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.

AIM :

• To 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.

	Fig 1	fig 2	fig 3
Restraint of floor shrinkage	The shear walls are placed at the comers, 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	The edges of floors are restricted to shortening, therefore the corners are prone to shortening with frame system	The floor is not enclosed symmetrically with reinforced wall, so this floor will have more shrinkage effect
Lateral Stiffness	The RC walls are not prasent in the principal plane, so this arrangement possess the less stiffness	The RC walls are in the direction of principal plane, so this arrangement possess greater stiffness as compared to other arrangements	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	There is no eccentricity, so the centre of mass and centre of stiffness coincids and it shows results in less prone to torsion	There is no eccentricity, so the centre of mass and centre of stiffness coincids and it shows results in less prone to torsion	The centre of mass and centre of stiffness does not coincids and it shows results in more torsion
Vertical Rebars required at the base	The RC walls are not prasent in the principal plane, so the amount of reinforcement required for these walls is less as compared to other walls	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	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	The walls are symmetrically placed and due to this, the centre of mass and the centre of stiffness coincides so there is no any eccentricity occurs	The walls are symmetrically placed and due to this, the centre of mass and the centre of stiffness coincides, so there is no any eccentricity occurs	The walls are not symmetrically placed and due to this, the centre of mass and the centre of stiffness doess not coincides, so eccentricity occurs to this arrangement
System's Redundancy	The RC walls are not prasent in the principal plane, so these wall not carry much more load created due to lateral forces, so this arrangement results in less redundency	The RC walls are prasent in the principal plane, so these walls carry much more load created due to lateral forces, so this arrangement results in good redundency	The walls are not symmetrically placed and due to this arrangement it has the poor redundency
Foundation System	Isolated footing connected with tie beam is suitable	The shear walls are spread across the 4 edges of the structure, a raft foundation or box type foundation is suitable for this system.	Strip footing for X-directionn RC walls and Isolated footing for Y direction RC walls
Architectural Constraints	The walls are presented at the corners and hence it will not obstruct to any other elements	The walls are presented at the centre of all sides and hence it will obstruct to any other elements	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 comment on the suitability for earthquake resistance of the moment-resisting framing plan of a given three-storey building.
• To suggest an alternative to the plan. Also, see if there is torsional flexibility in the building plan.
• To check torsional flexibility in the building plan.
• Also observe if the two fundamental translational modes of vibration are larger than the fundamental torsional mode of vibration Obervation .

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 ony 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:

• The centre of mass and centre of stiffness does not coincide, so the building will definitely experience torsion about the vertical axis.
• Yes, two fundamental modes of translation are greater than the fundamental modes 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.

Obervation:

• 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 preffered 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 beacuse 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.

Plan:

• The foundation suitable for this arrangement based on wall type and column arrangement is Isolated footing.