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 concerning 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.
Ans:
CASE A
Restraint of floor shrinkage
observation - full restraint at all corner
Conclusion - option a will have higher restraint to shrinkage, thus leading to a crack in the floor; option B is average option C will not effectively control the shrinkage, so possibly fewer cracks
The lateral stiffness
observation - comparatively lower lateral stiffness in both X and Y
conclusion - option b will provide higher lateral stiffness for a pure seismic acceleration X and Y direction
Torsion with respective vertical axis
observation - Corners walls provide more resistance to twist
conclusion - option a will be the best option concerning torsional resistance, whereas option c is the worst one
Vertical reinforcement for similar base capacity
observation - walls are subjected to nominal flexural moment and heavy twisting moment
conclusion - only c will be required higher vertical support, and option b will be necessary the least
static eccentricity
observation structurally symmetric
conclusion - only option C has static eccentricity, and it is significant
system redundancy
observation of uniform placement of lateral load support in both the axes
conclusion option a and b are more redundant than c
foundation system
observation - Due to L shaped wall, the geometry of the foundation and its design will be critical
conclusion - option B and C will be incorporated with isolated/strip footing option a is recommended to have a peripheral box foundation
Architectural constraints
observation - walls obstruct only corners
conclusion - Architecturally speaking, option a, the preferred one, option b, is subject to discussion option c will not be accepted both architecturally and commercially
CASE B)
Restraint of floor shrinkage
observation - corners are left free but restrained along the edge
conclusion - option a will have higher control over shrinkage, thus leading to cracks in the floor; option B is average option C will not effectively restraint the shrinkage, so possibly fewer cracks
The lateral stiffness
observation - comparatively higher lateral stiffness in both X and Y
conclusion - option b will provide higher lateral stiffness for a pure seismic acceleration X and Y direction
Torsion with respective vertical axis
observation - edge walls provide good resistance to twist
conclusion - option a will be the best option concerning torsional resistance, whereas option c is the worst one
Vertical reinforcement for similar base capacity
observation - walls are subjected to nominal twisting moment
conclusion - only c will be required higher vertical support, and option b will be necessary the least
static eccentricity
observation - structurally symmetric
conclusion - only option C has static eccentricity, and it is significant
system redundancy
observation - uniform placement of lateral load support in both the axes
conclusion - option a and b are more redundant than c
foundation system
observation - walls are in line, and it is easy to fix the geometry and design of the foundation
conclusion - option B and C will be incorporated with isolated/strip footing option a is recommended to have a peripheral box foundation
Architectural constraints
observation - walls obstruct the faces of the building
conclusion - Architecturally speaking, option a, the preferred one, option b, is subject to discussion option c will not be accepted both architecturally and commercially
CASE C)
Restraint of floor shrinkage
observation - nonuniform restraints
conclusion - option a will have higher control over shrinkage, thus leading to cracks in the floor; option B is average option C will not effectively bind the shrinkage, so possibly fewer cracks
The lateral stiffness
observation - nonuniform lateral stiffness in both X and Y
conclusion - option b will provide higher lateral stiffness for a pure seismic acceleration X and Y direction
Torsion with respective vertical axis
observation - irregular walls provide feeble resistance to twist
conclusion - option a will be the best option concerning torsional resistance, whereas option c is the worst one
Vertical reinforcement for similar base capacity
observation - walls are subjected to nominal flexural moment and twisting moment
conclusion - only c will be required higher vertical support, and option b will be necessary the least
static eccentricity
observation - structurally un-symmetric
conclusion - only option C has static eccentricity, and it is significant
system redundancy
observation - concentrated lateral load support in both the axes
conclusion - option a and b are more redundant than c
foundation system
observation - walls are in line & concentrated, easy to fix the geometry of the foundation but critical in the design
conclusion - option B and C will be incorporated with isolated/strip footing option a is recommended to have a peripheral box foundation
Architectural constraints
observation - the vertical wall will not allow passage
conclusion - Architecturally speaking, option a, the preferred one, option b, is subject 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-story building depicted here (cross-sectional dimensions in cm), the eccentricity of the center of mass (as the centroid of floor plan) to the center of stiffness (from the moments of inertia of the columns) are shown. Suggest an alternative. Also, is there torsional flexibility? Are the two translational vibration modes more significant than the fundamental torsional mode? Discuss qualitatively.
Ans:
Solution:
Indirect Lateral load Transfer in X and Y direction :
The beam connects to another shaft which is ineffective during lateral load transfer. In such conditions, the primary beam is prone to shear failure.
Eccentricity
the longer the distance between the center of mass and the center of stiffness, the higher the torsional moment of the building as per the given plan eccentricity. The building is subjected to a higher torsional moment in both X and Y direrction
Intense beam Weak column possibility
The column size is 25 cm X 25cm, but all the beams have much deeper section inertia of the beam virtually higher than the column. If the column reinforcement is adequately greater than that of the shaft, we are ok, and since we do not have the reinforcement detail, this isn't very certain. It is recommended to have slightly bigger sizes for the column.
Alternate scheme
Question 3:
A multi-story building with a basement with a quadrilateral (nonsymmetrical floor plan) plan has interior columns in an irregular (not in a grid) pattern in a program that serves architectural and functional considerations. Partition walls and internal beams supporting the slab have a different layouts 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 choosing the lateral-load-resisting system and its foundation.
Ans:
Floor plan:- The floor plan of the building is not uniform or symmetric. So naturally, any lateral load induced in the floor will not have 100% influence in the same direction. A special lateral load resistance system for these torsional moments should be accommodated.
Random internal columns:- Since the interior Columns are lucky, they cannot transfer the lateral loads efficiently and cannot achieve desirable building response. So we have to assume and design those columns for only gravity loads.
Floor-to-floor variation in partition walls and beams:- Partitions provide important mass control in and building, and Beams plan a crucial role in shear transfer from floor to Beam. All these elements are not in order. So heavy distortion distribution of loads will happen.
- This plan is unacceptable for heavy seismic zone areas.
- In this plan, interior columns are unsymmetric.
- The partition wall is provided through to the base of the beam, which should support the lateral deformation due to the structure.
- The Interior beams will support the slab, then the lateral load resisting the failure due to earthquakes.
- For these irregular columns in the plan, we provide the flat slab because it directly stays in the column centroidal Axis.
- For here, the beams at different locations are irregular in plan, continuous, and disallowed to resist the seismic load in the region.
- The solution of the structure, we provide the shear wall from the system's foundation through vertical components; it should minimize the lord of a second failure occurring due to lateral forces acting on the structure.