Conceptual design of a building with columns and shear walls

  Answer 1 :-

  Given :-

• The building shown, 20 × 35 m in the 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.

  AIM :-

• To 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.

  1) Restraint of floor shrinkage :-

  For Case A :-

• In this case, since the shear walls are placed at the corners, it has good restraint against floor shrinkage.
• These walls at the corners will tightly hold the floor in position and possess good control of shrinkage.

  For Case B :-

• Here, the shear walls are placed along the edges of the Floor.
• This wall will provide better stability to the floor near it but the corner portions of the floor are prone to shrinkage.

  For Case C :-

• Here, the floor is not enclosed with shear walls in both principal directions.
• This floor will have a high shrinkage effect.

  2) Lateral Stiffness :-

  For Case A :-

• As the shear walls are placed at the corners of the floor, the edges of the floor do not have any support.
• During the earthquake excitation, the forces tend to act along the edges of the floor, this placement of shear walls will have the least stability and hence the lateral stiffness will also be less.

  For Case B :-

• The shear walls here are placed along the edges which is the same direction of earthquake excitation, the structure will have more stability and thus possess high stiffness in both the principal directions.

  For Case C :-

• In this system, the stiffness is effective along the X-direction as there are two shear walls at both edges of the floor.
• Whereas in the Y-direction, there is only one shear wall which leads to the concentration of seismic force in that wall and reduces the lateral stiffness in that direction.

  3) Torsion with respect to vertical axis :-

  For Case A :-

• Here the placement of shear walls is symmetric, hence there is no eccentricity, so the centre of mass and centre of stiffness coincide, so it is less prone to torsion.

  For Case B :-

• The symmetricity is maintained in this arrangement also, hence there is no eccentricity, so the centre of mass and centre of stiffness coincide, so it is less prone to torsion.

  For Case C :-

• In this arrangement, the shear wall placement is unsymmetrical along the Y-direction. So, so the centre of mass and centre of stiffness will not coincide. Thus this arrangement will experience torsion during the earthquake.

  4) Vertical Rebars required at the base :- 

  For Case A :-

• As the shear reinforcements are placed at the corners, not in the principal plane, it does not take part much in the resistance of the lateral forces as compared to the other parts of the walls.
• Thus, the amount of reinforcement required for these walls will be less.

  For Case B :-

• Here, a huge amount of the lateral forces are taken by the shear walls as they are placed along with the principal directions.
• Thus, these walls required more vertical reinforcement than system A.

  For Case C :-

• In this arrangement, as the shear walls are placed asymmetrically, so these walls will experience extreme lateral forces.
• These walls need the highest amount of vertical rebars.

  5) Static Eccentricity :- 

  For Case A :-

• The shear walls are symmetrically placed at the corners and the centre of mass and centre of stiffness coincide and there is no eccentricity.

  For Case B :-

• The shear walls are symmetrically placed along the edges and the centre of mass and centre of stiffness coincide and there is no eccentricity.

  For Case C :-

• Here, the shear walls are not symmetrically placed in the Y-direction and the centre of mass and centre of stiffness didn't coincide and thus eccentricity occur in this arrangement.

  6) System's Redundancy :-

  For Case A :-

• In this arrangement, shear walls are placed at the corners of the floor and thus, these walls do not actively take part in resisting the lateral force.
• Hence, a huge amount of the lateral force has to be taken care of by the other part of the structure and thus, the structure is less redundant.

  For Case B :-

• In this arrangement, the shear walls are along the mid half of each edge and the lateral forces will be equally shared among them.
• Hence, this arrangement has really good redundancy.

  For Case C :-

• This arrangement of shear walls is asymmetric and also the concentration of load is at the left edge.
• Thus, this arrangement has poor redundancy.

  7) Foundation System :-

  For Case A :-

• As the shear walls are placed at the corners of the structure, an isolated footing with a tie beam arrangement is suitable for this system.

  For Case B :-

• Since the shear walls are spread across the 4 edges of the structure, a raft foundation or box type foundation is suitable for this system.

  For Case C :-

• In this arrangement, two shear walls are provided along the X-direction so for this a combined footing can be provided along Y-direction connecting these two shear walls.
• The other shear walls at the left t edge can be provided with isolated footing.

  8) Architectural Constraints :-

  For Case A :-

• The wall at the corners of the floor, thus, is Architecturally very effective as it will not obstruct any other elements.

  For Case B :-

• From the architectural point of view, this arrangement may not be recommended as there is a chance that these shear walls may obstruct the other elements.

  For Case C :-

• This arrangement has two walls on the right side along X direction is architecturally fine. But the shear wall at the left edge along Y-direction occupies almost half of the wall, which can cause hindrance to the open space.

  Answer 2 :-

  Given :-

• Plan of a three-storey building with cross-sectional dimensions in cm.
• The eccentricity of the centre of mass (as the centroid of floor plan) to the centre of stiffness (from the moments of inertia of the columns) are shown.

  AIM :- 

• To observe the suitability for earthquake resistance of the moment-resisting framing plan of a given three-storey building.
• To suggest an alternative to the plan. Also, see if there is torsional flexibility in the building plan.
• Also observe if the two fundamental translational modes of vibration are larger than the fundamental torsional mode of vibration.

  Obervation :-

• From the seismic point of view, the earthquake with moderate intensity will affect this structure due to the complexity in load transferring in both X and Y- directions.
• The columns and beams are not placed in grid patterns. They are offset from their path due to which load does not transfer effectively.

  Alternative Plan :- 

• Some rearrangement of columns and beams can be done in the plan so that the load can be transferred more effectively.

• All the columns and beams are now in a grid pattern which exerts better resistance for lateral force.
• In the alternative plan, we can see each beam has two columns at both ends for the effective transfer of load. Hence the complexity has been removed.

  Torsional Impact of the building :- 

• The centre of mass and centre of stiffness does not coincide, so the building will definitely experience torsion about the vertical axis.
• Yes, two fundamental modes of translation are greater than the fundamental modes of torsion.

  Answer 3 :-

  Given :-

• A multi-storey building with a basement, with a quadrilateral (non-symmetrical floor plan) plan.
• The plan has interior columns in an irregular (not in a grid) pattern that serves architectural and functional considerations.
• Partition walls and interior beams supporting the slab have a different layout in different stories.
• Also, there is no constraint to the type, location and size of the lateral force-resisting components and sub-systems on the perimeter.

  AIM :- 

• To make an observation of the building plan and justify the choice of the lateral-load-resisting system and its foundation.

  Obervation :-

• As we can see from the plan view that the floor area is asymmetric as it is in the shape of an irregular quadrilateral and the mass(load) is not uniformly distributed.
• Clearly, the centre of mass will situate on the left side portion of the floor plan, as the area(mass) of the floor is larger on the left side.
• The Columns and Beams are not placed as per the grid pattern.

  Lateral Load Resisting System :-

• Since the floor plan is an irregular quadrilateral, so during the Earthquake, the influence of a one-direction(X or Y-direction) earthquake will also have an effect on another direction (Y or X-direction).
• So, an L-shaped corner RC wall arrangement can be provided as a lateral load resisting system, which has bi-directional strength to resist seismic forces.
• By providing this shear wall, torsional rigidity can also be maintained for the structure by distributing the mass accordingly.

  Placement of wall could be :-

• The foundation suitable for this arrangement is Isolated footing with a tie-beam connection or Box type foundation.