Projefct 1_Comparative study of different storey buildings for Seismic forces
FACTORS INFLUENCING NATURAL PERIOD OF BUILDING:
Ans 1: Effect of Stiffness on T: The fundamental natural periods of building E is given below
and The fundamental natural periods of F is given below
Explanation: E and F both are 10 storey buildings. But the columns in E are 600x600 upto 5th storey and above that columns are 400x400. While in F columns are 600x600 in the whole building.
All the three natural periods in E are less than that of F. In E the sizes of columns are decreased for top 5 storey which decreases the overall stiffness of the building as compared to that in F building. In F the same column size is continued to the top storey. Modal mass participation factor for all the three modes is nearly 80% in E while in F it is nearly 83%.
Effect of mass on T : The Fundamental natural period of G is given below
and The fundamental natural period of building H is given below
Explanation: G and H both are 25 storeys buildings. In G the column size is 800x800 for bottom 10 storeys, column size is 600x600 for middle 10 storeys and for remaining 5 storeys it is 400x400. While in H all the storeys have same column size that is 800x800.
It can be seen from analysis that because of decrease in column size in G the stiffness decreases. The natural period of G is less than than of H, which shows that as the stiffness increases the fundamental natural period also increases.
Ans 2: Fundamental natural periods of H are given below
and for fundamental natural periods of J are given below
The fundamental natural periods of K are given below
Explanation: In J the imposed mass is increased by 10% that of H, it becomes 3.3 kN/m2. While in K the imposed mass is increased by 20% that of H, it becomes 3.6 kN/m2.
It can be seen from the above values of natural periods that as the mass increases the natural period of vibration also increases.
Ans 3 : Fundamental natural periods of A are given below
Fundamental natural periods of B are given below
Fundamental natural periods of F are given below
Fundamental natural periods of H are given below
Explanation: The storeys in buildings A,B,F and H are 2,5,10 and 25 respectively. The height of each storey is 3m.
It can be seen from the diagrams above that as the height of building increases the fundamental natural period of vibration also increases.
Ans 4 : Fundamental natural periods of B are given below
Fundamental natural periods of C are given below
Fundamental natural periods of D are given below
Explanation : All the Three buildings B,C and D are 5 storey buildings. In B the column size is 400x400 while in C and D the column size is 550x300 and 300x550 respectively. There is difference in orientation of column in C and D.
In B there is square column size, we can see from the above diagrams that building B is showing normal tendency of two translation mode of vibration are greater than fundamental rotational mode of vibration.
While in case of C with column size 550x300 with columns orientation along X i.e the length 550 mm is along X direction. It can be seen that the natural period along Y direction is more, while the natural period along X is less than that of rotational natural period.
While in case of D with column size 300x550 with column orientation along Y i.e the length 550 mm is along Y direction. It can be seen that the natural period along X direction is more, while the natural period along Y direction is less than that of rotational natural period.
Conclusion : The direction along which there is orientation of column or the direction along which there is larger dimension of column, the natural period along that direction decreases. In above cases it even becomes less than torsional natural period.
FACTORS INFLUENCING MODE SHAPE OF OSCILLATIONS:
Ans 1: Effect of Flexural Stiffness of Structural Elemants on mode shapes:
Fundamental mode shapes of Building B when C400x400 and B150x230 are given below
Mode 1 below:
Mode 2 below:
Mode 3 below:
Fundamental mode shapes of Building B when C400x400 and B300x400 are given below:
Mode 1 below:
Mode 2 below :
Mode 3 below:
Fundamental modes of building B when C400x400 and B 400x600 are given below:
Mode 1 given below:
Mode 2 given below :
Mode 3 given below:
Conclusion: It can be seen from the above values of fundamental natural periods of modes that as the Flexural stiffness of Beam increases the fundamental natural period decreases. In all the cases it is done by keeping the size of columns same and increasing the size of beam.
Ans 2: Effect of Axial Stiffness of vertical members on mode shapes:
Fundamental modes of building H when C300x300 and B300x400 are given below:
Fundamental modes of Building H when C800x800 and B300x400 are given below:
Conclusion: It can be seen from the above fundamental modes that as the Axial stiffness of vertical member increases the natural period decreases.
Ans 3: Effect of degree of Fixity at column bases on mode shapes:
Fundamental modes of Building B when column bases are pinned are given below:
Mode 1 below:
mode 2 below:
mode 3 below:
Fundamental modes when building B is fixed at column bases are given below:
Mode 1 below:
mode 2:
mode 3:
Conclusion : It can be seen from the above values of natural periods that the fundamental natural periods decreases when columns bases are converted from PINNED support to FIXED support. It indicates that when column bases are fixed for same other overall properties the Fundamental natural period decreases.