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.

Ans.

Restraint to floor shrinakge:

Figure 1	Figure 2	Figure 3
Restraint to shrinkage will be more in this due to position at corners and this lead to more cracks formation.	Restraint to shrinkage will be average as the position of shear walls are in the middle and due to this there is least possibility of formation of cracks	Restraint to shrinkage will be less due to unsymmentrical arrangement and due to this crack will be less too

Lateral Stiffness:

Figure1	Figure 2	Figure 3
Lower lateral stiffness than 2 due to its shear wall arrangement in corners in both x and y direction	More lateral stiffness due to uniform distribution in both x and y direction	non uniform arrangement which leads to non uniform lateral stiffness

Torsion with respect to vertical axis:

Corner wall provide more resistance to twist

edge walls provide less resistance to twist than previous

Irregualar positioning tends to very poor resistance to twist

Vertcal reinforcement for smilar base capacity:

Nominal flexular moment and heavy twisting and due to this require second largest reinforcement between the three arrangement

Nominal twisting moment an due to this require least reinforecement

Heavy both flexural and twisting movement due to irregular positioning and due to this require more reinforcement

	Figure 1	Figure 2	Figure 3
Static eccentricity	symmetric and c.g coincides along the pane therfore no eccentricity	symmetric and c.g coincides along the pane therfore no eccentricity	centre of mass tends to move towards y direction more due to irregular symmetry therefore more eccentricity
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	Box footing with tie beam arrangement is suitable for this system.	Isolated 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.

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.

Ans.

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.The given figure is of weak column strong beam example. It has its more eccentricity in y direction than in x direction as shown in the figure(ey=1.65 > ex =1.505)

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.

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.

Ans.

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.

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.

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.

Out of which box type foundation should be preferable.