Conceptual design of a building with columns and shear walls
Ans 1 : Lateral stiffness :
The lateral stiffness of second arrangement is more than the other two arrangements. The order of decreasing lateral stiffness is second, first and third arrangements. Reason : The lateral stiffness of second is more than the other two because the same cross section area is symmetrically distributed along both the axis and covering the middle area. The lateral stiffness of first is more than third because in the first arrangement the cross sectional area is symmetrically distributed along both axis which is not in the third arrangement.
Torsion about vertical axis:
There is most torsion about vertical axis in the third arrangement because the cross section is not symmetrically distributed. The centre of mass not coinside with the centre of stiffness. In the first and second arrangement there is no torsion about vertical axis because of symmetrical distribution about vertical axis, the centre of mass coinsides with centre of stiffness.
Vertical reinforcement required:
The decreasing order of vertical reinforcement required is third, first and second arrangements. The second requires less vertical reinforcements because the cross sectional area is symmetrical about both the axis and the placement is also better that is in the middle of four faces. The first requires more because the placement because the placement is at the corner. The third requires most because to counteract the torsion about vertical axis the reinforcement must be increased.
Static Eccentricity:
The static eccentricity of third is less than the other two. Because in case of third there is not symmetrical distribution about both the axis and the centre of mass does not coinside with the centre of stiffness.
System redundancy:
The decreasing order of system redundancy is second, first and third, because in first and second more number of shear walls are placed in the cross sectional area but in second the shear walls are in the the middle and in first the shear walls are at the corners. The third system is least redundant because of placement of only three shear walls with large span between.
Foundation System:
The foundation of third arrangement needs to designed to avoid overturning. The shear walls in first and second requires less reinforcement because of symmetrical distribution. The decreasing order third, first and second.
Architectural Constrains:
There is more constrains of placements in second because of shear walls in the middle, the architectural elements like windows are provided only at corners and not in the middle of the face or it needs to be discontinued at middle of faces.
In first the architectural elements are constrained at the corners and in third there is less architectural contrains for top, bottom and right side faces but for left side there is presence of long shear wall.
Ans 2 : In the given diagram 250*250 columns are not suitable for supporting large spans. The provided depth of beam is suitable for given large spans. It generally shows strong beam weak column design which is not suitable during earthquake and may leads to collapse of whole structure. In other words the overall stiffness of columns and structure is less.
Secondly some beams are rested on other (primary and secondary) which is generally not allowed for designing for earthquakes.
The fundamental translation modes of vibration is less than torsional mode of vibration.
Alternative provision: The size of columns is increased or more columns should be provided to increase stiffness of overall structure and the depth of beams may be decreased or remains the same. The beams should not rest on one another.
Ans 3: In the given diagram accordingly four shear walls needs to be provided each at the middle of each face because there is no architectural constrain. Foundation provided is box type with retaining walls at the periphery in basement. In this way of providing shear walls and foundation the overall stiffness of structure is increased (depending on the number of stories provided).