Concept on positioning of Columns
Question 1:
Comment on the layout of the framing plan concerning earthquake resistance in the two horizontal directions X or Y (dots are columns, lines depict beams). Look into aspects of symmetry, redundancy and bi-directional stiffness and ductility.
Solution:
Symmetry
In X-direction: It is symmetrical in x-direction, the columns and beams placed are symmetric to each other
In Y-direction: The building is symmetrical in y-direction too, the columns beams placed are symmetric to each other.
The distribution of mass and stiffness across the plan has good symmetrical aspects.
This tends to reduce the horizontal displacements in the two horizontal directions.
Redundancy:
In X-direction, the columns at top and bottom are less comparetively, whereas at the center they are more and placed symmetrically. So the redundancy will be less at top and bottom.
In Y-direction, the columns are lesser than x-direction. The mass and stiffness carried by y-directional columns will be more than x-directional columns. The building is also redundant in y-direction but less redundant than x-direction.
As the columns are missing at top and bottom in X-direction and also at left and right in Y-direction. This causes the uneven distribution of earthquake action effects in non linear range across the plan.
The energy dissipation across the structure is very low which results in non -reliable structure.
Bi-directional Stiffness:
In X-direction, the columns are connected with beams in continuous manner without any missing beam in between. So the seismic force in x-direction distributes and passes from left to right without any deviation. So less possibility of force diversion in x-direction.
In Y-direction, we can see that all the columns are not connected with beam in continuous manner. For some of the columns no beam is connected. So the lateral force from south of building will get tranfered to east and west beams to reach next bay ( as there is no beam connected in y-direction). The resistance and stiffness in y-direction is less compared to x-direction.This results in force diversion in y-direction. It can be concluded that the builsing is weak in Y-direction with respect to bi-directional stiffness.
Ductility:
Ductility is inversely proportional to stiffness. In X-direction, the mass distribution and stiffness is more compared to Y-direction. The force passes and distributes within beams and columns in X-direction whereas in Y-direction due to discontinuous connected beams, there would be force diversion.The building may not be able resist the elastic earthquake forces in Y-direction.So it may result in inelastic Response. The reduction in design force in the shorter direction (Y-axis) is to be compensated by Ductility.
This implies structure is more ductile in Y-directiont than in X-direction
Question 2:
What are the possible sources of irregularity in the building shown here? Explain how, as an engineer, each of these irregularities should be dealt with.
Solution:
Possible sources of irregularity in the building
Soft storey: There is an opening in sixth floor. There are no partition walls are constructed and left the 6th floor as an opening with no occupancy. This will lead to plastic hinge formation at the columns and failure of the structure
Vertical ireegularity: There is no symmetry in Y-direction. The plan area is large in bottom stories compared to the top floors. The floor area got reduced with the increase in levels. The distribution of mass and stiffness across the plan is not symmetric and may result in horizontal displacements due to lateral forces
Slope: A slope base is present on one side of the building. This also leads to variations in the stiffness and building may be subjected to soft storey mechanism.
The process to deal with irregularities
One should follow the guidelines of code IS:1893-2016 when constructing a building with the irregularities.
For soft storey, it is given in figure 4A of code about stiffness irregularity
For vertical irregulartity, one can refer table-6 and follow the limitations
For slope base, follow the figure 5E to check on construction of storeys at different slope and base
Question 3:
A 4-storey hotel building has an open ground floor for the restaurant. Story 2 to 4 have one row of rooms along each long side in plan, separated by a corridor. The two short sides of the perimeter are fully in-filled in all storeys, except for certain openings at the ends of the corridor at storeys 2 to 4 and along the right-hand side of the ground floor. There is a staircase near the upper left-hand corner, with straight flights between landings at floor levels and in-between floors. Cross-section dimensions are written next to the member no. in meters.
Comment on the features of the structural design and of the layout of infills which are important for earthquake resistance and seismic performance. How do they relate to the almost full collapse of this building (the extreme left-hand bay with the staircase survived, as well as one long-side façade in the rear end, and the frame along the right-hand side in plan).
Reasons for collapse of building
1. Open ground floor: It is given that building has an open ground floor for the restaurant. This resulted in soft storey mechanism and collapse of building
2. Rooms from storey 2 to 4 separated by an open corridor: It is given that story 2 to 4 have one row of rooms along each long side in plan and separated by a corridor. Mass ireegularity comes into picture here. The bays filled with rooms have higher mass than the middle bay which is left open for corridor. Due to mass irregularity it results in horizontal displacements.
3. Two short sides covered with infill walls: It is also given that the two short sides of the perimeter are fully in-filled in all storeys. It implies the left and right sides of building are more stiffer compared to the remaining portion of building during seismic force. This also results in stiffness irregularity and also cause shear which would lead to collapse..
4. Staircase portion: Staircase and lift portions have concentrated contrete elements and are stiffer than other parts. As it has more stiffness compared to all other parts in the building, so it has survived from collapse.
5. No framing along y-direction: No structural beams are provided in the vertical direction for columns. The force that needs to be transfered in y-direction is only transfered through the left and right most beams which keeps building more at risk during north south seismic force.
6. Beams connected along X-direction: The columns have longer dimension in Y-direction. They are stiffer along y-direction, but beams are connected along x-direction. In x-direction beams attract lesser lateral forces and hardly transfers it in case of seismic force. So it is hard for the building to restrain the seismic force in any direction due to no framing along y-direction and due to longer dimension of columns in Y-direction with beams connected along x-direction.
7. Variation in column sizes: Columns have different sizes in the building. The internal columns have higher sizes than the exterior columns. This will lead to significant difference in lateral drift of columns. So the concrete floor might have suffered heavy out-of-plane shear which would led to collapse.