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.

AIM: To comment on different criteria on the building shown having the same total cross-sectional area of the shear walls in three alternative arrangements.

1) The restraint of floor shrinkage:

• In plan A, there is full restraint at all corners this leads to higher restraint to shrinkage, thus leading to cracks in the floor
• In plan B, Corners are left free but restraints along the edge lead to average cracks
• In plan C, Non-uniform restraints will not be effectively restraints so possibly less crack

2) The lateral stiffness:

• Plan A comparatively has lower lateral stiffness in both X & Y
• Plan B is uniform and comparatively provides higher lateral stiffness for a pure seismic acceleration in both X & Y directions
• Plan C non-uniform lateral stiffness in both X & Y

3) Torsion with respect to verticle axis:

• In Plan A, corner walls provide more resistance to twist and it is the best option with respect to torsional resistance
• In plan B, Edge walls provide good resistance to twist but not much as in Plan A
• In plan C, Irregular walls provide very poor resistance to twisting and it is worst than plan A & B

4) The verticle reinforcement for similar base capacity:

• In Plan A, walls are subjected to nominal flexural moment and heavy twisting moment and require less verticle reinforcement than in Plan C and more than in Plan B
• In Plan B, walls are subjected to nominal twisting moment and require least verticle reinforcement than Plan A & C
• In plan C, walls are subjected to heavy flexural moment and twisting moment and require higher verticle reinforcement than in Plan A & B

5) Static eccentricity:

• Plan A is Structurally symmetric and has no static eccentricity
• Plan B is structurally Symmetric and has no static eccentricity
• Plan C is structurally Unsymmetric and has a static eccentricity

6) System's redundancy:

• In Plan A, the Uniform placement of lateral load supports in both the axis is more redundant than in Plan C
• In plan B, the Uniform placement of lateral load supports in both the axis is more redundant than in Plan C
• In plan C, Concentrated lateral load supports both the axis and has low redundancy than in plan A & B

7) Foundation systems:

• In plan A, the geometry of the walls is 'L' shaped and the foundation is critical so box type foundation is preferred
• In plan B, the walls are in line and the strip-type foundation is preferable
• In plan C, the walls are in line and concentrated, a strip / isolated foundation is preferable

8) Architectural constraints:

• In Plan - A walls obstruct only corners and it is preferred over plan B & C
• In plan - B walls obstruct the face of the buildings
• In plan - C walls especially the bigger wall will not allow the passage and are not be accepted 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.

AIM: To suggest an alternative option to the shown structural framing of the three-storey building for earthquake resistance and also to check for torsional flexibility.

A) DIFFICULTY OF LATERAL LOAD TRANSFER IN X & Y DIRECTIONS:

• In X-direction the C5 column size or position is not effective in terms of seismic load transfer, C8 column is not effective in seismic load transfer.
• In Y-direction in between C5 & C6, there is no column is provided in that junction so while seismic load transfer in Y-direction that particular junction is prone to failure or collapse.

B) STRONG BEAM WEAK COLUMN POSSIBILITY:

• All the beams have a size of 25cmX50cm but the size of columns is 25cm X25cm so the beams have deeper sections (50cm).
• so that the columns require higher reinforcement than the beam but due to the size constrain in the column we cannot achieve more reinforcement in the column than the beam.
• We can clearly observe that a strong beam weak column in the given structural framing

C) TORSIONAL FLEXIBILITY:

• The longer the distance between the centre of mass and centre of stiffness, the higher the torsional moment (torsional flexibility) of the building as per the given plan the centre of mass and centre of stiffens is not coinciding, the building is subjected to higher torsional flexibility in both X&Y directions.

D) ALTERNATIVE STRUCTURAL FRAMING:

• 

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.

AIM: To justify the choice of the lateral load resisting system and its foundation of the given plan.

A) 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 defiantly a special lateral load resisting system for these torsional moments should be accommodated.
• The red lines in the plan show extension for the symmetry of the plan.

B) RANDOM INTERVAL COLUMNS:

• Since the internal columns are random, they are unable to transfer lateral loads efficiently and can not achieve a desirable building response. So we have to assume and design these columns for only gravity loads.

C) FLOOR TO FLOOR VARIATIONS IN PARTITION WALLS AND BEAMS:

• Partition walls provide an important mass control in 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.

D) SUGGESTIONS ON THE LATERAL LOAD SYSTEMS & IT'S FOUNDATIONS:

• Heavy torsional forces should be controlled by the respective lateral load systems. So "corner shear walls" are suggested.
• The partition of the floor area is greater on the left side than on the right-side [irregular quadrilateral]. So corner shear walls on the left side is should be heavier.
• 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 those isolated footings can be connected with shear walls through tie beams.