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 :
Restraints of floor shrinkage
Structure (a)
By observing the given structure(a), the shear walls are at the four corners so the structure is full restraint at all the corners.
This will have higher restraint to shrinkage which will lead to cracks in the floor
Structure (b)
By observing the given structure(b), the shear walls are at the four faces of the structure so the corners are left free so there will be restraint at all the corners.
There will less cracks at the floor when compare to structure(a)
Structure (c)
By observing the given structure(c), the shear walls are non uniform so the restraints will be non uniform.
The structure is not effectively restraints to shrinkage, so there will be possibly less cracks.
Lateral Stiffness
Structure (a)
The structure has comparatively lower lateral stiffness in both x and y direction
The structure has less lateral stiffness for seismic acceleration at both x and y direction
Structure (b)
The structure is uniformly and comparatively higher lateral stiffness in both x and y direction
Thus the structure will provide higher lateral stiffness for a pure seismic acceleration at both x and y direction.
Structure (c)
Since the shear walls are not placed uniformly so there will be non uniform lateral stiffness in both x and y direction
The structure has less lateral stiffness for seismic acceleration at both x and y direction
Torsion with respect to vertical axis
Structure (a)
The shear walls are at the corners so the corner walls will provide more resistance to twist
So the structure is best with respect to torsional resistance
Structure (b)
The shear walls are at four faces of the structure so the edge of the walls will provide good resistance to twist
So the structure has less torsional resistance to twist when compared to structure (a)
Structure (c)
The shear wall is non uniform so there will be very poor resistance to twist
So the structure is the worst one when compared to other to structures
Vertical reinforcement for similar base capacity
Structure (a)
The walls are subjected to nominal flexural moment and heavy twisting moment
Structure (b)
Walls are subjected to nominal twisting moment
The structure will require least vertical reinforcement
Structure (c)
The walls are subjected to heavy flexural moment and twisting moment
The structure will require higher vertical reinforcement
Static eccentricity
Structure (a)
Structure is structurally symmetric
Structure (b)
Structure is structurally symmetric
Structure (c)
Structure is structurally un symmetric
The structure will have static eccentricity and it is significant
System’s redundancy
Structure (a)
The shear walls are uniformly placed at lateral loads support in both the direction
The structure is more redundant
Structure (b)
The shear walls are uniformly placed at lateral loads support in both the direction
The structure is more redundant
Structure (c)
The shear walls are not uniformly placed there will be concentrated lateral load supports in both the directions
The structure is less redundant when compared to the other two structure
Foundation system
Structure (a)
Due to L shaped walls, the geometry of foundation and its design is very critical
The structure is recommended to have peripheral box foundation
Structure (b)
Walls are in line, easy to fix the geometry and design the foundation
The structure shall be incorporated with isolated or strip footings.
Structure (c)
Walls are in line and concentrated, easy to fix the geometry of foundation but critical to design
The structure shall be incorporated with isolated or strip footings.
Architectural restraints
Structure (a)
Walls are obstructed only at the corners
The structure is preferred for construction
Structure (b)
Walls are obstructed at the faces of the building
The structure is subjected to construction
Structure (c)
Vertical wall will not allow passage
The structure will not be accepted both architecturally and commercially
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 :
The beams are connecting to another beams which is ineffective during lateral load transfer, so there is indirect lateral load transfer in both x and y direction as per the given plan. In such conditions, the primary beam is prone to shear failure.
Eccentricity : The longer the distance between the centre of mass and centre of stiffness, there will be higher torsional moment of the building. As per the given plan the building is subjected to higher torsional moment in both x and y directions.
There will be possibility of strong beam and weak possibility because as per the given plan the size of column majorly mentioned as 25x25cm but the beams have much deeper section 25x50cm, so the inertia of the beam is visually higher than column. If the column reinforcement is adequately greater than that of beams, we are okay and we do not have reinforcement detail it is doubtful. It is recommended to have slightly bigger size of column.
Alternate scheme
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 :
Observation
The floor plan of the building is neither uniform or symmetric. So naturally any lateral load induced in the floor will not have 100% influence in the same direction, definitely a special lateral load resisting system for these torsional moment should be accommodated.
As per the given plan the internal columns are randomly placed, so they are unable to transfer the lateral load efficiently and cannot achieve desirable building response. So we have to assume and design those columns for gravity loads only.
Partition walls provide an important mass control in a building and beam plays an key role in shear transfer from floor to beam. All these element will not be placed in order as there will variation in floor plan of the each floor. 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 portion of floor area is greater on the left side than the right side because it is a irregular quadrilateral. So that the corner shear walls on the left side should be heavier than the right side.
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, this isolated footings can be connected with shear walls through tie beams.