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.

Floor shrinkage-

• Option a has shear wall is corners therefore more restraint to shrinkage which means more cracks, option c has non uniform placement of shear walls on the edges which could mean less restraint to floor shrinkage.

Lateral stiffness-

• Option (a) will have low lateral stiffness in both x and y direction. Option (b) will have comparatively more lateral stiffness due to uniform shear walls being on the edges. Option (c) will have non uniform lateral stiffness in both x and y direction.

Torsion stiffness-

• Option (a) provide best torsional resistance with shear walls being in the corners. Option (b) also provides good torsional resistance. Option (c) provide the worst torsional resistance since the shear walls are non-uniformly placed.

Static eccentricity-

• Both option (a) and (b) are symmetric so their static eccentricity is not considered but option (c) having non symmetric structure will have significant static eccentricity.

System redundancy-

• Both option (a) and (b) are symmetric so they have good redundancy but option (c) having non symmetric structure will have less system redundancy.

Foundation system-

• Option (a) having L shape structure the foundation design has to be critical. Option (b) have the walls in line so the foundation can be easily designed. Option (c) have the walls in line but the since they are non uniformly placed the foundation design is critical.

Architectural constraints-

• Option (a) is preferred here as walls in the corners will affect the architecture design very little. Option (b) can tricky since the walls are in the middle. Option (c) is least preferrable since the 10m wall makes the whole structure not usable from the left side.

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.

• The suitability for this moment resisting frame for earthquake resistance is not good. We can observe that when the lateral loads are applied in both x and y directions they failed to transfer the loads uniformly in beams. Shear failure of beams could occur due to this.
• As observed the centre of mass and centre of eccentricity have large distance between them this will lead to greater torsional moment in the building.
• Weak column strong beam is observed here based on the measurements of the column and beam provided. Column sizes are 25x25 whereas beam sizes are 25x50. More reinforcement in column than beam could tackle this problem to make columns stronger than beam.
• Alternative design.
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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.

• The above plan is unsymmetric which means the lateral loads applied an the building will not have 100% influence in the same direction. Therefore a special lateral load resisting for torsion should be suggested.
• Shear walls in the corners of the structure are suggested as it can resist the torsional moment.
• In the foundation the corner shear wall is to be supported by box foundation and the columns are to be supported by isolated footing connecting through tie beams.