Conceptual design of a building with columns and shear walls
Question 1:
The building shown, 20 × 35 m in plan, has columns on a 5 × 5 m grid and shear walls (with dimensions shown in m, 250 mm in thickness) in three alternative arrangements, (a), (b), (c), all with the same total cross-sectional area of the shear walls. Compare the three alternatives, taking into account the restraint of floor shrinkage, the lateral stiffness and the torsional one with respect to the vertical axis, the vertical reinforcement required for the same total flexural capacity at the base, the static eccentricity, the system’s redundancy, foundation systems, architectural constraints etc.
RESTRAIN OF FLOOR SHRINKAGE:
fig a:
For this structure is considered as it is as symmetric in nature.
The shear walls are placed at the corners, it has good restraint against floor shrinkage. These walls at the corners will tightly hold the floor in position and possess good control of shrinkage
fig b:
For this structure frame can be considered as symmetric in placed the shear walls.
The edges of floors are restricted to shortening; therefore, the corners are prone to shortening with frame system.
fig c:
For this structure can be considered as asymmetric in nature, because of the shear wall are provided are not arranged in two orthogonal horizontal directions.
The floor is not enclosed symmetrically with reinforced wall, so this floor will have more shrinkage effect.
LATERAL STIFFNESS:
fig a:
The RC walls are not present in the principal plane, so this arrangement possess the less stiffness.
fig b:
The RC walls are in the direction of principal plane, so this arrangement possess greater stiffness as compared to other arrangements.
fig c:
The RC wall is arranged only along X-axis, so this arrangement is stiffer along X-axis and not stiffer along with Y-axis.
Torsion with respect to vertical axis:
fig a:
There is no eccentricity, so the Centre of mass and Centre of stiffness coincides and it shows results in less prone to torsion.
fig b:
There is no eccentricity, so the center of mass and center of stiffness coincides and it shows results in less prone to torsion.
fig c:
The center of mass and center of stiffness does not coincide and it shows results in more torsion.
Vertical Rebars required at the base:
fig a:
The RC walls are not present in the principal plane, so the amount of reinforcement required for these walls is less as compared to other walls.
fig b:
The RC walls are in the direction of principal plane, so this arrangement will resist greater force, so this arrangement required much more reinforcement to resist these forces.
fig c:
The RC wall is arranged only along X-axis, so this arrangement required heavily reinforcement to the left wall to resist the lateral forces.
Static Eccentricity:
fig a:
The walls are symmetrically placed and due to this, the center of mass and the center of stiffness coincides so there is no any eccentricity occurs.
fig b:
The walls are symmetrically placed and due to this, the center of mass and the center of stiffness coincides, so there is no any eccentricity occurs.
fig c:
The walls are not symmetrically placed and due to this, the center of mass and the center of stiffness does not coincide, so eccentricity occurs to this arrangement.
System's Redundancy:
fig a:
The RC walls are not present in the principal plane, so these walls not carry much more load created due to lateral forces, so this arrangement results in less redundancy.
fig b:
The RC walls are present in the principal plane, so these walls carry much more load created due to lateral forces, so this arrangement results in good redundancy.
fig c:
The walls are not symmetrically placed and due to this arrangement, it has the poor redundancy.
Foundation System:
fig a:
Isolated footing connected with tie beam is suitable.
fig b:
The shear walls are spread across the 4 edges of the structure, a raft foundation or box type foundation is suitable for this system.
fig c:
Strip footing for X-direction RC walls and Isolated footing for Y direction RC walls is suitable.
Architectural Constraints:
fig a:
The walls are presented at the corners and hence it will not obstruct to any other elements.
fig b:
The walls are presented at the center of all sides and hence it will obstruct to any other elements.
fig c:
This arrangement is ok by architectural constrains.
Question 2:
Discuss the suitability for earthquake resistance of the moment resisting framing plan of a three-storey building depicted here (cross-sectional dimensions in cm), the eccentricity of the centre of mass (as centroid of floor plan) to the centre of stiffness (from the moments of inertia of the columns) are shown. Suggest an alternative. Also, is there torsional flexibility? Are the two fundamental translational modes of vibration larger than the fundamental torsional mode of vibration. Discuss qualitatively.
AIM:
To observe the given structural framing in terms of seismic influence and to suggest better alternative for the same. Also, the given system needs to be assessed for torsional flexibility.
OBSERVATION:
It will not withstand when subjected to the effect of earthquake due to incomplete load transfer path of the structure in both X and Y direction
The columns and beams are not placed in grid patterns.
As we can see the beam-to-beam connection is irregular (B5 and B6, B3 and B4)
The beam(B7) is supported only by beams and not providing the column at intersection of B7 and B4, which leads to translational deformation.
Alternative Plan:
Some rearrangement of columns and beams can be done in the plan so that the load can be transferred more effectively.
All the columns and beams are now in a grid pattern which exerts better resistance for lateral force.
In the alternative plan, we can see each beam has two columns at both ends for the effective transfer of load. Hence the complexity has been removed.
Torsional flexibility:
It is defined as the angle of twist produced by the unit torque applied.
Torsional Impact of the building:
Since the center of mass and center of stiffness of the building is not coinciding, the building will definitely experience torsional with respect to vertical axis. Still, the plan aspect ratio is less than 3 (within the IS1893 limit), by which we may assume the given system is well proportioned.
Also, the given structural floor system is not effective in transferring lateral loads to vertical elements due to too much offsets and beam to beam connections. The response of building in fundamental mode of translations is worst.
The two fundamental modes of translation may be still higher than the fundamental mode of torsion.
Question 3:
A multi-storey building with basement, with a quadrilateral (non symmetrical floor plan) plan as, has interior columns in an irregular (not in a grid) pattern in plan that serves architectural and functional considerations. Partition walls and interior beams supporting the slab have different layout in different stories. However, there is no constraint to the type, location and size of the lateral force resisting components and sub-systems on the perimeter. Proposals are to be made and justified for the choice of the lateral-load-resisting system and its foundation.
AIM:
To make an observation of the building plan and justify the choice of the lateral-load-resisting system and its foundation.
Observation:
This quadrilateral plan having irregular column pattern and wall supporting the slab may differ in each floor.
The floor area is not uniformly distributed
Simplicity, regularity and symmetry is not achieved in the plan.
Rectangular shaped or square shaped building is always preferred as compared to trapezoidal shaped.
The columns and beams are not placed as per the grid pattern.
As we can see the center of mass and center of stiffness differ center of mass lies in left side of the building because of the size when compared to right portion of the building.
Lateral Load Resisting System:
Since the floor plan is an irregular quadrilateral, so during the Earthquake, the influence of a one direction (X or Y direction) earthquake will also have an effect on another direction (Y or X-direction)
So, an L-shaped corner RC wall arrangement can be provided as a lateral load resisting system, which has bi-directional strength to resist seismic forces.
By providing this shear wall, torsional rigidity can also be maintained for the structure by distributing the mass accordingly.
we can go with two possible foundation options. One is, isolated footings with tie beam connection. The other is, whole box type foundation.
Corner shear walls shall preferably be supported over a box foundation. Shear walls should be connected by link beams to transfer shear from one to the other.
The internal columns shall be supported by isolated footings. Those isolated footings can be connected with shear walls through tie beams.
