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.

Criteria		Option a		Option b	Option c
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.

Issue in the given framing plan:

Indirect lateral load transfer in X&Y directions-

In X&Y direction, the main beam will be subjected to heavy shear force from the secondary beam, so the primary beam is prone to shear failure. We can see in picture the horizontal and vertical beam is not connected to the column directly, the beams are connecting to another beams which is ineffective during lateral load transfer. This beam will transfer the Load to secondary beam.

Eccentricity-

the difference between centre of mass and centre of stiffness as the issues in both X & Y directions. In X direction also they have eccentricity and in Y direction also they have eccentricity. So, the longer the distance between the centre of mass and centre of stiffness, the higher torsional moment of the building it generates eccentricity.

Strong Beam weak Column Possibility-

The depth of the beam is higher. The moment of inertia of the beam will definitely be higher than that of column because the size of columns majorly mentioned as 25cm x 25cm. but all the beams have much deeper section (50cm). Inertia of beam is visually higher. If the column reinforcement is adequately greater than that of beams, we are okay. But we don’t have the reinforcement detail, this is doubtful. it is recommended to have slight bigger sizes for column. Because if the beams are so stronger than columns, then strong beam weak column mechanism will take place and column will collapse first. This is completely prohibited. In terms of lateral building failure.

Alternate Scheme/Revised Framing Plan-

Advised to change and we have to avoid the connection of beams with the other one. the beam should be supported over columns only. We have to shift the column to be in line

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.

Observation

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.

Propose schematic plan of lateral load system-

    

Super structure                                                                                                             sub-structure