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:

• We can see in the first and second figures that all the four shear walls are symmetrical and are uniform in size so there will be a uniform distribution of seismic forces. But in the third figure, the walls are dissimilar and unsymmetric, so the wall which is stronger will yield first.
• The torsional stiffness of the first one is more when compared to the second one because it is directly proportional to the stresses and the torsional stiffness of the second one will be lesser, and it will be higher when compared to the 3 one.
• Redundancy will be higher in the first and second one when compared to the third one because the left side of the structural system of the wall will not carry the load equally in either direction in the third due to unsymmetric size.
• In the 1 fig, the L shape walls are given so these walls will have high strength in both horizontal directions and be subjected to biaxial bending and bidirectional shears during the earthquake.
• When most of the walls are placed around the staircase and lift corner area and it produces large eccentricity in the plan or creates a torsionally sensitive building.
• Shear walls will carry the earthquake load to the foundation and the structure has greater strength and stiffness in the direction of their orientation.
• Shrinkage in the longitudinal direction can be ignored. However, that may not be the case for perpendicular to gain shrinkage.
• In the first figure, there is no architectural disturbance as the walls are L-shaped and in the other two diagrams, they are on the front face to the extent they contribute to the architectural constraints of those plans.

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:

There is a 2-way eccentricity in the frame along with the X & Y directions also with Stiffness the eccentricity in the X direction is larger when compared to the Y direction.

There are only two frames in the structure that is B1 and B2 in the X direction and B9, B10 and B11, B12 in the Y-direction, and all other beams are broken at the midway in the frame.

There will be torsional flexibility in the structure. To avoid torsional restraints, it is better to make the room dimensions even in both X and Y directions and place the columns at the junction of two walls if it is feasible better to provide a shear wall at the appropriate location.

The fundamental translation mode of vibration is larger than the fundamental torsional mode of vibration.

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:

The above plan is given totally unsuitable for normal areas and in earthquake-prone areas.

In the seismic region, the lateral and vertical loads play important criteria because it helps in resisting the failure against the earthquake as the loads. The resultant will not coincide with the center of the mass of the structure it becomes eccentric and not suitable for any type of area.

In this plan, a flat slab is more appropriate than a regular beam-column junction as it provides support to the columns without any provision of the beam which reduces the weight of the building and helps in the ductility which indirectly helps to maintain the structure in the earthquake-prone areas.

A 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.