Seismic Vulnerability Assessment and Strengthening of Existing Reinforced Concrete Buildings

    Seismic Retrofitting

    The earthquakes in India and different parts of the world have caused loss of human lives and damage to property due to the collapse of structures. Though, an earthquake cannot be prevented, the loss of life and property can be minimized by taking necessary steps on the existing buildings to reduce the damages. It becomes essential to carry out first an assessment, then identify the deficient members and finally, carry out appropriate strengthening. This paper gives guidelines for seismic vulnerability assessment and strengthening of existing reinforced concrete buildings.

    Dr. Rajeev Goel and GK Sahu, Senior Principal Scientist, CSIR-Central Road Research Institute, Delhi-Mathura Road, New Delhi

    Introduction

    Some of the severe earthquakes that occurred across the world after the year 2005 are Nepal M 7.8 (2015), Haiti M 7.0 (2010), Southern Sumatra, Indonesia M 7.5 (2009), Eastern Sichuan, China M7.9 (2008), and Java, Indonesia M 6.3 (2006). Several buildings have consistently exhibited poor performance in the past earthquakes around the world. The structural performance of the buildings during earthquake provides a lot of information about the merits and demerits of the design and construction practices in a region. Earthquake hazard can be minimised with proper understanding of behaviour of buildings during earthquake and careful planning, design and construction. Based on this information, codes have been prepared / upgraded worldwide.

    In India, a code (IS:15988) giving guidelines for seismic evaluation and strengthening of existing reinforced concrete buildings was released in 2013. This code provides a method to assess the ability of an existing building to reach an adequate level of performance related to life-safety of occupants and thus identifies unfavourable characteristics of the building that could result in damage to either part of a building or the entire structure. By using the provisions of this code, the risk of death and injury can be reduced that may result from the damaging effects of earthquake on building which predate the current seismic codes or have not been designed for earthquake forces.

    Assessment methodology

    A preliminary assessment of building is first carried out which involves broad assessment of its physical condition, robustness, structural integrity and strength of structure, including simple calculations. If the results of preliminary assessment for strength, overall stability and integrity reveal that building is acceptable to take the seismic loads safely, then no further action is required. Else a detailed assessment is required, in which numerical checks on stability and integrity of the whole structure as well as the strength of each member is to be performed.

    The seismic performance of existing buildings is assessed in relation to the performance criteria in use for new buildings. Basic inputs for determination of seismic forces such as seismic zone, building type, response reduction factor needs to be taken directly from IS:1893 (Part-1) or from the site-specific seismic design criteria developed along the principles described in IS:1893 (Part-1). Modification to seismic forces and to material strengths then needs to done for both preliminary and detailed assessments.

    retrofit expanse

    Lateral Seismic Force Modification Factor

    The lateral seismic force determined for strength related checks needs to be modified for reduced useable life of the building. The useable life factor U, is to be multiplied to the lateral seismic force (i.e. base shear) for new building as specified in IS:1893 (Part-1). U will be determined as

    U = (Trem/Tdes)0.5 ≥ 0.7
    where,
    Trem = Remaining useful life of the building
    Tdes = Design useful life of the building

    Material Modification Factor

    Strength capacities of existing building components shall be based on the probable or measured material strengths in the building. Probable or measured nominal strengths are best indicator of the actual strength and may only be obtained by field or lab tests on a series of samples. These strength values need to be further modified by multiplying with a Knowledge Factor, K (which varies from 1.0 to 0.5) for the uncertainty regarding the reliability of available information, and present condition of the component.

    Preliminary Assessment

    The preliminary assessment is a quick procedure to establish actual structural layout and assess its characteristics that may affect its seismic vulnerability. It is a very approximate procedure based on conservative parameters to identify the potential earthquake risk of a building and may be used to screen buildings for detailed assessment.

    Site Visit

    A site visit is to be done to verify available existing building data or collect additional data, and to determine the condition of the building and its components. The following information needs to be confirmed/collected during the site visit:
    1. General information: Number of storeys and dimensions, year of construction
    2. Structural system description: Framing vertical lateral force-resisting system, floor and roof diaphragm connection to walls, basement and foundation system
    3. Building type and site soil classification as in IS:1893 (Part-1)
    4. Building use and nature of occupancy
    5. Adjacent buildings and potential for pounding and falling hazards
    6. General conditions: Deterioration of materials, damage from past earthquakes, alterations and additions that could affect earthquake performance
    7. Architectural features that may affect earthquake performance, especially location of masonry infill walls
    8. Geological site hazards and foundation conditions: Susceptibility for liquefaction and conditions for slope failure and surface fault rupture
    9. Special construction anomalies and conditions
    cta force enlargement

    Acceptability Criteria

    A building is said to be acceptable to withstand seismic forces, if it meets the following configuration-related checks as well as strength-related checks.

    Configuration-Related Checks
    1. Load Path: The structure shall contain at least one rational and complete load path for seismic forces from any horizontal direction so that they can transfer all inertial forces in the building to the foundation.
    2. Redundancy: The number of lines of vertical lateral load resisting elements in each principal direction shall be greater than or equal to 2. In the case of moment frames, the number of bays in each line shall be greater than or equal to 2. Similarly, the number of lines of shear walls in each direction shall be greater than or equal to 2.
    3. Geometry: No change shall be made in the horizontal dimension of lateral force resisting system of more than 50% in a storey relative to adjacent stories, excluding penthouses and mezzanine floors.
    4. Weak Storey: The strength of the vertical lateral force resisting system in any storey shall not be less than 70% of the strength in an adjacent storey.
    5. Soft Storey: The stiffness of vertical lateral load resisting system in any storey shall not be less than 60% of the stiffness in an adjacent storey or less than 70% of the average stiffness of the three storeys above.
    6. Vertical Discontinuities: All vertical elements in the lateral force resisting system shall be continuous from the root to the foundation.
    7. Mass: There shall be no change in effective mass more than 100% from one storey to the next. Light roofs, penthouses, and mezzanine floors need not be considered, in mass irregularity.
    8. Torsion: The estimated distance between a storey center of mass and the storey centre of stiffness shall be less than 30% of the building dimension at right angles to the direction of loading considered.
    9. Adjacent Buildings: The clear horizontal distance between the building under consideration and any adjacent building shall be greater than 4 percent of the height of the shorter building, except for buildings that are of the same height with floors located at the same levels.
    10. Short Columns: The reduced height of a column due to surrounding parapet, infill wall, etc. shall not be less than five times the dimension of the column in the direction of parapet, infill wall, etc. or 50% of the nominal height of the typical columns in that storey.
    11. Mezzanines/Loft/Sub-floors: Interior mezzanine/loft/sub-floor levels shall be braced independently from the main structure, or shall be anchored to the lateral-force-resisting elements of the main structure.
    Strength-Related Checks
    1. Shear Stress in Reinforced Concrete Frame Columns: The average shear stress in concrete columns, τcol, computed in accordance with the following equation shall be lesser of 0.40 MPa; and 0.10 √fck , where fck is characteristic cube strength of concrete:
      τcol = ( Nc / ( Nc - Nf ) ).( Vj / Ac )
      where,
      Nc = Total number of columns;
      Nf = Total number of frames in the direction of loading;
      Vj = Storey shear at level j; and
      Ac = Total cross-sectional area of columns.
    2. Shear Stress in Shear Walls: Average shear stress in concrete and masonry shear walls, τwall, shall be computed by the following equation:
      τwall = ( Vj / Awall )
      where,
      Vj = Storey shear at level j
      Awall = Total area of shear walls in the direction of the loading
      Average shear stress shall be less 0.40 MPa for concrete shear walls, 0.10 MPa for unreinforced masonry load bearing walls, 0.30 MPa for reinforced masonry infill walls, and 0.10 MPa for the unreinforced masonry infill walls.
    3. Axial Stress in Moment Frames: The maximum compressive axial stress in the columns of moment frames at base due to overturning forces alone (Fo) as calculated using the following equation shall be less than 0.25 fck.
      Fo= 2 / 3 ( Vb / Nf ) . ( H / L )
      where,
      Nf = Total number of frames in the direction of loading
      Vb = Base shear at level j
      H = Total height
      L = Length of the building
    Detailed Assessment

    Detailed assessment of the building needs to be done, if any of the following conditions are met:
    1. Building fails to comply with the requirements of the preliminary assessment
    2. A building is having 6 storeys or more
    3. Building is located on incompetent or liquefiable soils and/or located within a distance of 15 km from active faults and/or with inadequate foundation details
    4. Building is having inadequate connections between primary structural members, such as poorly designed and/or constructed joints of pre-cast elements
    Condition of the Building Components

    During detailed assessment, the building needs to be checked for the existence of some of the following common indicators of deficiency:
    1. Deterioration of concrete: There shall be no visible deterioration of the concrete or reinforcing steel in any of the vertical or lateral force resisting elements.
    2. Cracks in boundary columns: There shall be no existing diagonal cracks wider than 3mm in concrete columns that encase masonry infills.
    3. Masonry units: There shall be no visible deterioration of masonry units.
    4. Masonry joints: The mortar shall not be easily scraped away from the joints by hand with a metal tool, and there shall be no areas of eroded mortar.
    5. Cracks in infill walls: There shall be no existing diagonal cracks (width more than 3mm) in infill walls that extends throughout a panel or have out-of-plane offsets in the bed joint greater than 3mm.
    Condition of the Building Materials

    An assessment of the present day strength of materials needs to be performed using on-site non-destructive testing and laboratory analysis of samples taken from the building. Field tests are usually indicative tests and therefore shall be supplemented with proper laboratory facilities for accurate quantitative results.

    Retrofitting with RC Column Jacketing
    Assessment Procedure Probable Flexure and Shear Demand

    First of all, the probable flexural and shear strengths of the critical sections of the members and joints of vertical lateral force resisting elements shall be estimated. The calculations shall be performed as per respective codes for various building types and modified with knowledge factor K.

    Design Base Shear

    Calculate the total lateral force (design base shear) as per IS:1893 (Part-1) and multiply it with U, a factor for the reduced useable life.

    Analysis Procedure

    Perform a linear equivalent static or a dynamic analysis of the lateral load resisting system of the building in accordance with IS:1893 (Part-1) for the modified base shear determined in the previous step and determine resulting member actions for critical components.
    1. Mathematical model: Mathematical model of the physical structure shall be such as to represent the spatial distribution of mass and stiffness of the structure to an extent that is adequate for the calculation of significant features of its distribution of lateral forces. All concrete as well as masonry elements shall be included in the model.
    2. Component stiffness: Component stiffness shall be determined based on some rational procedure. Some standard values are given in Table-1.
    Table-1: Some Effective Stiffness Values
    Sl. No. Component Flexural Rigidity Shear Rigidity Axial Rigidity
    i) Beam, non pre-stressed 0.5 Ec Ig
    ii) Beam, pre-stressed 1.0 Ec Ig Ec Ag
    iii)  Column in compression (P > 0.5fc’Ag) 0.7 Ec Ig 0.4 Ec Aw Ec Ag
    iv)  Column in compression (P ≥ 0.5fc’Ag ) 0.5 Ec Ig Ec Ag
    v) Walls - Uncracked 0.8 Ec Ig Ec Ag
    vi)  Walls - Cracked 0.5 Ec Ig Ec Ag
    vii) Flat slab To be determined based on rational procedure

    Demand-Capacity Ratio

    Evaluate the acceptability of each component by comparing its probable strength with the member actions.

    Inter-storey Drift

    Calculate whether the inter-storey drifts and decide whether it is acceptable in terms of the requirements of IS:1893 (Part-1).

    Acceptability Criteria

    A building is said to be acceptable if either of the following two conditions are satisfied along with ductility and detailing related compliance as given below:
    1. All critical elements of lateral force resisting elements have strengths greater than computed actions and drift checks are satisfied.
    2. Except a few elements, all critical elements of the lateral force resisting elements have strengths greater than computed actions and drift checks are satisfied. Further, it should be ensured that the failure of these few elements shall not lead to loss of stability or initiate progressive collapse. This needs to be verified by a non-linear analysis such as pushover analysis, carried out up to the collapse load.
    Ductility and Detailing Related Assessment
    Moment Resisting Reinforced Concrete Frame Buildings

    For RC moment frame buildings designed using response reduction factor R equal to 5, the following supplemental criteria need to be satisfied. Any deficiency should be considered in suitably reducing the value of R.
    1. No shear failures: Shear capacity of frame members shall be adequate to develop the moment capacity at the ends, and shall be in accordance with provisions of IS:13920 for shear design of beams and columns.
    2. Concrete columns: All concrete columns shall be adequately anchored into the foundation from top face of pedestal of base slab.
    3. Strong column/weak beam: The sum of the moment of resistance of the columns shall be at least 1.1 times the sum of the moment of resistance of the beams at each frame joint.
    4. Beam bars: At least two longitudinal top and two longitudinal bottom bars shall extend continuously throughout the length of each frame beam. At least 25 percent of the longitudinal bars located at the joints for either positive or negative moment shall be continuous throughout the length of the members.
    5. Column-bar splices: Lap splices shall be located only in the central half of the member length. It should be proportioned as a tension splice. Hoops shall be located over the entire splice length at spacing not exceeding 150 mm centre to centre. Not more than 50 percent of the bars shall preferably be spliced at one section. If more than 50 percent of the bars are spliced at one section, the lap length shall be 1.3 Ld where Ld is the development length of bar in tension as per IS 456.
    6. Beam-bar splices: Longitudinal bars shall be spliced only if hoops are located over the entire splice length, at a spacing not exceeding 150 mm. The lap length shall not be less than the bar development length in tension. Lap splices shall not be located (1) within a joint; (2) within a distance of 2d from joint face; and (3) within a quarter length of the member near supports where flexural yielding may occur under the effect of earthquake forces. Not more than 50 percent of the bars shall be spliced at one section.
    7. Column-tie spacing: The parallel legs of rectangular hoop shall be spaced not more than 300 mm centre to centre. If the length of any side of the hoop exceeds 300 mm, the provision of a cross tie should be there. Alternatively, a pair of overlapping hoops may be located within the column. The hooks shall engage peripheral longitudinal bars.
    8. Stirrup spacing: The spacing of stirrups over a length of 2d at either end of a beam shall not exceed (1) d/4, or (2) 8 times the diameter of the smallest longitudinal bar; however, it need not be less than 100mm. The first hoop shall be at a distance not exceeding 50mm from the joint face. In case of beams vertical hoops at the same spacing as above shall also be located over a length equal to 2d on either side of a section where flexural yielding may occur under the effect of earthquake forces. Elsewhere, the beam shall have vertical hoops at a spacing not exceeding d/2.
    9. Joint reinforcing: Beam-column joints shall have ties spaced at or less than 150mm.
    10. Stirrup and tie hooks: The beam stirrups and column ties shall preferably be anchored into the member cores with hooks of 135°.
    Concrete Shear Wall Buildings

    Concrete shear wall buildings can be either the ordinary reinforced type or ductile shear wall type. Some of the provisions mentioned below are applicable to both types of shear walls while some are applicable only for ductile shear walls. Applicable provisions shall indicate the suitable choice for the response reduction factor R.
    1. Thickness: The thickness of any part of an ordinary shear wall shall preferably, not be less than 100 mm while for ductile shear wall it shall not be less than 150 mm. In case of coupled shear walls, the thickness of the walls shall be at least 200 mm.
    2. Overturning: All shear walls shall have aspect ratio less than 4 to 1, else the foundation system shall be investigated for its adequacy to resist overturning moments. Wall piers need not be considered.
    3. Reinforcement:
      1. Shear walls shall be provided with reinforcement in the longitudinal and transverse directions in the plane of the wall to resist bending moment and to prevent premature shear failure. The minimum reinforcement ratio for ordinary shear walls shall be 0.001 5 of the gross area in each direction. For ductile shear walls this value is increased to 0.002 5 in the horizontal direction. This reinforcement shall be distributed uniformly across the cross-section of the wall.
      2. The stirrups in all coupling beams over openings for doors, passages, staircases, etc. shall be spaced at or less than d/2 and shall be anchored into the core with hooks of 135° or more. The shear and flexural demand on coupling beams which are non-compliant and their adequacy is checked. If they are found inadequate, then their adequacy is checked as if they were independent.
    4. Opening in walls: Total length of openings shall not be greater than 75 percent of the length of any perimeter wall. The adequacy of remaining wall for shear and overturning resistances shall be evaluated. Shear transfer connection between the diaphragm and walls shall also be evaluated and checked for adequacy.
    Reinforced Concrete Frames with Masonry Infill Walls

    The provisions, mentioned above for moment resisting RCC framed buildings needs to be satisfied by reinforced concrete frames with masonry infill walls also. In addition, the infill walls shall be checked for the following additional criteria:
    1. Wall connections: All infill walls shall have a positive connection to the frame to resist out-of-plane forces.
    2. Out-of-plane stability: The unreinforced masonry wall height-to-thickness ratios shall be less than as given in Table-2. The frame element beams are assumed to provide necessary lateral support for the unreinforced masonry wall in out-of-plane direction.
    3. Unreinforced masonry parapets: The maximum ratio of height to thickness of an unsupported unreinforced masonry parapet shall not exceed 1.5 and 2.5 for the parapet walls in seismic zone-V and other remaining seismic zones respectively.
    Table-2: Allowable Height-to-Thickness Ratios of Unreinforced Masonry Walls
    Sl  No. Wall Type Zone II and III Zone IV Zone V
    i) Top storey of multistorey building 14 14 9
    ii) First storey of multistorey building 18 16 15
    iii) All other conditions 16 16 13

    If the required parapet height exceeds this maximum height, a bracing system designed for the forces shall support the top of the parapet. The minimum height of a parapet above any wall anchor shall be 300 mm. If a reinforced concrete beam is provided at the top of the wall, the minimum height above the wall anchor may be 150 mm.

    Seismic Strengthening

    Strengthening options
    Seismic strengthening for improved performance in the future earthquakes can be achieved by adopting one of the following options.

    Strengthening of deficient Members
    1. Existing buildings with a sufficient level of strength and stiffness at the global level may have some members, which lack adequate strength, stiffness or ductility. If such deficient members are small in number, an economical and appropriate strategy is to modify these deficient members alone while retaining the existing lateral-force resisting system.
    2. Member level modification shall be undertaken to improve strength, stiffness and/ or ductility of deficient members and their connections strengthening measures shall include such as jacketing of columns or beams.
    Eliminating or Reducing Structural Irregularities
    1. Irregularities related to distribution of strength, stiffness and mass result in poor seismic performance. Often these irregularities exist because of discontinuity of structural members. Simple removal of such discontinuities may reduce seismic demand on other structural components to acceptable levels.
    2. An effective measure to correct vertical irregularities such as weak and/or soft storey is the addition of shear walls and braced frames within the weak/soft storey. Braced frames and shear walls may also be effectively used to balance stiffness and mass distribution within a storey to reduce torsional irregularities. Shear wall can be placed such that it forms an integral part of load flow path for lateral loads. Minimum two number of shear wall needs to be constructed in each orthogonal direction in opposite side of shear centre away from centre as far as possible to add better torsional resistance to the entire structure. The stiffness centre of the complete structure at a floor level after adding shear wall shall be such that eccentricity with respect to centre of gravity of mass is reduced to a minimum.
    3. Seismic gaps (or movement joints) needs to be created between various parts of a building with irregular plan geometry to separate it into a number of regular independent structures. However, care shall be exercised to provide sufficiently wide gaps to avoid the problem of pounding.
    Strengthening at Structural Level

    In RCC buildings, where more than a few critical members and components do not have adequate strength and ductility, an effective way is to strengthen the structure so that the overall displacement demand is reduced. This strengthening of structure may enhance force demands on some other elements, which may require further strengthening. Braced frames and shear walls are an effective means of adding stiffness and strength.

    Seismic isolation and supplemental damping
    Seismic Retrofitting
    Seismic isolation and supplemental damping are rapidly evolving strategies for improving the seismic performance of structures. Base isolation reduces the demands on the elements of the structure. This technique is most effective for relatively stiff buildings with low profiles and large mass compared to light, flexible structures. Energy dissipation helps in the overall reduction in displacements of the structure. This technique is most effective in structures that are relatively flexible and have some inelastic deformation capacity.

    Methods of Analysis and Design for Strengthening

    The performance criteria for the design of strengthening measures shall be same as for assessment process. Member capacities of existing elements shall be based on the probable strengths, used for detailed assessment. The analysis of the building shall be done by the same method, which was used during the assessment process.

    Strengthening Options for Reinforced Concrete Framed Structures

    Jacketing

    Members requiring strengthening or enhanced ductility can be jacketed by reinforced concrete jacketing, steel profile jacketing, and steel encasement or wrapping with FRP. The deficient members shall first be stress relieved by propping, where possible.
    1. Reinforced concrete jacketing of columns:
      Reinforced concrete jacketing improves column flexural strength and ductility. Closely spaced transverse reinforcement provided in the jacket improves the shear strength and ductility of the column. The procedure for reinforced concrete jacketing is as follows:
      1. The seismic demand on the columns, in terms of axial load P and moment M is obtained.
      2. The column size and section details are estimated for P and M as determined above.
      3. The existing column size and amount of reinforcement is deducted to obtain the amount of concrete and steel to be provided in the jacket.
      4. The extra size of column cross-section and reinforcement is provided in the jacket.
      5. Increase the amount of concrete and steel actually to be provided as follows to account for losses.
        Ac = ( 3 / 2 ) Ac’ and As = ( 4 / 3 ) As
        Where
        Ac and As = actual concrete and steel to be provided in the jacket; and
        A’c and A’s = concrete and steel values, obtained for the jacket after deducting the existing concrete and steel from their respective required amount.
      6. The spacing of ties to be provided in the jacket in order to avoid flexural shear failure of column and provide adequate confinement to the longitudinal steel along the jacket is given as:
        s = fy / √fck ( d2 h / tj )
        where fy = yield strength of steel,
        fck = cube strength of concrete,
        dh = diameter of stirrup, and tj = thickness of jacket.
      7. If the transfer of axial load to new longitudinal steel is not critical then friction present at the interface shall be relied on for the shear transfer, which shall be enhanced by roughening the old surface.
      8. Dowels which are epoxy grouted and bent into 90° hook shall also be employed to improve the anchorage of new concrete jacket.
    2. The minimum specifications for jacketing columns are:
      1. Strength of the new materials shall be equal or greater than those of the existing column. Concrete strength shall be at least 5 MPa greater than the strength of the existing concrete.
      2. For columns where extra longitudinal reinforcement is not required, a minimum of 12j bars in the four corners and ties of 8φ @ 100 c/c should be provided with 135° bends and 10j leg lengths.
      3. Minimum jacket thickness shall be 100 mm.
      4. Lateral support to all the longitudinal bars shall be provided by ties with an included angle of not more than 135°.
      5. Minimum diameter of ties shall be 8 mm and not less than one-third of the longitudinal bar diameter.
      6. Vertical spacing of ties shall not exceed 200 mm, whereas the spacing close to the joints within a length of ¼ of the clear height shall not exceed 100 mm. Preferably, the spacing of ties shall not exceed the thickness of the jacket or 200 mm whichever is less.
    3. Fibre jacketing of a beam:
      Dimensions of FRP jacket is determined assuming composite action between fiber and existing concrete. The rupture strength of FRP is used as its limiting strength.
      Ultimate flexure strength of a beam after strengthening is determined based on the assumption that compressive concrete reaches a strain of 0.0035 and FRP reaches its maximum strain.
      Shear strength of a beam after strengthening is determined from the flowing equation:
      V = Vcon+ Vs + VFRP
      where,
      Vcon = Shear contribution of concrete = Tc × b × D
      Vs = Shear contribution of steel = 0.87 × fy × Asv × (d/sv)
      VFRP = Shear contribution of FRP sheet = Af × ff × (d/s)
      Tc = Shear strength of concrete
      b = Width of beam
      D = Overall depth of beam
      fy = Yield strength of steel
      ff = Yield strength of fibre
      Asv = Area of shear stirrups
      sv = Spacing of shear stirrups
    Addition of New Structural Elements

    Shear walls and steel bracing can be added as new elements to increase the strength and stiffness of the structure.
    1. Addition of reinforced concrete shear wall

      Addition of new reinforced concrete shear walls provides the best option of strengthening an existing structure for improved seismic performance. It adds significant strength and stiffness to framed structures. The design of shear walls shall be done as per provisions of IS:13920.
      1. Where vertical shear walls are inserted between existing columns shear transfer reinforcement (dowel bars), perpendicular to the shear plane, is given by:
        Avf = ( Vu / μ fy ) η where,
        Vu = allowable shear force not greater than 0.2fck Ac or 5.5 Ac (Ac is the area of concrete section resisting shear transfer);
        µ = coefficient of friction;
        = 1.0 for concrete placed against hardened concrete with surface intentionally roughened;
        = 0.75 for concrete anchored to as rolled structural steel by headed studs or by reinforcing bars; and
        η = efficiency factor = 0.5
      2. The number of bars required for resisting shear at the interface are given by:
        n = Avf / A’ vf
        where, A’vf = cross-section area of a single bar.
      3. The minimum anchorage length of the grouted-in longitudinal and transverse reinforcement of the shear wall in to the existing components of the building shall not be less than 6 times the diameter of the bars.
      4. Wherever thickness of column is 250 mm or less, shear wall shall encase the column by wrapping shear wall reinforcement around column after roughening reinforced concrete column surface. In case where shear wall spans perpendicular to the larger dimension of column, the transverse reinforcement of shear wall shall be anchored and wrapped around the column surface.
    2. Addition of steel bracing
      Steel diagonal braces shall be added to existing concrete frames. Braces shall be arranged so that their centre line passes through the centres of the beam-column joints. Angle or channel steel profiles shall be used. Some of the design criteria for braces are given below:
      1. Slenderness of bracing member shall be less or equal to 2500 / √fy.
      2. The width-thickness ratio of angle sections for braces shall not exceed 136/ √fy. For circular sections the outside diameter to wall thickness ratio shall not exceed 8960/fy, and rectangular tubes shall have an out-to-out width to wall thickness ratio not exceeding 288/ √ fy .
      3. In case of Chevron (inverted-V) braces, the beam intersected by braces shall have adequate strength to resist effects of the maximum unbalanced vertical load applied to the beam by braces. This load shall be calculated using a minimum of yield strength Py for the brace in tension and a maximum of 0.3 times of load capacity for the brace in compression Pac.
      4. The top and bottom flanges of the beam at the point of intersection of V-braces shall be designed to support a lateral force equal to 2 percent of the beam flange strength fy .bf .tf.
      5. The brace connection shall be adequate against out-of-plane failure and brittle fracture.
    3. Pre-fabricated steel bracing sub assemblages can also be used, for ease of construction, Braces of X-, V-and inverted V- shape can be arranged inside a heavy rectangular steel frame, which is then placed in frame bay and firmly connected.
    Conclusions

    The codal based methodology for the seismic assessment and strengthening of existing reinforced concrete structures is discussed in this paper. Using this, a proper seismic assessment and strengthening of existing reinforced concrete structures can be done so that they can withstand the seismic forces.

    Acknowledgements

    Authors are thankful to Director, CSIR-Central Road Research Institute, New Delhi for his continuous encouragement and support to publish the paper.

    References
    1. IS:15988-2013, “Seismic Evaluation and Strengthening of Existing Reinforced Concrete Buildings - Guidelines”, Bureau of Indian Standards, New Delhi.
    2. IS:1893 (Part-1)-2016, “Criteria for Earthquake Resistant Design of Structures – Part-1: General Provisions and Building”, Bureau of Indian Standards, New Delhi.
    3. IS:13920-2016, “Ductile Design and Detailing of Reinforced Concrete Structures subjected to Seismic Forces – Code of Practice”, Bureau of Indian Standards, New Delhi.
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