Annex E(Clause 24.2)

Effective Length of Columns

E-1 In the absence of more exact analysis, the effective length of columns in framed structures may be obtained from the ratio of effective length to unsupported length $l_{\mathrm{ef}} / l$ given in Fig. 32 when relative displacement of the ends of the column is prevented and in Fig. 33 when relative lateral displacement of the ends is not prevented. In the latter case, it is recommended that the effective length ratio may not be taken to be less than 1.2.

F-1 General

F-1.1 This annex covers the requirements for designing and detailing of members of reinforced concrete (RC) structures designed to resist lateral effects of earthquake shaking, so as to give them adequate stiffness, strength and ductility to resist severe earthquake shaking without collapse. This annex addresses lateral load resisting structural systems of RC structures composed of,

a) RC moment resisting frames;

b) RC moment resisting frames with unreinforced masonry infill walls;

c) RC moment resisting frames with RC structural walls; and

d) RC structural walls.

F-1.2 Provisions of this annex shall be adopted in all lateral load resisting systems of RC structures located in Seismic Zone III, IV or V. The annex is optional in Seismic Zone II.

F-1.3 The provisions for RC structures given herein apply specifically to monolithic RC construction, and not for precast RC structures. Precast and/or prestressed concrete members may be used, only if they are designed to provide similar level of ductility as that of monolithic RC structures during or after an earthquake. Likewise, flat slab structures shall have a lateral load resisting system capable of providing similar level of performance as envisioned in this Section and shall be designed for drift compatibility as per F-10. Specialist literature shall be referred to for design and construction of such structures. The adequacy of such designs shall be demonstrated by adequate, appropriate experimentation and non-linear dynamic structural analyses.

F-1.4 All RC frames, RC walls and their elements in a structure need not be designed to resist lateral loads and the designer can judiciously identify the lateral load resisting system based on relative stiffness and location in the building and design those members for full lateral force. RC monolithic members assumed not to participate in the lateral force resisting system (see F-2.7) shall be permitted provided that their effect on the seismic response of the system is accounted for. Consequence of failure of structural and non-structural members not part of the lateral force resisting system shall also be considered in design.

For the purpose of this annex, the following definitions shall apply.

F-2.1 Beams — These are members (generally horizontal) of moment resisting frames with flexural and shearing actions.

F-2.2 Boundary Elements — These are portions along the ends of a structural wall that are strengthened by longitudinal and transverse reinforcement. They may have the same thickness as that of the wall web.

F-2.3 Columns — These are members (generally vertical) of moment resisting frames with axial, flexural and shearing actions.

F-2.4 Cover Concrete — It is that concrete which is not confined by transverse reinforcement.

F-2.5 Transverse Reinforcement — It is a continuous bar having a $135^{\circ}$ hook with an extension of 6 times diameter (but not < 65 mm) at one end and a hook not less than $90^{\circ}$ with an extension of 6 times diameter (but not < 65 mm) at the other end. The hooks shall engage peripheral longitudinal bars. In general, the hooks of two successive crossties engaging the same longitudinal bars shall be alternated end for end. Transverse reinforcement (also called hoops) in columns is typically called stirrups and that in beams is called cross-ties.

For the purpose of this annex, the following letter symbols shall have the meaning indicated against each; where other symbols are used, they are explained at the appropriate place. All dimensions in millimetre, loads in Newton and stresses in MPa, unless otherwise specified.

$A_{e}$ = Effective cross-sectional area of a joint $A_{ej}$ = Effective shear area of a joint $A_{g}$ = Gross cross-sectional area of column, wall = Horizontal reinforcement area within spacing = Area of concrete core of column = Reinforcement along each diagonal of coupling beam = Area of cross-section of bar forming spiral or link = Area of uniformly distributed vertical reinforcement = Vertical reinforcement at a joint = Width of beam = Width of column = Effective width of a joint D = Overall depth of beam = Diameter of column core measured to the outside of spiral or link d = Effective depth of member = Diameter of longitudinal bar = Effective depth of wall section

F-4.1 The design and construction of reinforced concrete buildings shall be governed by provisions of this Subsection 5A, except as modified by the

provisions of this annex for those elements participating in lateral force resistance.

F-4.2 Minimum grade of structural concrete shall be M 20, but M 25 for buildings,

a) more than $15\mathrm{m}$ in height in Seismic Zones III, IV and V; and

b) but not less than that required by provisions of Subsection 5A based on exposure conditions.

F-4.3 Steel reinforcement resisting earthquake-induced forces in RC frame members and in boundary elements of RC structural walls shall comply with F-4.3.1 to F-4.3.3.

F-4.3.1 Steel reinforcements used shall be,

a) of grade Fe 415 or less {conforming to accepted standard [6-5A(36)]}; and

b) of grade Fe 500 and Fe 550, that is; high strength deformed steel bars produced by thermo-mechanical treatment process having elongation more than 14.5 percent, and conforming to accepted standard [6-5A(36)].

F-4.3.2 The actual 0.2 percent proof strength of steel bars based on tensile test shall not exceed their characteristic 0.2 percent proof strength by more than 20 percent.

F-4.3.3 The ratio of the actual ultimate strength to the actual 0.2 percent proof strength shall be at least 1.15.

F-4.4 In RC frame buildings, lintel beams shall preferably not be integrated into the columns to avoid short column effect. When integrated, they shall be included in the analytical model for structural analysis. Similarly, plinth beams (where provided), and staircase beams and slabs framing into columns shall be included in the analytical model for structural analysis.

F-4.5 RC regular moment-resisting frame buildings shall have planar frames oriented along the two principal plan directions of buildings. Irregularities listed under 5 of Part 6 ‘Structural Design, Section 1 Loads, Forces and Effects’ of the Code shall be avoided. Buildings with any of the listed irregularities perform poorly during earthquake shaking; in addition, buildings with floating columns and set-back columns also perform poorly. When any such irregularities are adopted, detailed nonlinear analyses shall be performed to demonstrate that there is no threat to loss of life and property.

Requirements of this section shall apply to beams resisting earthquake-induced effects, in which the

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5A PLAIN AND REINFORCED CONCRETE

factored axial compressive stress does not exceed $0.08 f_{ck}$ . Beams, in which the factored axial compressive stress exceeds $0.08 f_{ck}$ , shall be designed as per requirements of F-6.

F-5.2.1 The longitudinal reinforcement in beams shall be as below:

a) Beams shall have at least two 12 mm diameter bars each at the top and bottom faces.

b) Minimum longitudinal steel ratio $\rho_{min}$ required on any face at any section is:

34A PLAN VIEW OF A BEAM COLUMN JOINT SHOWING EFFECTIVE BREADTH AND WIDTH OF JOINT

34B MAXIMUM EFFECTIVE WIDTH OF WIDE BEAM AND REQUIRED TRANSVERSE REINFORCEMENT

FIG. 34 BEAM COLUMN JUNCTIONS

When adopted, closed links shall be provided over the entire length over which the longitudinal bars are spliced. Further,

a) the spacing of these links shall not exceed 150 mm (see Fig. 36).

b) the lap length shall not be less than the development length of the largest longitudinal reinforcement bar in tension.

c) lap splices shall not be provided,

1. within a joint ;

2. within a distance of $2d$ from face of the column; and

3. within a quarter length of the beam adjoining the location where flexural yielding may occur under earthquake effects.

d) not more than 50 percent of area of steel bars on either top or bottom face shall be spliced at any one section.

FIG. 36 LAP LENGTH AT LOCATION OF SPLICING OF LONGITUDINAL BARS IN BEAM

Mechanical couplers {conforming to accepted standard [6-5A(38)]} shall be used when longitudinal steel bars have to be continued for beam spans larger than their manufacture lengths. Further,

a) only those mechanical splices conforming to the above code and capable of developing the specified tensile strength of spliced bar shall be permitted within a distance equal to two times the depth of the member from the member face or in any location where yielding of reinforcement is likely to take place; and

b) the spacing between adjacent longitudinal bars shall be based also on the outer size of the coupler to allow easy flow of concrete.

F-5.2.6.3 Welded splices

Welded splices shall not be used in beams for a distance equal to two times the depth of the member from the member face or in any location where yielding of reinforcement is likely to take place. At any location, not more than 50 percent of area of steel bars shall be spliced at any one section.

Welding of links, ties, inserts or other similar elements to vertical reinforcement bars required as per design is not permitted, in any seismic zone.

F-5.3.1 Only vertical links shall be used in beams (see Fig. 37A); inclined links shall not be used; and,

a) in normal practice, a link is made of a single

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5A PLAIN AND REINFORCED CONCRETE

bent bar. But, it may be made of two bars also, namely a U-link with a $135^{\circ}$ hook with an extension of 6 times diameter (but not less than 65 mm) at each end, embedded in the core concrete, and a cross-tie (see Fig. 37B).

b) the hooks of the links and cross-ties shall engage around peripheral longitudinal bars. Consecutive crossties engaging the same longitudinal bars shall have their $90^{\circ}$ hooks at opposite sides of the beam. When the longitudinal reinforcement bars are secured by cross-ties in beams that have a slab on one side, the $$ hooks of the cross-ties shall be placed on that side.

Requirements of this section shall apply to columns and inclined members resisting earthquake-induced effects, in which the factored axial compressive stress due to gravity and earthquake effects exceeds $0.08 f_{ck}$ . The factored axial compressive stress considering all load combinations relating to seismic loads shall be limited to $0.40 f_{ck}$ in all such members, except in those covered in 10.

F-6.2.1 At each beam-column joint of a moment-resisting frame, the sum of nominal design strength of columns meeting at that joint (with nominal strength calculated for the factored axial load in the direction of the lateral force under consideration so as to give

FIG. 39 DETAILS OF TRANSVERSE REINFORCEMENT IN BEAMS

FIG. 40 MINIMUM SIZE OF RC COLUMNS BASED ON DIAMETER OF LARGEST LONGITUDINAL REINFORCEMENT BAR IN BEAMS FRAMING INTO IT

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5A PLAIN AND REINFORCED CONCRETE

least column nominal design strength) along each principal plane shall be at least 1.4 times the sum of nominal design strength of beams meeting at that joint in the same plane (see Fig. 41).

In the event of a beam-column joint not conforming to above, the columns at the joint shall be considered to be gravity columns only and shall not be considered as part of the lateral load resisting system.

F-6.2.1.1 The design moments of resistance of a beam shall be estimated based on the principles of mechanics and the limiting strain states of the limit state design method enunciated in this Subsection 5A. The design moment of resistance of a column shall be estimated as in case of beams corresponding to zero axial force on the design P-M interaction diagram.

F-6.2.1.2 This check shall be performed at each joint for both positive and negative directions of shaking in the plane under consideration. Further, in this check, design moments of resistance in beam(s) meeting at a joint shall be considered in the same direction, and similarly the design moments of resistance of column(s) at the same joint shall be considered to be in the direction opposite to that of the moments in the beams.

F-6.2.1.3 This check shall be waived at all joints at roof level only, in buildings more than 4 storeys tall.

The provisions of F-6.2 are not applicable for flat slab structures.

When adopted, closed links shall be provided over the entire length over which the longitudinal bars are spliced. Further,

a) the spacing of these links shall not exceed $100\mathrm{mm}$.

b) the lap length shall not be less than the development length of the largest longitudinal reinforcement bar in tension.

c) lap splices shall be provided only in the central half of clear column height, and not

1. within a joint, or

2. within a distance of $2d$ from face of the beam.

d) not more than 50 percent of area of steel bars shall be spliced at any one section.

e) lap splices shall not be used for bars of diameter larger than 32 mm for which mechanical splicing shall be adopted,

F-6.3.2.2 Mechanical couplers

Mechanical couplers {see accepted standard [6-5A(38)]} shall be used. Further, only those mechanical splices conforming to the above standard and capable of developing the specified tensile strength of spliced bar shall be permitted within a distance equal to two times the depth of the member from the column face in any location where yielding of reinforcement is likely to take place.

Welded splices shall not be used in columns for a distance equal to two times the depth of the member from the member face or in any location where yielding of reinforcement is likely to take place. At any location, not more than 50 percent of area of steel bars shall be spliced at any one section. But, welding of links, ties, inserts or other similar elements to vertical reinforcement bars required as per design is not permitted, in any seismic zone.

FIG. 41 STRONG COLUMN - WEAK BEAM

F-6.3.3 A column that extends more than 100 mm beyond the confined core owing to architectural requirement (see Fig. 42) shall be detailed in the following manner:

a) When the contribution of this area is considered in the estimate of strength of columns, it shall have at least the minimum longitudinal and transverse reinforcement given in this Subsection 5A.

b) When the contribution of this area is not considered in the estimate of strength of columns, it shall have at least the minimum longitudinal and transverse reinforcement given in this Subsection 5A.

F-6.4 Transverse Reinforcement

F-6.4.1 Transverse reinforcement shall consist of closed loop,

a) spiral or circular links in circular columns, and

b) rectangular links in rectangular columns.

In either case, the closed link shall have $135^{\circ}$ hook ends with an extension of 6 times its diameter (but not < 65 mm) at each end, which are embedded in the confined core of the column (see Fig. 43A).

a) the minimum diameter permitted of transverse reinforcement bars is 8 mm, when diameter of longitudinal bar is less than or equal to 32 mm, and 10 mm, when diameter of longitudinal bar is more than 32 mm;

b) the maximum spacing of parallel legs of links shall be 300 mm centre-to-centre;

c) a cross-tie shall be provided, if the length of any side of the link exceeds 300 mm (see Fig. 43B); the cross-tie shall be placed perpendicular to this link whose length exceeds 300 mm. Alternatively, a pair of overlapping links may be provided within the column (see Fig. 43C). In either case, the hook ends of the links and cross-ties shall engage around peripheral longitudinal bars. Consecutive cross-ties engaging the same longitudinal bars shall have their 90° hooks

FIG. 42 REINFORCEMENT REQUIREMENT IN COLUMNS WITH PROJECTION MORE THAN 100 mm BEYOND CORE

on opposite sides of the column. Crossties of the same or smaller bar size as the hoops shall be permitted; and,

d) the maximum spacing of links shall be half the least lateral dimension of the column, except where special confining reinforcement is provided as per F-7.

The design shear force demand on columns is the larger of,

a) factored shear force demand as per linear structural analysis; and

b) factored equilibrium shear force demand when plastic hinges are formed at both ends of the beams given by:

1. For sway to right:

a) Design shear stress demand acting horizontally along each of the two principal plan directions of the joint shall be estimated from earthquake shaking considered along each of these directions, using,

FIG. 48 PLAN VIEW OF A BEAM COLUMN JOINT SHOWING EFFECTIVE BREADTH AND WIDTH OF JOINT

$\tau_{\mathrm{jdX}} = \frac{V_{\mathrm{djX}}}{b_{\mathrm{j}}w_{\mathrm{j}}}$ for shaking along plan direction X of earthquake shaking,

F-8.2.1 Confining Reinforcement in Joints

a) When all four vertical faces of the joint are having beams framing into them covering at least 75 percent of the width on each face,

1. At least half the special confining reinforcement required as per F-7 at the two ends of columns, shall be provided through the joint within the depth of the shallowest beam framing into it; and

2. Spacing of these transverse links shall not exceed 150 mm.

b) When all four vertical faces of the joint are not having beams framing into them or when all four vertical faces have beams framing into them but do not cover at least 75 percent of the width on any face,

1. special confining reinforcement required as per F-7 at the two ends of columns shall be provided through the joint within the depth of the shallowest beam framing into it, and

2. spacing of these transverse links shall not exceed 150 mm.

F-8.2.2 In the exterior and corner joints, all $135^{\circ}$ hooks of cross-ties should be along the outer face of columns.

F-9 Special Shear Walls

F-9.1.1 The requirements of this clause apply to special shear walls that are part of lateral force resisting system of earthquake-resistant RC buildings.

F-9.1.2 The minimum thickness of special shear walls shall not be less than,

a) $150\mathrm{mm}$; and

b) 300 mm for buildings with coupled shear walls in any seismic zone.

The minimum thickness provided shall conform to the fire resistance requirements based on occupancy as laid down in this Subsection 5A.

F-9.1.3 The minimum ratio of length of wall to its thickness shall be 4.

F-9.1.4 Special shear walls shall be classified as squat, intermediate or slender depending on the overall height $h_{\mathrm{w}}$ to Length $L_{\mathrm{w}}$ ratio as:

F-9.2.1 Nominal shear stress demand $\tau_{\mathrm{v}}$ on a wall shall be estimated as:

F-9.3.1 Design moment of resistance $M_{u}$ of the wall section subjected to combined bending moment and compressive axial load shall be estimated in accordance with requirements of limit state design method given in this Subsection 5A, using the principles of mechanics involving equilibrium equations, strain compatibility conditions and constitutive laws.

The moment of resistance of slender rectangular structural wall section with uniformly distributed vertical reinforcement may be estimated using expressions given in F-9.9. Expressions given in F-9.9 are not applicable for structural walls with boundary elements,

F-9.3.2 The cracked flexural strength of a wall section shall be greater than its uncracked flexural strength.

F-9.3.3 In structural walls that do not have boundary elements, at least a minimum of 4 bars of $12\mathrm{mm}$ diameter arranged in 2 layers, shall be concentrated as vertical reinforcement at the ends of the wall over a length not exceeding twice the thickness of RC wall.

Boundary elements are portions along the wall edges that are strengthened by longitudinal and transverse reinforcement even if they have the same thickness as that of the wall web. It is advantageous to provide boundary elements with dimension greater than thickness of the wall web.

F-9.4.1 Boundary elements shall be provided along the vertical boundaries of walls, when the extreme fibre compressive stress in the wall exceeds $0.2f_{\mathrm{ck}}$ due to factored gravity loads plus factored earthquake force. Boundary elements may be discontinued at elevations where extreme fibre compressive stress becomes less than $0.15f_{\mathrm{ck}}$. Extreme fibre compressive stress shall be estimated using a linearly elastic model and gross section properties.

F-9.5.1 Coplanar special structural walls may be connected by means of coupling beams.

F-9.5.2 If earthquake induced shear stress $\tau_{\mathrm{ve}}$ in coupling beam exceeds,

F-9.6.1 Shear strength of a wall with openings should be checked at critical horizontal planes passing through openings.

F-9.6.2 Additional steel reinforcement shall be provided along all four edges of openings in walls. Further,

a) the area of these vertical and horizontal steel should be equal to that of the respective interrupted bars, provided half on either side of the wall in each direction.

b) these vertical bars should extend for full height of the storey in which this opening is present.

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5A PLAIN AND REINFORCED CONCRETE

c) the horizontal bars should be provided with development length in tension beyond the edge of the opening.

F-9.7 Construction Joints

Vertical reinforcement across a horizontal construction joint shall have area, $A_{\mathrm{st}}$ is given by:

When adopted, closed links shall be provided over the entire length over which the longitudinal bars are spliced. Further,

a) the spacing of these links shall not exceed $150\mathrm{mm}$.

b) the lap length shall not be less than the development length of the largest longitudinal reinforcement bar in tension.

c) lap splices shall be provided only in the central half of clear wall height, and not,

1. within a joint; or

2. within a distance of $2d$ from a location where yielding of reinforcement is likely to take place.

d) not more than 50 percent of area of steel bars shall be spliced at any one section.

F-9.8.3.2 Mechanical couplers {conforming to accepted standard [6-5A(38)]} shall be used. Further, only those mechanical splices conforming to the above standard and capable of developing the specified tensile strength of spliced bar shall be permitted within a

distance equal to two times the depth of the member from the beam-column joint or in any location where yielding of reinforcement is likely to take place

Welded splices shall be avoided as far as possible. In no case shall they be used for a distance equal to two times the depth of the member from the member face or in any location where yielding of reinforcement is likely to take place. At any location, not more than 50 percent of area of steel bars shall be spliced at any one section.

Welding of links, ties, inserts or other similar elements to vertical reinforcement bars required as per design is not permitted, in any seismic zone.

F-9.8.4 In buildings located in Seismic Zones II and III, closed loop transverse links shall be provided around lapped spliced bars larger than 16 mm in diameter. The minimum diameter of such links shall be $1/4^{th}$ of diameter of spliced bar but not less than 8 mm at spacing not exceeding 150 mm centres.

The moment of resistance $M_{\mathrm{u}}$ of a slender rectangular structural wall section with uniformly distributed vertical reinforcement may be estimated as: