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.

Answer :

* Restraint of floor shrinkage :

• Structure 1: In this case, since the shear walls are placed at the corners, it has good restraint against floor shrinkage. These shear walls at the corners will tightly hold the floor and shrinkage will be in control.

• Structure 2 : The shear walls are placed along the edges of the wall in all four sides. This wall will provide better stability to the floor near it but the corner portions of the floor are subjected to shrinkage, where there is no shear walls.

• Structure 3: Since the shear walls are not placed symmetrical, Both the long edges and right short edge of the wall is prone to shrinkage as there is no shear wall at the right side.

* Lateral stiffness:

• Structure 1:  As the shear walls are placed at the corners of the floor, the edges of the floor does not have any support , the earthquake force or the seismic force tends to act along the edges of the floor. This placement of shear walls will have least stability and hence the lateral stiffness will also be less..

• Structure 2 : As the shear walls are placed along the edges, the structure will have more stability and as such the lateral stiffness will also be more along both the principal planes.

• Structure 3 : Along the x direction there are two shear walls which enhance the stiffness in that direction, whereas in the y direction, there is only one shear wall at the left which leads to the concentration of seismic force and causes instability and reduces the lateral stiffnes.

* Torsional stiffness with respect to vertical axis:

• Structure 1 :Here the placement of shear walls is symmetric, hence there is no eccentricty between the center of mass and centre of stiffness, so it is less prone to torsion and can be regarded as torsionally stiff model.

• Structure 2 : In this, the placement of shear walls is symmetric and there is no  eccentricity between the centre of mass and centre of stiffness. Hence, this is also less prone to torsion. 

• Structure 3 :In this the shear wall placement is unsymmetrical along the y direction. So, the centre of stiffness shifts towards the left edge which leads to torsional instability in this arrangement.

 * The vertical reinforcement required at the base :

• Structure 1 :As the shear reinforcements are placed at the corners, there is no resistance of the lateral forces as compared to the other parts of the wall. As such the amount of reinforcement required for these walls will be less.

• Structure 2 : In this, the huge amount of the lateral forces are taken by shear walls as it is placed along the principal directions. Hence, these walls should be provided with more reinforcement to resist forces.

• Structure 3 :  In this, as the shear walls are asymmetrically placed, large amount of lateral fores will be taken especially the wall at the left edge. Hence, these walls needs to be reinforced heavily.

* The static eccentricity :

• Structure 1 : In this, as the shear walls are symmetrically placed at corners, the centre of mass and centre of stiffness coincides and there is no eccentricity.

• Structure 2 : As the shear walls are symmetrically placed along the edges, the centre of mass and centre of stiffness coincides and there is no eccentricity.

• Structure 3 : The shear walls are symmetrically placed along one of the principal direction ( x direction), but in the y direction there is only one shear wal. Due to this, the centre of stiffness shifts to the left side and hence, there is eccentricty in the arrangement.

* The system’s redundancy :

• Structure 1 : It has shear walls at its corner and it does not actively take part in resisting the lateral force so huge amout of the lateral force have to be taken care of by the other part of the structure. Hence, this is less reduntant.

• Structure 2 : Due to the symmetric arrangement of shear walls along the mid half of each edges, the forces are equally shared among them. Hence, this has good redundancy.

• Structure 3 : As this arrangement of shear walls is asymmetric and concentratn of load at the left edge, this arrangement has poor redundancy.

* Foundation systems :

• Structure  1 : As the shear walls are placed at the corners of the structure, an isolated footing with a tie beam can be provided as foundation.

• Structure 2 : In this as the shear walls are spread across the four edges of the structure, a raft foundation or box type foundation can be provided.

• Structure 3 : In this the two shear walls are provided at the along the x direction so for this a combined footing can be provided along y direction connecting these two shear walls.

* Architectural constraints :

• Strutcure 1 : The shear wall is from architecture point of view, and it does not hinders with any other elements like door, windows etc.

• Structure 2 : This is a stable arrangement, but from architectural point of view there is a chance that these shear wall may hinder with the wall openings which is not suitable.

• Structure 3 : In this , the two walls at the right side along X direction is architecturally fine but the shear wall at left edge along y direction can cause hinderance to the open spaces.

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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.

Answer :

• There is a two way eccentricity in the frame along X direction and Y direction also when compared to stiffness the eccentricity in X direction is large when compared to Y direction.
• There is only two continuous frames in the structure that is B1 nd B2 in the X-direction and whereas B9, B10, B11, B12 and all other beams are broken at midway in the frame.
• There will be torsional flexibility in the structure to avoid torsional restraints which is better to make the room dimension even in both X and Y direction packing the columns at the junction of the two wall.
• The fundamental translation mode of vibration is larger than the fundamental torsional mode of vibration.
• Beams with long span may have their top reinforcement at the supports governed by factor gravity load, rather than by the seismic design situations.

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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.

Answer :

• As per the observation,this plan is totally unsuitable for heavy seismic zone areas.
• In this plan, the interior columns are unsymmetric.
• The partition wall are provided through the base of beam, should support the lateral deformation due to the structure.
• The interior beams will support the slab, then the lateral load resisting the failure due to earthquakes.
• For here, the beams at different locations is irregular in plan and are continuous and is disallowed to resist the seismic load in the region.
• For the solution of this structure, the shear wall from the foundation of structure through vertical components  should minimize the loss of sudden failure occur due to lateral force acting on structure.
• The flat slab is more appropriate than a regular beam column junctions, because it provides a support to the columns without any provisions of the beam..
• These types of plans can be supported over a box type foundation.

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