Conceptual design of a building with columns and shear walls

Q.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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Criteria
Restraint of Floor shrinkage	Since all four corners of floor is restricted to experience shortening, this RC wall system possess good control of shrinkage.	The edges of Floor are restricted to floor shortening. Whereas the corners are prone to shortening/shrinkage with frame system.	In both the principle directions, the floor is not enclosed with RC wall system at two sides. So this floor will have more shrinkage effect.
Lateral Stiffness	During earthquake excitation, the principle directions will be exposed to lateral movements. At such incidents, since the given RC wall system is not across the principle planes but in diagonal location. So it will possess less stiffness.	The RC walls are right across the lateral force direction. They possess better stiffness compared to other systems.	The RC wall system is effective and stiffer in X-direction. But not stiffer in Y-direction due to concentration of RC wall at only one side.
Torsion with vertical axis	Center of mass and center of stiffness will coincide. So less prone to Torsion.	Center of mass and center of stiffness will coincide. So less prone to Torsion.	Center of mass and center of stiffness will not coincide in both the principle directions. So this system will experience more torsion during earthquake.
Vertical rebar at Base	As they will experience lesser lateral forces, the amount of reinforcement may be lesser than other systems.	This system will take all lateral loads in either principle directions. So the amount of vertical rebar will be heavier than the previous system.	The RC wall arrangement is so eccentric that these walls will experience extreme lateral and torsional moments. This system will have the highest amount of vertical rebar.
Static eccentricity	The system is centric with respect to mass-stiffness comparison.	The system is centric with respect to mass-stiffness comparison.	The system is more eccentric with respect to mass-stiffness comparison.
System’s redundancy	Since the RC wall is less effective to collect lateral forces, the frame structures will need to take part in lateral load resisting system.	RC wall system is effective in this case and mirror with right angle. They possess good redundancy.	The system is worst in terms of redundancy because of concentration of load at one sides.
Foundation system	Isolated footing with tie beam arrangement is suitable for this system.	Box type foundation is suitable for this system.	Strip footing for Y-direction RC wall and isolated footing for X-direction RC wall is suitable.
Architectural constraints	Architecturally very effective, since only corners are obstructed.	Architecturally may not be recommended since all four side entrances are partially obstructed. This RC wall arrangement may disturb open space requirement.	Left side is completely arrested. All other sides are okay with respect to architectural point of view.

Q.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.

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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 of given system:-

In seismic point of view, the lateral load transferring mechanism from floor to foundation is efficiently dealt in the given structural drawing. Even though it is just 3 storey building, any moderate earthquake will affect this structure due to its complexity in load transferring mechanism as stated below images. Also, the depth of the beam is greater than the depth of the column, such phenomenon will create strong beam and weak column principal, which could cause failure.

Alternative structural framing:

With effective arrangement of columns, we shall avoid the complexity in load path. Also we can achieve the beam framing from column to column, which will help easiest flow of lateral forces.

Just by shifting the right top column and left bottom columns, the beam scheme is efficiently revised from column to column. This resembles grid pattern of floor which will exert better resistance for lateral loading.

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.

Q.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.

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Observation on given structural framing:

As per the plan dimensions, we can understand that the center of mass will situate on the left side portion of the floor plan, as the area of floor is larger on the left side. So we have to position the lateral load resisting system in such a way their stiffness center should come near to the center of mass. This is mandatory to avoid torsional irregularity.

There are few more points to be considered:-

a)In the given figure there is no symmetry so therefore it has Symmetrical Irregularity.

b)the columns are in irregular/random pattern in plan to serve architectural and functional considerations so This creates disturbances in the Symmetry as well as it creates Translational and Torsional effects in the Building. Also such irregular column pattern will be unable to transfer lateral loads effectively and can transfer gravity load.

c)In the seismic region the lateral and vertical loads play important role because it helps in resisting the failure against the earthquake as the loads. Resultant will not coinside with the center of the mass of the structure it becomes eccentric and not suitable for any type of areas.

d)The Best lateral loading system applicable is the WALL SYSTEM or DUCTILE WALL SYSTEM.so the wall system acts as a Vertical cantilever,not prone to Soft storey mechanism and overshadows all the constraints in the proposal.

e)The suitable foundation for this type of building is RAFT or MAT foundation only if the Total area of the construction of the footing exceeds 50% of the Total area of the construction site and if the soil has low bearing capacity.

The suitable Lateral load resisting system:-

Since the floor plan is an irregular quadrilateral, the influence of X-direction earthquake will also have effect in Y-direction, and vice versa. So a lateral load resisting system which should have bi-directional strength to resist seismic forces. So we can suggest L-shaped corner RC wall arrangement. The proportion of floor area is greater on the left side than the right side (Irregular quadrilateral). So, corner shear walls on the left side should be heavier than the right.

For this L-shaped RC wall irregular corner arrangement, 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.