Conceptual design of a building with columns and shear walls

Question 1-

Aim- 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.

Answer-

properties	case1	case2	Case3
Restraint of floor shrinkage	Shear walls are positioned at corners. These shear walls at the corners will tightly hold the floor in postion and the shrinkage will be in control.	Shear walls are positioned along the wall's margins on all sidewalls. This wall will provide better stability to the floor near it but the corner portions of the floor are subjected to shrinkage	Shear walls are placed in an order less manner and are incomplete shear walls are not placed symmetrical. Both the long edges and right short edge of the wall is prone to shrinkage
The lateral stiffness	As the Shear walls are positioned only at corners this placement of shear walls will have least stability and hence the lateral stiffness will also be less	The structure will have better stability and lateral stiffness along both principal planes because the shear walls are placed along the edges which is the same direction of earthquake excitation	Because there are two shear walls in the x-axis that increase the stiffness in that direction. But there is only one shear wall in the y-axis, which concentrates the seismic force in that wall, causing instability and reducing the lateral stiffness in that direction.
Torsional stiffness with respect to the vertical axis	There is no eccentricity between the center of gravity and the center of rigidity; both coincide, making the model less susceptible to torsion and allowing it to be classified as a torsionally stiffened model.	There is no eccentricity between the center of mass and the center of stiffness because the shear walls are placed symmetrically and as a result this configuration is less prone to twisting.	The shear wall is located asymmetrically in the y-direction, so as a result the center of stiffness moves to the left edge, resulting in an eccentricity between the center of mass and the center of stiffness, causing torsional instability in this configuration.
Static eccentricity	There is no eccentricity because the shear walls they are symmetrically located at the corners, the centre of mass and stiffness coincides in this layout	There is no eccentricity because the shear walls are symmetrically arranged around the edges, the centre of mass and stiffness coincide in this arrangement	There will be eccentricity in the arrangement because there is only one shear wall along the left edge with a larger mass than the other two shear walls in the y direction. As a result, the centre of stiffness shifts to the left, resulting
System’s redundancy	The structure will have less redundancy, because this design contains shear walls at its corners which does not actively participate in resisting the lateral force, so the other parts of the structure must take care of a large portion of the lateral force.	The structure will have less redundancy, because this design contains shear walls at its corners which does not actively participate in resisting the lateral force, so the other parts of the structure must take care of a large portion of the lateral force.	The structure has the lowest redundancy as the shear walls is placed asymmetric and there is a concentration of load at the left edge.
Foundation systems	As the shear walls are at the structure's corners, an isolated footing with a tie beam can be used as a foundation.	A raft foundation or a box foundation can be used.	a combined footing can be provided along the y direction and isolated footing in X direction
Vertical reinforcement at base	Since the shear reinforcements are positioned at the corners, they play a little role in the lateral force resistance to the remainder of the wall As a result, less reinforcement will be required for these walls.	Here the shear walls are arranged along the main directions, they absorb a substantial amount of lateral forces. As a result, considerably more reinforcing should be added to these walls in order to withstand these forces.	The shear walls are asymmetrically arranged here, the shear walls will take up a significant amount of lateral forces. Especially the wall on the left side of the room. As a result, these walls must be heavily reinforced.
Architectural constraints	From an architectural standpoint, this shear wall configuration is pleasing. since it does not interfere with other elements such as doors, windows	While this design is stable, there is a potential that these shear walls will interfere with the wall openings, which is not ideal.	In this configuration, the two walls on the right side along the X direction are architecturally sound, but the shear wall on the left edge along the y direction takes up over half of the wall, obstructing open spaces

Question 2-

Aim- 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.

Answer-

1. This structural frame has a two-way eccentricity of the center of mass relative to the center of rigidity, with the eccentricity in the x direction being greater than the eccentricity in the y direction.
2. Since the beams in this building are stronger than the columns, it can be considered a weak column strong beam in nature.
3. Consequently, when transverse forces are applied around the structure, a shear wall is required to prevent column failure.
4. The combination of shear wall and column tends to prevent the structure from collapsing when seismic forces strike.
5. The beam alignment is uniformly continuous for B1 and B2 in the X direction and Bll & B12, B9 and B10 in the Y direction as shown in the frame plan.
6. However, since all the beams in the structural frame are arranged discontinuously, it is difficult to transfer the load evenly throughout the structure due to the action of lateral forces.
7. The top reinforcement in the supports of long-span beams may be determined by calculated dead loads rather than seismic design considerations. As a result, this structure will rotate into a better portal with a better offset.
8. Joints between column beams should have the correct cross-sectional area to achieve lateral stiffness, mass regularity and moment resistance factor.
9. We believe that the beam sway mechanism in strong-column/weak-beam frames is better because it achieves a consistently distributed global inelastic displacement requirement in all stories at the roof level.

Question 3-

Aim- 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.

Answer-

• The three main systems for resisting lateral loads in a building include:- Shear wall or RC wall system:- Moment resistant frame system:
• Normal frame of beams, columns, rigid or semi-rigid connections. Stiffness and strength are proportional to floor height and column spacing.
  - Dual frame and wall systems
• Due to the irregular shape of the floor plan, the most suitable type of lateral load resistance system is a shear wall system or an RC wall system that can be secured at the corners.
• By providing this shear wall, the torsional stiffness of the structure can also be maintained.