes.
• Effect of Axial stiffness of Structural Elements on mode shapes.
• Effect of degree of fixity at Column base on mode shapes.

PROCEDURE:

Modelling of the building is done in Etabs for the following specification,

Sizes of Elements:

• Beam-300x400mm
• Column-400x400,600x600,550x300,300x550,800x800mm.

Material Properties:

• M30-Grade of Concrete.
• Fe415-Grade of Steel.

Loading Details:

• Dead Load-Self weight
• Imposed load- Load from infilled wall=10kNm UDL on all Beams
• Live Load -3kN/Sq.m.

Pinned supports are considered.

Elevation:

• Plinth Beam Height=1.5m
• Storey height=3m

Modelling of Building-A:

Modelling of Building-B:

Modelling of Building-C:

Modelling of Building-D:

Modelling of Building-E:

Modelling of Building-F:

Modelling of Building-G:

Modelling of Building-H:

Modelling of Building-J:

Modelling of Building-K:

By using all the specifications different 10 models are modelled for compression of characteristics of the building for dynamic response.

Comparison of Time periods for various conditions:

Effect of stiffness on Time period.

Comparing E/F & G/H:

Criteria	Model	Analysis Result-Fundamental natural Time period	Conclusion
Effect of stiffness on Time period	Building -E (10 Storey with different column size)	1.726 seconds	While comparing the model with time period for the varying column sizes, in top floor the column sizes reduced which will reduces the mass in the top floor will directly reduce the displacement.
	Building -F (10 Storey with similar column size)	1.73 seconds
	Building -G (25 Storey with different column size)	4.17 seconds
	Building -H (25 Storey with similar column size)	4.417 seconds

We have considered uniform and varying column sizes in the model E/F & G/H, where the minor changes in the column sizes does not shows major change in the fundamental natural period of the building.

Effect of mass on Time period:

Comparing H/J/K:

Effect of mass on Time period	Building -H (25 Storey with 3kN/sq.m)	4.417 seconds	Variations of the mass for the same height increase the time period of the vibration
	Building -J (25 Storey with 3.3 kN/sq.m)	4.426 seconds
	Building -K (25 Storey with 3.6 kN/sq.m)	4.436 seconds

As per the time period formula, Time period of the system is directly proportional to the mass of the structure.

`Tundersetn()=2pi sqrtfrac{m}{k}`,

From the comparison and Time period-mass of the system relation we can understand that the increase of mass increases the time period of the system.

Effect of Building height on Time period:

Comparing A/B/F& H:

Effect of Building height on Time period	Building -A (2Storey)	0.496 seconds	Increase of the height, increases the time period of the system due to the vertical cantilever behaviour of building while lateral force acting.
	Building -B (5Storey)	1.029 seconds
	Building -F (10 Storey)	1.73 seconds
	Building -H (25 -Storey)	4.417 seconds

In simple way, the increase of the height increases the time period of the system.

We can understand by imagining simple behaviour of the building will like vertical fixed beam with one end fixed and another end free. Then the free end will create higher deformation and vibration when the span increases. Here the span of the beam will be the height of the building.

For one end fixed and another end free stiffness formula is,`frac{3EI}(h^3}`

Stiffness of the system is inversely proportional to the height of the building. And the stiffness of the building is also inversely proportional to the time period.

`T undersetn() prop frac{1}{k}`

Effect of column orientation on Time period:

Comparing B/C& D:

Effect of column orientation on Time period	Building -B (All floor column size 400x400)	1.029 seconds	Longer direction of the column provides higher stiffness in the respective direction and then the stiffness is lesser in that direction.
	Building -C (All floor column size 550x300) in X-Direction	1.137 seconds
	Building -D (10 Storey with 3.6 kN/sq.m) (All floor column size 300x550 in Y-Direction	1.17 seconds

Symmetric Stiffness (Building-B):

Column dimension same in all sides and stiffness similar in both direction.

Column dimension X-Direction longer (Building-C):

Column dimension Y-Direction longer (Building-D):

By comparing the orientations of the column, we can understand the logic that the longer direction column provides stiffness to the system which is inversely proportional to the time period of the system.

Effect of Flexural stiffness of Structural Elements on mode shapes:

By comparing the model of Building-B with Modified same model for Stiffness of Beam as 0.1,

Criteria	Model	Cases	Analysis Result	Conclusion
Effect of Flexural stiffness of Structural Elements on mode shapes	Building -B	Flexural Stiffness of beam considered as nil (Inertia=0)	2.6 seconds	Neglecting the stifness of the beam,the system become more flexible
		Full Flexural Stiffness of Beams (Regular)	1.029 seconds

Effect of Axial stiffness of Structural Elements on mode shapes:

By comparing the model of Building-B with Modified same model with axial stiffness 0,

Criteria	Model	Cases	Analysis Result	Conclusion
Effect of Axial stiffness of Structural Elements on mode shapes	Building -H	Axial Stiffness of Column considered as nil (Inertia=0)	5.99 seconds	Axial stiffness play minor role in mode shapes , since it is based only on vertical vibration not depend on horizontal/lateral forces
		Full Axial Stiffness of Column (Regular)	4.389seconds

The lateral deflection is less depnd on the vertical properties of the system.

Effect of degree of fixity at Column base on mode shapes:

Criteria	Model	Cases	Analysis Result	Conclusion
Effect of degree of fixity at Column base on mode shapes	Building -B	Column Support pinned (Regular)	1.029 seconds	More the fixity lesser the deflection
		Column Support fixed	0.935 seconds

When the fixity of the column increases then the system becomes more stiffer and reduces the time period of the system.

Conclusion:

All the Etabs model are compared for different conditions and investigation is done for different characteristics effects of the system with respect to the Time period.