Conceptual design of a building with columns and shear walls

Q1. 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 of Floor shrinkage

Observation

(a) Full restraints at all corners.

(b) Corners are left free but restraints along the edge.

(c) Non-uniform restraints.

Conclusion

Option(a) will have higher restraint to shrinkage, thus lead to cracks in the floor. Option(b) is average. Option(c) will not effectively restrain the shrinkage, so possibly less cracks.

The Lateral Stiffness

Observation

(a) Comparatively lower lateral stiffness in both X and Y.

(b) Uniform and comparatively higher lateral stiffness in both X and Y.

(c) Non uniform lateral stiffness in both X and Y.

Conclusion

Option(b) will provide higher lateral stiffness for a pure seismic acceleration in X and Y directions.

Torsion with respect to Vertical Axis

Observation

(a) Corner walls provide more resistance to twist.

(b) Edge walls provide good resistance to twist.

(c) Irregular walls provide very poor resistance to twist.

Conclusion

Option(a) will be best option with respect to Torsional resistance whereas Option(c) is the worst one.

Vertical Reinforcement for similar Base Capacity

Observation

(a) Walls are subjected to nominal flexural moment and heavy twisting moment.

(b) Walls are subjected to nominal twisting moment.

(c) Walls are subjected to heavy flexural moment and twisting moment.

Conclusion

Option(c) will require higher vertical reinforcement and Option(b) will require the least.

Static Eccentricity

Observation

(a) Structurally symmetric

(b) Structurally symmetric

(c) Un-symmetric

Conclusion

Only Option(c) will have static eccentricity and it is significant

System's Redundancy

Observation

(a) Uniform placement of lateral load supports in both the axes.

(b) Uniform placement of lateral load supports in both the axes.

(c) Concentrated lateral load supports in both the axes.

Conclusion

Option(a) and Option(b) are more redundant than Option(c)

Foundation Systems

Observation

(a) Due to 'L' shaped walls, the geometry of foundation and its design will be critical.

(b) Walls are in line. Easy to fix the geometry and design of foundation.

(c) Walls are in line and concentrated. Easy to fix the geometry and design of foundation, but critical in design.

Conclusion

Option(b) and Option(c) shall be incorporated with isolated footings/strip footings. Option(a) is recommended to have peripheral box foundation.

Architectural Constraints

Observation

(a) Walls obstruct only corners.

(b) Walls obstruct the faces of building.

(c) Vertical wall will not allow passage.

Conclusion

Architecturally speaking, Option(a) is the preferred one. Option(b) is subjected to discussion. Option(c) will not be accepted both architecturally and commercially.

Q2. 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:

Issues in the given Framing Plan

a) Indirect lateral load transfer in X and Y directions: The beams are connecting to another beams which is ineffective during lateral load transfer. In such conditions, the primary beam is prone to shear failure.

b) Issues in the given Framing plan: Eccentricity- The longer the distance between center of mass and center of stiffness, the higher torsional moment of the building. As per the given plan eccentricity, the building is subjected to higher torsional moment (Torsional flexibility) in both X and Y directions.

c) Strong beam Weak Column possibility: The size of columns majorly mentioned as 25 cm x 25 cm. But all the beams have much deeper section (50cm). Inertia of beam is visually higher than column. If the column reinforcement is adequately greater than that of beams, we are okay and since we do not have the reinforcement detail, this is doubtful. It is recommended to have slight bigger sizes for column.

Alternate Scheme

Q3. 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:

Observations in the given Framing Plan

a) Floor plan: The floor plan of building is not either uniform or symmetric. So naturally any lateral load induced in the floor will not have 100% influence in same direction. Definitely a special lateral load resisting system for these torsional moments should be accommodated.

b) Random internal columns: Since the internal columns are random, they are unable to transfer lateral loads efficiently and can not achieve desirable building response. So we have to assume and design those columns for only gravity loads.

c) Floor to floor variations in partition walls and beams: Partition walls provide an important mass control in a building and beams play key role in shear transfer from floor to beam. All these elements are not in order. So heavy distortion and distribution of lateral loads will happen.

Suggestion on the Lateral Load System and its Foundation

• Heavy torsional forces should be controlled by respective lateral load system. So "Corner Shear walls" are suggested.
• 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.
• 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.

Proposed Schematic Plan of Lateral Load System

a) Superstructure

b) Sub-structure