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. (i) Restraint of floor shrinkage: (a) Arrangement a:

. As we can see at the above given image,we can see there are 4 shear walls which are provided at the corners of the wall. So because of the positioning of the shear wall which is placed at the edges of each wall,it means that they offer strong resistance to the floor shrinkage. Which means that the floor will be tightly held at the place because of the shear walls that are positioned at the corner. And the shrinkage will be controlled.

(b) Arrangement b:

. As we can see at the above given image, the shear walls are positioned at the centre of the wall on all the four sides. Which means that it has better stability to floors that are near to the floors.But the shrinkage can occur at the corner of the walls,because at the corners there are no shear wall placed as we can see at the above given image.

(c) Arrangement c:

. As we can see at the above given image,the shear wall that can be seen in the above image are not symmetrically arranged. It is arranged assymmetrically along the given walls. And it is not in a complete shape as we can see at the above image.  So the shear walls are positioned assymetrically and arranged in an orderless manner,we can say that there is high chances of shrinkage of the floor.

CONCLUSION:  After the above discussion we can conclude that arrangement a will have higher restraint to the shrinkage which may leads to the cracks in the floor. Arrangement b is considered to be an average option. But the arrangement c is not restraint to the shrinkage which means it may not cause craks to the floor.

(ii) The Lateral Stiffness: (a) Arrangement a:

. As we can see at the above given image,the shear walls are positioned only at the corners of the walls. So when there is a possibility of earthquake,the seismic forces will tends to acts along the edges of the floors. Which means that the walls where the shear walls are positioned at the corners of the walls only,will have low lateral stiffness and low have low stability also.

(b) Arrangement b:

.As we can see at the above given image,the shear walls positioned along the edges will have better stability and have better lateral stiffness along both the principal planes i.e, X-Y directions, and this is because of the positioning of the shear walls.

(c) Arrangement c:

.As we can see at the above given image,there are two shear walls in the X-direction but there is only one shear wall in the Y-direction.  Which means that this shear wall will increase the lateral stiffness in the X-direction. And the shear wall in the Y-direction,it will only concentrate earthquake forces in that wall where there is only one shear wall i.e, in the Y-direction.

CONCLUSION: After the above discussion we can conclude that the arrangement b will provide high lateral stiffness other than the arrangement a and arrangement c.

(iii) Vertical Reinforcement at the base: (a) Arrangement a: As we can see at the above given image, these shear walls are positioned at the corners of the walls. So because of the positioning of shear walls,there are very little role of the lateral force resistance. Which means these walls will not required huge amount of reinforcement, less reinforcement is required.

(b) Arrangement b: As we can see in the above image the shear walls are positioned along the main directions. Which means they absorb a good amount of lateral forces. Because of this, more reinforcement should be added to these walls in order to withstand the lateral forces.

(c) Arrangement c: As we can see at the above given image,we can say that the shear walls are not in symmetric order. They are asymmetrically arranged in the above given image. So it means these shear walls will take up some or significant amount of lateral forces. We can see that the left side of the room will take up a significant amount of lateral forces. Therefore, these walls must be heavily reinforced in order to prevent the significant amount of lateral forces.

CONCLUSION: After the above discussion we can conclude that the arrangement c will require high vertical reinforcement. Arrangement b will require the least reinforcement than the arrangement c.

(iv) Static eccentricity: (a) Arrangement a: As we can see at the above given image there is no eccentricity because the positioning of the shear walls.  As the shear walls are positioned at the corner of the walls and they are symmetric in nature it means there is no eccentricity . But the center of mass end the stiffness both of them coincides in this above given plan.

(b) Arrangement b: As we can see at the above given image there is no eccentricity because the positioning of the shear walls. As the shear walls are positioned at the corner of the walls and they are symmetric in nature it means there is no eccentricity. But the center of mass end the stiffness both of them coincides in this above given plan.

(c) Arrangement c: As we can see at the above giving image,there will be an eccentricity in the arrangement. Because as we can see that the positioning of the shear wall at the left side of the plan or layout,there is only one shear wall along that side with a larger mass as compared to the other two walls in the Y-direction. As a result the centre of stiffness will shift towards the left side of the shear wall.

CONCLUSION: After the above discussion we can conclude that the arrangement c will have higher static eccentricity other the arrangement a and arrangement b.

(v) Foundation system: (a) Arrangement a: As we can see at the above given image,the shear walls are placed at the corner of the walls. Therefore, we can provide an isolated footing with a tie beam which can be used as a foundation.

(b) Arrangement b: In this layout we can use a raft foundation or box foundation.

(c) Arrangement c: As we can see at the above given image, we can conclude that this type of layout will have strip footing. It is best if we provide this strip footing for the walls in the X-direction and an isolated footing or a combined footing in the Y-direction walls.

CONCLUSION: After the above discussion arrangement b and arrangement c should be provided with isolated and strip footing. And arrangement a is recommended to have a box foundation.

(vi) Architectural constraints: (a) Arrangement a: As we can see at the above given image, the walls are symmetrically arranged end arrange in an order. Therefore these walls blends well with the architectural design. These walls does not cause any clashes with any architectural components because they are arranged in a very systematic manner.

(b) Arrangement b: As we can see at the above given image, we can say that these walls are not in symmetric manner or we can say that these walls are irregularly arranged so because of this,these walls may clash with the other architectural components as opening. Because we knew that any openings in these walls are not advisable.

(c) Arrangement c: As we can see at the above given image, that there are two walls at the right side. In these two walls blends well with the other architectural components. As we can see that there there is only one wall at the left side in the Y-directions so these walls may clash with the architectural design.

CONCLUSION: After the above discussion we can conclude that the arrangement a is the most preferrable one other than the arrangement b and c. But we can say that the arrangement c can not be accepted either architecturally nor commercially.

(vii) System's redundancy: (a) Arrangement a: As we can see at the above given image,the shear walls that are positioned at the corner of the walls does not take large amount of lateral force,so because of this the other parts of this plan needs to take the good amount of lateral force. That's why we can say that this structure is less redundant.

(b) Arrangement b: As we can see at the above given image, the shear walls are arranged at the mid-portion of the walls, this means they experience the forces in equal amount in both the direction. So that is why this structure is less redundant.

(c) Arrangement c: As we can see at the above given image. The shear walls are positioned asymmetrically in the Y-direction, which means Y-direction will leads to concentrate large amount of loads at the left side of the layout. So because of this layout it has poor redundancy because of the asymmetrical arrangement of the shear walls in the Y- direction.

CONCLUSION: After the above discussion we can conclude that the arrangement a and arrangement b are the most redundant than the option c.

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. From the above given floor plan following are the observations that are discussed below in detail: First point that I observe in the given plan is that the beam B6 has been attached to only one vertical member at the left hand side of the plan as we can see in the below given plan.

. There are another two beams that are not in their correct position and those beams are B7 and beam B3. As we can see in the below given plan B3 has been attached to the only one vertical member at the right end. Similarly there is another beam B7 which is attached to only one vertical member at the top of the right hand side of the plan as we can see in the below given image.

. Hence there will be difficulty in transferring the loads at these three points as shown in the below figure:

. In the above given plan we can observe that the beams are stronger than the column elements and this will arise a problem of the weak column and strong beam conditions. Below is the image of the plan,in that plan we can clearly understand the concept of strong beam and weak column conditions:

.So because of the strong beam and the weak column there is a possiblity that,when the lateral forces operates around the structure,then we need a shear wall in order to prevent it from the column failure. We can say that the combination of the shear wall and the column keeps the structure from collapsing due to the seismic force acting on the building. As we look see at the given plan we can say that there is no proper symmetry in the plan. The plan is asymmetrical in nature. And this structural frame has a two way eccentricity of the centre of the mass in relation to the centre of the stiffness. We can say that the eccentricity of the X-direction is greater than the eccentricity of the Y-direction.  The connection between the column and the beams should have a proper cross section area.

CONCLUSION: First of all we can re-arrange the columns in such a way that each horizontal member of this plan supproted by both the ends. All the beams and the columns should be in grid form. So because of the strong beam and the weak column there is a possiblity that,when the lateral forces operates around the structure,then we need a shear wall in order to prevent it from the column failure. Below is the re-arranged plan of this given plan with possible corrections:

. I have arranged this plan in a systematic way so that load tranfer will be easy in the above layout. 

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: Here are the few observations that have been made after analysing the above given plan. So below here are the some observations which are made after analyzing the above given plan: First of all this layout is not at all suitable for the earthquake prone areas due to its uneven symmetry. This type of plan is not at all adviseable for the earthquake prone areas.

. Secondly the columns in this given layout is not symmetrically arranged. It is in asymmetrically arranged as we can see in the below image:

. Columns and the beams are not placed as per the grid patterns. So we can say that the centre of mass lies towars the left side of the plan because as we can see that the area at the left hand side of the layout is bigger that the area of the right hand side as we can see at the below given image:

.So as we can see that the given above layout is not at all suitable for the earthquake prone area because of its asymmetrical shape. It is quadrilateral in shaped and this shape is not suitable for the earthquake prone areas. And because of this asymmetric shape the centre of mass of the building is towards the left side of the layout because this side has larger space that the right side of the layout. So to shift the centre of stiffness little bit towards the centre of the mass of the system we need to provide the lateral resisting system in order to avoid the torsional irregularities. And we must provide L shaped shear wall at the each corner of the layout to obtain the bi-directional strength of the frame. By providing the shear walls at the edges of the walls we can also reduce the torsional rigidity. We can also provide the tie beams and the box foundation in the above given plan.