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.

ARRANGEMENT(a) ARRANGEMENT(b) ARRANGEMENT(c)

ANSWERS:-

1.RESTRAINT OF FLOOR SHRINKAGE

• ARRANGEMENT(a):-

Shear walls are placed symmetrically at the four corners of the layout.This type of wall system has good restraint against floor shrinkage as all the corners of the floor is restricted to experience shortening.

• ARRANGEMENT(b):-

In this arrangement the shear walls are placed at four edges of the layout in both directions symetrically.Therefore this type of system has good restriction against floor shrinkage at edges only.Also the corner points are subjected to shrinkagea as there is no walls are present there.

• ARRANGEMENT(c):-

Here in this arrangement the reinforcement walls have no symmentrical enclosure and therefore it will have greater effects of shrinkage.

2.lateral stiffness

• ARRANGEMENT(a):-

This arrangement is not favorable earthquake movements because it has poor stiffness.During earth quake excitations edges or principle planes are exposed to deformations or failure.Here all the wall systems are present at the corner portions and no edges of floor system has no supports and therefore less stable.

• ARRANGEMENT(b):-

Here the arrangements have shear walls in the principle plane direction and there for it possess better lateral stiffness compared to the other arrangements.Because Principle plane or edges are more exposed to earth qauke excitations.Also all the walls are of same cross sections enhances the stiffness of the arrangement.

• ARRANGEMENT(c):-

Arrangement have two symetrically placed walls in X direction and only one shear walls in Y direction with a different cross section from the other one.Hence leads to an enhanced stiffness condition in X direction and less stiffness condition in Y direction which will ulitimately concentrates all the seismic loads in that single wall in Y direction causes instability.

3.Tortional Stiffness with respect to vertical axis.

• ARRANGEMENT(a):-

It is clear that all the walls are placed symetrically in all the four corners of the layout, there is no chance of creating eccentricity as the centre of mass and centre of stiffness coincides.This is a case of torsionally stiff model.Hence less vulnerable to torsion.

• ARRANGEMENT(b):-

This arrangement is also a case of symmetrically placed wall systems at all the four edges of the floor.Therefor no chance of creating eccentricity as the centre of mass and centre of stiffness coincides.This is a case of torsionally stiff model.Hence less vulnerable to torsion.

• ARRANGEMENT(c):-

Assymetrically placed shear wall system will leads to create eccentricity as the centre of mass and centre of stiffness do not coincide eacch other.Because there is 2 shear walls are placed in the X direction and only one wall is placed in the Y direction.This wiill lead to the create more torsion during earth qauke.

4.Vertical Rebar at the base:-

• ARRANGEMENT(a):-

The shear walls are not placed in the principal plane direction,instead they are placed at the corners of the model.Walls at corners do not take part much in the resistance of taking the lateral forces and therefore the quanitity of reinforcement required would be lesser than that of other parts.

• ARRANGEMENT(b):-

The shear walls are placed in both the principal plane, so this arrangement will resist greater lateral force and the requires more lateral strength.So quantity of reinforcement taken for the design of these walls should be greater.

• ARRANGEMENT(c):-

The wall arrangement in this case are designed in an asymetrical way.Large amount of lateral forces are taken by the wall at left end because there is only one wall is present in that direction.Hence large quanitity of reinforcement is required to resistance the lateral force.

5.The static eccentricity:-

• ARRANGEMENT(a):-

The shear walls are symmetrically placed at the corners, the centre of mass and centre of stiffness coincides and there is no chance for eccentricity.

• ARRANGEMENT(b):-

In this arrangement, as the shear walls are symmetrically placed along the edges, the centre of mass and centre of stiffness coincides and there is no eccentricity.

• ARRANGEMENT(c):-

In this situatuion the shear walls are symmetrically placed along one of the principal direction, but in the y direction there is only one shear wall at the left edge with a larger cross section compared to other two shear walls. Hence, the centre of stiffness shifts to the left side and there occurs eccentricty in the model.

6.System’s redundancy:-

• ARRANGEMENT(a):-

The shear walls at corners of the model does not actively take large amount of lateral force and therefor the other parts are needed to take large lateral forces.Hence this arrangement is less reduntant.

• ARRANGEMENT(b):-

The symetrically arranged shear walls at the mid portion of the edges will share the forces eqaully in both the direction.Hence this arrangement is less reduntant.

• ARRANGEMENT(c):-

Assymetrical arrangement of the shear walls in Y direction will leads to concentrate large loads at the left edge.Hence it is a situation of poor redundancy.

7.Foundation systems:-

• ARRANGEMENT(a):-

Isolated footing with a tie beam of appropriate dimension can be provided as foundation at all the 4 corners.

• ARRANGEMENT(b):-

Raft or box type of foundations are advisable as the shear walls are placed along all the 4 edges.

• ARRANGEMENT(c):-

Strip footing for walls in the x direction and isolated footing or combined footing for Y direction walls.

8.Architectural constraints:-

• ARRANGEMENT(a):-

The four walls at the corners of the floor blends or appeal with architectural design. As it does not causes any clash with any architectural components.

• ARRANGEMENT(b):-

In this arrangement the shear walls may clash with the architecural components as openings are not advisable in shear walls.

• ARRANGEMENT(c):-

Here the two walls at the right end along the x direction and they appeal with the architectural model and the wall the left edge in the Y direction may clash with the architectural design.

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.

ANSWERS:-

OBSERVATION:-

1. Beam element B3 has been attached to only one vertical member at left end.
2. Beam element B6 has been attached to only one vertical member at right end.
3. Beam element B7 has been attached to only one vertical member at the top.
4. Hence there is complexity in load transfer at these 3 positions.
5. The columns and beams are not placed in grid positions infact they are offseted from their path due to which load does not transfer effectively.
6. Proper symmetry is not achieved.
7. Beams are found to be stronger than the column elements will leads to the weak column strong beam condition.

ALTERNATIVE

• Rearrange the columns in such a way that each horizontal members are supported with two vertical members at both ends.
• All the beams and columns should be placed in the form of grid pattern.
• Providing shear walls at suitable places provide better resistance in taking lateral forces.

(ALTERNATIVE PLAN)

Torsional flexibility

• Here in the structural frame has a two way eccentrecity with the centre of mass in relation to the centre of stiffness, with the eccentricity of the X direction is greater than the eccentricity of Y direction.
• Hence the centre of mass does not coincide with the centre of stiffness leads to the experiance toryion in the vertical axis.

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.

Observations:-

• Non uniform floor system layout.
• Assymetrically placed columnn sections.
• Columns and beams are not placed as per grid pattern.
• Here the centre of mass lies towards left portion of the layout as the area over there is larger than the right part and leads to torsional irregularity.

⇒ Since the irregular quadrilateral layout concentrates the centre of mass of the system towards the left as the area is larger there.So we have to provide laeteral resisting system in such a way that the centre of stiffness should come near the centre of mass in order to avoid the torsional irregularities.Also when the seismic forces occur the movements in both directions will affect both the directions of layout.

• L shaped shear walls can be provided at each corner which acquires the bi directional strength for the structure when lateral forces occur.
• Torsional rigidity can also be reduced by providing shear wallss.
• For this type of shear wall arrangement,a box type foundations can act together.