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:

Criteria		A	B	C
Restraint of Floor Shrinkage	Observation	Full Restrains at all the corners.	Corners are left free but restrained along the edge.	Non-uniform restraints.
	Conclusion	Will have high higher restraint to shrinkage, thus leading to cracks in the floor.	Average.	Will not effectively restrain the shrinkage, So possibly fewer cracks.
The Lateral stiffness	Observation	Comparatively lower lateral stiffness in both X and Y.	Uniform and comparatively higher lateral stiffness in both X and Y.	Non-uniform lateral stiffness in both X and Y.
	Conclusion		Will provide higher lateral stiffness for a pure seismic acceleration in X and Y directions.
Torsion with respect to the vertical axis	Observation	Corner walls provide more resistance to twisting.	Edge walls provide good resistance to twists.	Irregular walls provide very poor resistance to twists.
	Conclusion	Will be the best option with respect to torsion resistance.		Is the worst one.
Vertical reinforcement for similar base capacity	Observation	Walls are subjected to nominal flexural moment and heavy twisting moment.	Walls are subjected to nominal twisting moment.	Walls are subjected to heavy flexural moments and twisting moments.
	Conclusion		Will require higher vertical reinforcement	Will require the least.
Statis eccentricity	Observation	Structural Symmetric.	Structural Symmetric.	Un-symmetric.
	Conclusion			Will have static eccentricity and significance.
System's redundancy	Observation	Uniform placement of lateral load supports in both axes.	Uniform placement of lateral load supports in both axes.	Concentrated lateral load supports in both axes.
	Conclusion	More redundant	More redundant	Lesser than options A and B
Foundation systems	Observation	Due to 'L' shaped walls, the geometry of the foundation and its design will be critical.	The walls are in the line. Easy to fix the geometry and design of the foundation.	The walls are in line and concentrated. Easy to fix the geometry of the foundation but it is critical in design.
	Conclusion	Recommended to have a peripheral box foundation.	Shall be incorporated with isolated footings/strip footings.	Shall be incorporated with isolated footings/strip footings.
Architectural constraints	Observation	Walls obstruct only corners.	Walls obstruct the faces of a building.	A vertical wall will not allow passage.
	Conclusion	Architecturally speaking, this is the preferred one.	Architecturally speaking, this is subjected to discussion.	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 the 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:

Indirect lateral load transfer in X and Y directions:- The beams are connecting to another beam which is ineffective during lateral load transfer. The main beam will be subjected to heavy shear force from the secondary beam which leads to shear failure. In such conditions, the primary beam is prone to shear failure.

Incomplete lateral load transfer in the X-Direction:

Incomplete lateral load transfer in the Y-Direction:

Eccentricity:- The longer the distance between the centre of mass and the centre of stiffness, the higher the 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.

TORSIONAL INFLUENCE DURING X-DIRECTION EXCITATION.

TORSIONAL INFLUENCE DURING Y-DIRECTION EXCITATION.

Strong beam weak column possibility:- The size of the columns is majorly mentioned as 25 cm x 25 cm. But all the beams have much deeper sections (50cm). The inertia of the beam is visually higher than a column. If the column reinforcement is adequately greater than the beams, we are okay and since we do not have the reinforcement details, this is doubtful. It is recommended to have slightly bigger sizes columns.

BEAM SIZE: 25cm X 50cm

COLUMN SIZE: 25cm X 25cm

Alternative Scheme:

Question 3:

A multi-storey building with a basement, with a quadrilateral (non-symmetrical floor plan), plan as, has interior columns in an irregular (not in a grid) pattern in a plan that serves architectural and functional considerations. Partition walls and interior beams supporting the slab have a 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:

Floor plan:- The floor plan of the building is not either 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 moments should be accommodated.

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

Floor-to-floor variations in Partition walls and Beams:- Partition walls provide important mass control in a building and beams play a 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 the respective lateral load system. So 'Corner shear walls' are suggested.
  
  
• The proportion of floor area is greater on the left side than on 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 another.
  
  
• 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:

Superstructure

Sub-Structure