Project 1_Comparative study of different storey buildings for Seismic forces

1. Factors influencing the Natural Period of a 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? 

 Increase in the column size increases both stiffness and mass of buildings. when the percentage increase in stiffness as a result of increase in column size is larger than the percentage increase in mass, the natural period reduces, buildings are said to have shorter natural periods with increase in column size. 

Buildings E and F are two 10-storey buildings with different column sizes along the elevation building F has column size of (600×600) throughout the height, while building E has smaller column size (400×400) in the upper 5 storeys . Thus building F (600×600) is relatively stiffer than Building E and the fundamental period of the stiffer building F (1.99 s) is only marginally smaller than that of the building E (2.17 s). 

The deformed shape of the building indicates that most of the deformation is occurring only in the lower storeys because of shear-type of lateral deformation in the building, where the columns size is same, the effect on the overall natural period is not changed.

Between buildings G and H, the occuring is much stiffer. But, while increasing stiffness, the mass is also increased. In arriving at the natural period, the mass and stiffness compete to determine whether the natural period will increase or decrease, when both are changed.

2. 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? 

Mass of a building that is effective in lateral oscillation during earthquake shaking is called the seismic mass of the building. It is the sum of its seismic masses at different floor levels. Seismic mass at each floor level is equal to full dead load plus appropriate fraction of live load. The fraction of live load depends on the intensity of the live load and how it is connected to the floor slab. Seismic design codes of each country/region provide fractions of live loads to be considered for design of buildings to be built in that country/region. 

An increase in mass of a building increases its natural period. Buildings H, J and K are 25 storey buildings with the same plan size, elevation and column sizes, but with different floor mass. Imposed floor mass in building H and that of in buildings J and K are 10% and 20% larger, respectively. Fundamental translational natural periods of heavier buildings K (3.43 s) and J (3.29 s) are larger than that of building H (3.14 s).

3. 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?

As the height of a building increases, its mass increases but its overall stiffness decreases. Hence, the natural period of a building increases with increase in height. Buildings A, B, F and H have same plan size, but are of different heights. Taller buildings have more natural period than shorter building the fundamental translational natural periods of 25-storey building H, 10-storey building F, 5-storey building B and 2-storey building A are 0.84s, 1.16s, 1.99s and 3.2s, respectively.

4. Effect of Column Orientation on T: How does the fundamental natural periods of Buildings B, C and D change with change in column orientation?

Orientation of rectangular columns influences lateral stiffness of buildings along two horizontal directions. Hence, changing the orientation of columns changes the translational natural period of buildings. Buildings C and D are two 5-storey buildings with same column area, but with different orientation of rectangular columns. Longer side of 550mm×300mm columns is oriented along X-direction in building C, and along Y-direction in building D. Lateral stiffness of columns along longer direction is more. Hence, natural period of buildings along the longer direction of column cross-section is smaller than that along the shorter direction.

•  Factors influencing the Mode shape 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.

The lateral translational mode shapes depend on flexural stiffness of beams relative to the adjoining columns. The fundamental mode shape of buildings changes from flexural-type to shear-type as beam flexural stiffness increases relative to that of column 

when flexural stiffness of beams is small compared to that of the adjoining columns deformation is predominantly in single curvature bending leading to overall flexure-type deformation behavior of building 

when flexural stiffness of beams is large compared to that of the adjoining columns,  deformation is predominantly in double curvature bending within in each storey leading to overall shear-type deformation behavior of building 

But, increasing the flexural stiffness of a beam also increases its strength; this is not desirable when strengths of beams exceed that of columns into which they frame in, especially when beam strengths exceed those of the columns adjoining. 

Often in low-rise and mid-rise buildings that are designed as per codes, the relative stiffness of frame members lies in between the above two extreme cases. With the usual finite ratio of beam to column flexural stiffness, both beams and columns bend in double curvature and the response is almost of shear type. Thus, often, real buildings are idealized as shear buildings in structural analysis.

• 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.

Mode shapes depend on axial stiffness of columns and structural walls members in a building.Small axial stiffness causes significant axial compressive and tensile deformations in columns in addition to single or double curvature flexural deformations. Additional axial deformation changes the fundamental mode shape from shear type to flexural type, particularly in tall buildings. This can happen primarily in two circumstances 

when the axial load level is large,

when the axial cross-sectional area is small of vertical members. 

The fundamental mode shapes of the 25-storey building H discussed earlier are of flexure- and shear types for two conditions of very small and large axial stiffness of columns, respectively. Pure flexural response is not desirable because of large lateral sway, particularly at higher floors.

• 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

Two conditions determine the rotational flexibility of columns at the base of the building. The first condition is when the structural design and detailing deliberately creates rotational flexibility at those locations. 

And, the second is when the flexibility of soil underneath the footings of columns allows rotation of the columns; this happens when individual footings are used. flexible soils make column bases as good as hinged, and rocky layers below as good as fixed. The extent of fixity at column bases controls overall behaviour of buildings

Lack of rotational fixity at column base (hinged condition) increases the lateral sway in the lower storeys than in higher storeys, and the overall response of the building is more of shear-type. On the other hand, full rotational fixity at column base restricts the lateral sway at the first storey and thus, induces initial flexural behaviour near the base. The overall response of the building is still of shear-type due to flexural stiffness of beams.

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