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.

Answer:

Step 1:

Restraint Floor Shrinkage:

• Restrained shrinkage cracking occurs when concrete is prevented from making volumetric changes by a source of restraint.

Observation:

a) Full restraints at all corners

b) Corners are left free but restraints along the edge

c) Non uniform restraints

Conclusons:

a) Will have heigher restraint to shrinkage, thus lead to cracks in the floor.

b) This is average condition

c) Will not effectively restrain the shrinkage, so possibly less cracks.

Step 2:

The Lateral Stiffness:

• To apply the lateral force on a subject body, and if the body resistes lateral deflection, it is called lateral stiffness.

Observations:

a) Comparatively Lower lateral stiffness in both X and Y axis.

b) Uniform and comparetively higher lateral stiffness in both X and Y axis.

c) Non uniform lateral stiffness in both Xand Y axis.

Conclusions:

a) Lower Lateral Stiffness

b) Will provide higher lateral stiffness for a pure seismic acceleration in X and Y axis.

c) Non uniform lateral stiffness.

Step 3:

Torsion with respect to vertical axis:

• Torsional deflection is the inverse of torsional stiffness and is defined by deflection per unit torque.

Observations:

a) Corner walls provide more resistance

b) Edge walls provide good resistance to twist

c) Irregular Walls provide very poor resistance

Conclusions:

a) Will be best option with respect to Torsional resistance

b) will be good reistance

c) is the worst one

Step 4:

Vertical reinforcement for similar base capacity:

• The torsional moment are high near the corner therefore, torsional reinforcement is essential to prevent corner slab from lifting and prevents cracks.

Observations:

a) Walls are subject to nominal flexural moment and heavy twisting moment

b) Walls are subject to nominal twistin moment

c) Walls are subject to heavy flexural moment and twisting moment

Conclusion:

a) Will require average

b) Will require least

c) Will require higher vertical reinforcement

Step 5:

Static Eccentricity:

• The distance between the center of mass (CM) and the center of rigidity (CR) for a considered floor is called static eccentricity.

Observations:

a) Strucually symmetric

b) Strucually symmetric

c) Un symmetric

Conclusions:

Option c only have static eccentricity and it is significant

Step 6:

Systems's Redundancy:

• Any statically indeterminate structure may be said to be redundant.

Observations:

a) Uniform placement of lateral load supports in both the axis.

b) Uniform placement of lateral load supports in both the axis.

c) Concentrated lateral loads supports in both the axes.

Conclusions:

Option (a) and (b) are more reduntant than option (c)

Step 7:

Foundation Systems:

• Part of a structural system that supports and anchors the superstructure of a building and transmits its loads directly to the earth is called Foundation.

Observations:

a) Due to L shaped walls, the geometry of fpoundation and its design will be critical.

b) Walls are in line. Easy to fix the geometry and design of foundation

c) Walls are in line and concentrated. Easy to fix geometry foundation but crictical to design.

Conclusions:

a) It is recommended to have peripheral box foundation

b & c) Shall be incorporated with isolated footings or Strip footings.

Step 8:

Architectural Constraints:

Observations:

a) Walls abstruct only corners

b) Walls obstruct the faces of building

c) vertical will not allow passage

Conclusions:

a) It is the preffered one.

b) It is subjected to discussion

c) It is 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.

Answer:

i) Observations:

• Indirect Lateral load Transfer in X and Y direcrions.
• Incomplete lateral load transfer in X- direction
• Improper lateral load transfer in Y- Direction
• Eccentricity: Tortional influence during x and y are variation direction of excitation
• Strong and weak column is possible in given plan

ii) Explanation:

• It will not withstand when subjected to the effect of earthquake due to incomplete load transfer path of the structure in both X and Y direction.
• The columns and beams are not placed in grid patterns.
• The beam to beam connection is irregular(B5 and B6,B3 and B4)

iii) Conclusion:

• All the columns and beams are designed in by a grid pattern which exerts better resistance for lateral force.

iv) Result: Alternative Design of this given plan

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.

Answer:

Observations:

i) Floor Plan:

• The floor plan of building is not either uniform or symmetric. So naturally any lateral load induced in the floor will not have 100 % influence in same direction.
• Definitely a special lateral load resisting system for these torsional moments should be accommodated.

ii) Random Internal Columns:

• Since internal remdom columns are, they are unable to transfer lateral loads efficiency and can not achieve desireable loads in building responce.

iii) Floor to floor variation in parition walls and beams:

• Partion walls provide an important mass control in a building beams play key role in shear transfer form floor to beam.

Conclusions:

• 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 than the right side. So corner shear wall on the left side should be heavier than the right side.
• Corner shear walls shall preferably be supported over a box foundation.
• The internal columns shall be supported by isolated footings.

Result:

Proposed Footing plan ( Isolated footing)