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: We have to compare all the three alternatives given in the question by taking the restraint of floors, linkage, the little stiffness and that original 1. With respect to vertical axis and vertical reinforcement required for the same total flexural capacity at the base., the static eccentricity, the systems redundancy, foundation systems and architectural constraints.

Objective:

The criteria is given in the question. We have to conclude the observation and conclusion from the figures.

Explanation:

Restraint of floor shrinkage	Observation	Full restraint at all corner, means highly resistance to shrink	Corners are left free but restraints along the edge	Non- uniform restraints
Conclusion Option (a) will have higher restraint to shrinkage, thus lead to cracks in the floor. Option (b) is average. Option (c) will not effectively restrain the shrinkage, so possibly less crack
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 Option B will provide higher lateral stiffness for a pure seismic acceleration in X and Y direction
Torsion with respect to vertical axis	Observation	Corner walls provide more resistance to twist	Edge walls provide good resistance to twist	Irregular walls provide very poor resistance to twist
Conclusion Option(a) will be best option with respect to torsional resistance whereas option(c) is 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 moment and twisting moment
Conclusion Option(c) will require higher vertical reinforcement and option(b) will require the least
Static eccentricity	Observation	Structurally symmetric	Structurally symmetric	Un-symmetric
Conclusion Only option (c) will have static eccentricity and it is significant
Systems redundancy	Observation	Uniform placement of lateral load supports in the axes	Uniform placement of lateral load supports in both the axes	Concentrated lateral load supports in both the axes
Conclusion Option(a) and (b) are more redundant than option(c)
Foundation system	Observation	Due to ‘L’ shaped walls the geometric foundation and its design will be critical	Walls are in line. Easy to fix the geometric and design of foundation	Walls are in line and concentrated. Easy to fix the geometry of foundation but critical in design
Conclusion Option(b) and option(c) shall be incorporated with the isolated footings/strip footings. Option(a) is recommended to have peripheral box foundation.
Architectural constraints	Observation	Walls obstruct only corners	Walls obstruct the faces of building	Vertical wall will not allow passage
Conclusion Architecturally speaking, option(a) is the preferred one. Option(b) is subjected to discussion. Option(c) 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.

Aim:

To understand the suitability for earthquake resistance of the moment resisting framing plan of a three-storey building, the eccentricity of the centre of mass to centre of stiffness.

Given in the question:

And the beam sizes are given. Column sizes are given. And column locations. Be managements that is a 1.7 metre cantilever slab also given there and there is a different some longer column

Issues present in the framing plan:-

Indirect lateral load transfer in X and Y directions.

The beams are connecting to another beams which is ineffective during lateral load transfer in such conditions. The main beam will be subjected to heavy shear force from t the secondary beam, so the primary beam is prone to shear failure. As we see here right directional beam is not connected to the column directly, it is connecting to another beam. So this beam will transfer the load to this one and ultimately just think about lateral loading condition. the entire lateral load. As a shear, it will transfer to this main B model. So this main beam will be subjected to shear failure.

Issues in the framing plan:

1. Eccentricity:

As already mentioned in the question itself, the difference between centre of mass and centre of stiffness, the higher torsional moment of the building. the longer the distance between the centre of mass and centre of stiffness, the higher torsional moment of the building it generates eccentricity in both X and Y direction.

2. Strong and weak column possibility.

As mentioned the size of column is (25cm X 25cm) Initial of beam is visually higher, the size of the beam is higher. The depth of the beam is higher actually. So the initial second moment of inertia of the beam will definitely be higher than that of column. It is recommended to have slight bigger sizes for column because if the beams are so stronger than columns then the strong beam weak column for mechanism will take place and the column will collapse first. This is completely prohibited in terms of lateral building failure.

3. Alternate scheme for the plan:

For avoiding the failure we have to change the positioning of the columns and size of the columns and beams.

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:

Observation from the Image

Floor plan-

The floor plan of the building is not either uniform for symmetric. So naturally, any lateral load induced in the floor will not have 100 % influence in the same direction. 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 cannot achieve desirable building response. We have to assume and design those columns for gravity loads.

Floor to floor variations in partition walls and beams-

Partition walls provide an important mass control in a building and beams play key role in shear transfer from floor to beam. All these elements are not in order. Heavy distortion and distribution of lateral loads will happen.

Suggestions:

• Heavy torsional forces should be controlled by respective lateral load system, so corner shear walls are suggested.
• The proportion of floor area is greater on the left side then that right side. (Irregular quadrilateral). so, corner shear walls on the left side should be heavier than the right.
• Corner shear walls shall preferable be supported over a box foundation. Shear walls should be connected by link beams to transfer shares from one to other.
• The internal columns shall be supported by Isolated footings. Those isolated footing can be connected with shear walls through tie beams.