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.
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ANS-
Restraint of floor shrinkage
Observation- From figure a, it is observed that the shear wall has been placed at all four corner that means all corner is fully restraints. In figure b, corners left free and restrains along the edges whereas in figure c, the shear wall is placed none-uniformly which means it restrains non-uniformly.
Conclusion- Figure a, shows higher restraints to shrinkage which leads to cracks in the floor. Figure c will not effectively restrains to shrinkage, so possible less cracks.
The lateral stiffness
Observation- figure-a has comparatively lesser stiffness in both x and y direction. As compared to figure-a, and figure-b, the figure-c has uniform and higher stiffness in x as well as in y direction and figure-c has non uniform lateral stiffness in both direction.
Conclusion-Figure-b will provide higher lateral stiffness for a pure seismic acceleration in X and Y direction.
Torsion with respect to vertical axis
Observation – In figure-a, as the shear wall is provided in the corners, corner wall is more resistance to twist and in figure-b, the shear wall is provided in the edges of the structure which also provide more resistance to twist, but in case of figure-c, as the irregularity in the placement of the shear wall, it has poor resistance to twist.
Conclusion- Figure-a will give the best results to resist against the torsion whereas figure-c is worst condition.
Vertical reinforcement for the similar base capacity
Observation- figure-a are subject to nominal flexural moment and heavy twisting moment, figure-b is subjected to nominal twisting moment, whereas the figure-c is subjected to heavy flexural moment as well as twisting moment.
Conclusion- Figure-c will require higher vertical reinforcement and figure-b will require least vertical reinforcement.
Static eccentricity
Observation- In figure-a and figure-b, it is clearly seen that the structure is symmetric about both x and y direction, but structure in figure-c is un-symmetric.
Conclusion- structure in figure-c will have the static eccentricity and it is significant.
System redundancy
Observation- Structure in Figure-a and figure-b have uniform placement of lateral load support in both the axes, but in case of figure-c, the structure has concentrated lateral load supports in both the axes.
Conclusion- Structure in Figure-a and figure-b are more redundancy than structure in figure-c.
Foundation system
Observation- The shear wall in figure-a is L shaped, so the geometry of foundation and its design will be critical, but shear walls in figure-b are in line which is easy to fix the geometry and design of foundation. Shear walls in figure-c are in line and concentrated and easy to construct foundation, but critical in design.
Conclusion- structure in figure-b and c shall be incorporated with isolated footing and strip footing. Foundation for figure-a is recommended to have peripheral box foundation.
Architectural Constraints
Observation- Shear walls in figure-a obstruct only corners. Walls in figure-b obstruct the faces of building and shear walls in figure-c will not allow passage.
Conclusion- On architectural point of view, structure in figure-a is the preferred and structure in figure-c will not accepted both architecturally and commercially.
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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.
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ANS-
Indirect lateral load transfer in X and Y directions
The beams are connected to another i.e. secondary beams which is ineffective during lateral load transfer which cause the more shear forces on the primary beams.
The improper lateral load transfer in x and y direction have been shown below,
Strong column weak beams possibility
The size of the columns are 23cm × 25cm and beams size 25cm × 50cm which has much deeper section as compared to columns. The second moment of inertia of beam is visually higher than column. IF the columns reinforcement of columns is adequately greater than that of beams, then it is ok, but here reinforcement details has not been given, so it is doubtful. It is recommended to have slightly bigger size of the column.
Alternate scheme,
Alternate of the given plan has been suggested below,
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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.
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ANS-
Observation-
- Floor plan- From the given plan, it is clearly seen that the plan is not either uniform or symmetry. So any lateral load induced in this floor plan, the load will not transfer effectively in any direction and this will not have 100% influence in same direction. Definitely a special lateral load resisting system for these torsional moments should be accommodated.
- Location of column- Since the internal column are randomly placed, they are unable to transfer lateral loads effectively and cannot achieved desirable building response, so this is to assumed and design those columns only for gravity load.
- Floor to floor variation in partition walls and beams- Partition walls play an important roles in mass control in a building and beams play key role in shear transfer from floor to floor to beam. All the elements are not in order, so heavy distortion and distribution of lateral load will happen.
Suggestion
- As the floor plan is irregular in shape, heavy torsional forces should be controlled by respective lateral load system, so shear walls are to be provided on the corner of the floor plan.
- Because of irregular shape, some part of plan is greater that is on left side than the right side, so corner shear walls on the left side should be heavier than the right.
- For better transformation of the shear forces, the corner shear walls should be supported over the box type of foundation and the shear walls should be connected by link beams to transfer shear from one to another.
- And the internal columns shall be supported by isolated footing and those isolated footings can be connected with shear wall though the tie beams.
Proposed schematic plan of lateral load system
