Conceptual design of a building with columns and shear walls
AIM: 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.
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PROPERTIES |
CASE 1 |
CASE 2 |
CASE 3 |
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Restraint of floor shrinkage |
Shear walls are positioned at corners. It offers strong resistance to floor shrinkage. The floor will be tightly held in place by these shear walls at the corners, and shrinkage will be controlled. |
Shear walls are positioned along the wall's margins on all sidewalls. So better stability to floors near the walls. Shrinkage can occur at corners due to absence of shear walls |
Shear walls are placed in an order less manner and are incomplete, so high chances to shrinkage exposure. |
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The lateral stiffness |
As the Shear walls are positioned only at corners, in the case of an earthquake the forces tends to act along the edges of the floor and will have low lateral stiffness and stability |
The structure will have better stability and lateral stiffness along both principal planes because the shear walls are located along the edges, which is the same direction as the earthquake excitation. |
As there are two shear walls in the x axis that increase stiffness in that direction. But in the y axis, there is only one shear wall, which concentrates seismic force in that wall, causing instability and decreasing lateral stiffness in that direction. |
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Torsional stiffness with respect to the vertical axis |
There is no eccentricity between the centre of mass and the centre of stiffness; they both coincide, making the model less prone to torsion and allowing it to be classified as torsional stiffened model. |
There is no eccentricity between the centre of mass and the centre of stiffness as the shear walls are positioned symmetrically and As a result, this configuration is less vulnerable to torsion. |
The shear wall is placed asymmetrical in the y direction, so as a result, the centre of stiffness shifts to the left edge, resulting in an eccentricity between the centre of mass and the centre of stiffness, causing torsional instability in this configuration. |
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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. |
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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 |
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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 moderate to good redundancy, here as the forces are evenly distributed due to the symmetric placement of shear walls along the mid portion of each edge. |
The structure has the lowest redundancy as the shear walls is placed asymmetric and there is a concentration of load at the left edge. |
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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 |
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Architectural constraints |
From an architectural standpoint, this shear wall configuration is pleasing. since it does not interfere with other elements such as doors, windows, and so on |
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
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.
- This structural frame has a two-way eccentricity of the centre of mass in relation to the centre of stiffness, with the eccentricity of the x-direction being greater than the eccentricity of the y-direction.
- Because the beams in this building are stronger than the columns, it can be considered a weak column strong beam design in nature.
- As a result, when lateral forces operate around the structure, a shear wall is required to prevent column failure.
- The combination of a shear wall and a column tends to keep the structure from collapsing when seismic forces strike.
- The beam alignment is uniformly continuous of B1 and B2 in the X-direction, and Bll & B12, B9 & B10 in the Y-direction, as shown in the frame plan.
- However, because all beams are provided at a discontinuous in the structural frame, the transfer of load equally throughout the structure is difficult due to the action of lateral forces.
- Top reinforcement at the supports of long-span beams may be determined by calculated gravity load rather than seismic design circumstances. As a result, this structure will alternate to a better portal with a better offset in nature.
- The connections between the column beams should have a proper cross section area so that lateral stiffness, mass regularity, and moment resisting factor may be achieved.
- We believe that the beam-sway mechanism in strong column/weak beam design frames is superior because it achieves a consistently distributed global inelastic displacement requirement across all storeys at the roof level.
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.
- This layout is completely unsuited for earthquake prone locations.
- The internal columns in this plan are asymmetric.
- The partition wall is given through the base of the beam and should support the structure's lateral displacement.
- The slab will be supported by the internal beams, with the lateral load resisting failure due to earthquakes.
- We produced flat slabs for these uneven columns in plan because they directly stay in a column centroid axis.
- For example, the beams at various points are irregular in plan and continuous, making it unable to withstand the seismic stress in the area.
- In this layout, the flat sab is more suited than a normal beam column junction since it provides support to the columns without the use of a beam, lowering the building's weight and indirectly increasing the structure's ductility.
- We give a shear wall from the foundation of the structure through vertical components for this structure's solution, which should reduce the loss of unexpected collapse owing to lateral force operating on the structure.