Annex B(Clauses 17.2.2, 21.3.1, 21.7, 25.2.1.1 and 31.1) STRUCTURAL DESIGN (WORKING STRESS METHOD) B-1 General

B-1.1 General Design Requirements

The general design requirements of Section 5A (C) shall apply to this annex.

B-1.2 Redistribution of Moments

Except where the simplified analysis using coefficients (see 21.5) is used, the moments over the supports for any assumed arrangement of loading, including the dead load moments may each be increased or decreased by not more than 15 percent, provided that these modified moments over the supports are used for the calculation of the corresponding moments in the spans.

In the methods based on elastic theory, the following assumptions shall be made:

a) At any cross-section, plane sections before bending remain plain after bending.

b) All tensile stresses are taken up by reinforcement and none by concrete, except as otherwise specifically permitted.

c) The stress-strain relationship of steel and concrete, under working loads, is a straight line.

d) The modular ratio m has the value $\frac{280}{3\sigma_{cbc}}$

where $\sigma_{\mathrm{cbc}}$ is permissible compressive stress due to bending in concrete, in $\mathrm{N / mm^2}$, as specified in Table 25.

NOTE — The expression given for m partially takes into account long-term effects such as creep. Therefore this m is not the same as the modular ratio derived based on the value of $E_{c}$ given in 5.2.3.1.

B-2 Permissible Stresses

B-2.1 Permissible Stresses in Concrete

Permissible stresses for the various grades of concrete shall be taken as those given in Tables 25 and 27.

NOTE — For increase in strength with age, 5.2.1 shall be applicable. The values of permissible stress shall be obtained by interpolation between the grades of concrete.

For members in direct tension, when full tension is taken

by the reinforcement alone, the tensile stress shall be not greater than the values given below:

The tensile stress shall be calculated as:

where

$F_{\mathrm{t}} =$ total tension on the member minus pretension in steel, if any, before concreting;

$A_{e}$ = cross-sectional area of concrete excluding any finishing material and reinforcing steel;

$m =$ modular ratio; and

$A_{st}$ = cross-sectional area of reinforcing steel in tension.

B-2.1.2 Bond Stress for Deformed Bars

In the case of deformed bars conforming to accepted standard [6-5A(36)], the bond stresses given in Table 25 may be increased by 60 percent.

B-2.2 Permissible Stresses in Steel Reinforcement

Permissible stresses in steel reinforcement shall not exceed the values specified in Table 26.

B-2.2.1 In flexural member the value of $\sigma_{st}$ given in Table 26 is applicable at the centroid of the tensile reinforcement subject to the condition that when more than one layer of tensile reinforcement is provided, the stress at the centroid of the outermost layer shall not exceed by more than 10 percent the value given in Table 26.

Where stresses due to wind (or earthquake), temperature and shrinkage effects are combined with those due to dead and imposed load, the stresses specified in Tables 25, 26 and 27 may be exceeded up to a limit of $33\frac{1}{3}$ percent. Wind and seismic forces need not be considered as acting simultaneously.

B-3 Permissible Loads in Compression Members

The axial load $P$ permissible on a pedestal or short column reinforced with longitudinal bars and lateral ties shall not exceed that given by the following equation:

where

$\sigma_{cc} =$ permissible stress in concrete in direct compression,

$A_{c}$ = cross-sectional area of concrete excluding any finishing material and reinforcing steel,

$A_{\mathrm{sc}} =$ cross-sectional area of the longitudinal steel.

NOTE — The minimum eccentricity mentioned in 24.4 may be deemed to be incorporated in the above equation.

The permissible load for columns with helical reinforcement satisfying the requirement of 38.4.1 shall be 1.05 times the permissible load for similar member with lateral ties or rings.

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

The maximum permissible stress in a reinforced concrete column or part thereof having a ratio of effective column length to least lateral dimension above 12 shall not exceed that which results from the multiplication of the appropriate maximum permissible stress as specified under B-2.1 and B-2.2 by the coefficient $C_{\mathrm{r}}$ given by the following formula:

where

$C_{\mathrm{r}} =$ reduction coefficient;

$l_{ef}$ = effective length of column; and

$b =$ least lateral dimension of column; for column with helical reinforcement, $b$ is the diameter of the core.

For more exact calculations, the maximum permissible stresses in a reinforced concrete column or part thereof having a ratio of effective column length to least lateral radius of gyration above 40 shall not exceed those which result from the multiplication of the appropriate maximum permissible stresses specified under B-2.1 and B-2.2 by the coefficient $C_{\mathrm{r}}$ given by the following formula:

where $i_{\mathrm{min}} =$ least radius of gyration.

a) Allowable load — The allowable axial load P on a composite column consisting of structural steel or cast-iron column thoroughly encased in concrete reinforced with both longitudinal and spiral reinforcement, shall not exceed that given by the following formula:

where

$\sigma_{cc} = \text{permissible stress in concrete in direct compression;}$

$A_{c}$ = net area of concrete section; which is equal to the gross area of the concrete section $= A_{sc} - A_{m}$ ;

$A_{sc}$ = cross-sectional area of longitudinal bar reinforcement;

$\sigma_{\mathrm{mc}} =$ allowable unit stress in metal core, not to exceed $125~\mathrm{N / mm^2}$ for a steel core, or $70~\mathrm{N / mm^2}$ for a cast iron core; and

$A_{m} = \text{cross-sectional area of the steel or cast iron core.}$

b) Metal core and reinforcement — The cross-sectional area of the metal core shall not exceed 20 percent of the gross area of the column. If a hollow metal core is used, it shall be filled with concrete. The amount of longitudinal and spiral reinforcement and the requirements as to spacing of bars, details of splices and thickness of protective shell outside the spiral, shall conform to requirements of 25.5.3. A clearance of at least 75 mm shall be maintained between the spiral and the metal core at all points, except that when the core consists of a structural steel H-column, the minimum clearance may be reduced to 50 mm.

c) Splices and connections of metal cores — Metal cores in composite columns shall be accurately milled at splices and positive provisions shall be made for alignment of one core above another. At the column base, provisions shall be made to transfer the load to the footing at safe unit stresses in accordance with 33. The base of the metal section shall be designed to transfer the load from the entire composite columns to the footing, or it may be designed to transfer the load from the metal section only, provided it is placed in the pier or pedestal as to leave ample section of concrete above the base for the transfer of load from the reinforced concrete section of the column by means of bond on the vertical reinforcement and by direct compression on the concrete. Transfer of loads to the metal core shall be provided for by the use of bearing members, such as billets, brackets or other positive connections, these shall be provided at the top of the metal core and at intermediate floor levels where required. The column as a whole shall satisfy the requirements of formula given under (a) at any point; in addition to this, the reinforced concrete portion shall be designed to carry, according to B-3.1 or B-3.2 as the case may be, all floor loads brought into the column at levels between the metal brackets or connections. In applying the formula under B-3.1 or B-3.2 the gross area of column shall be taken to be the area of the concrete section outside the metal core, and the allowable load on the reinforced concrete section shall be further limited to $0.28 f_{ck}$ times gross sectional area of the column.

d) Allowable load on metal core only — The metal core of composite columns shall be designed to carry safely any construction or other loads to be placed upon them prior to their encasement in concrete.

B-4 Members Subjected to Combined Axial Load and Bending

A member subjected to axial load and bending (due to eccentricity of load, monolithic construction, lateral forces, etc) shall be considered safe provided the following conditions are satisfied:

where

$\sigma_{\mathrm{cc, cal}} =$ calculated direct compressive stress in concrete,

$\sigma_{\mathrm{cc}}$ = permissible axial compressive stress in concrete,

$\sigma_{\mathrm{cbc, cal}} =$ calculated bending compressive stress in concrete, and

$\sigma_{\mathrm{cbc}}$ = permissible bending compressive stress in concrete.

b) The resultant tension in concrete is not greater than 35 percent and 25 percent of the resultant compression for biaxial and uniaxial bending respectively, or does not exceed three-fourths, the 7 days modulus of rupture of concrete.

NOTES

1 $\sigma_{\mathrm{cc,cal}} = \frac{P}{A_{\mathrm{c}} + 1.5mA_{\mathrm{sc}}}$ for columns with ties where , and are defined in B-3.1 and is the modular ratio.

2 $\sigma_{\mathrm{cbc,cal}} = \frac{M}{Z}$ where $M$ equals the moment and equals modulus of section. In the case of sections subject to moments in two directions, the stress shall be calculated separately and added algebraically.

If the requirements specified in B-4.1 are not satisfied, the stresses in concrete and steel shall be calculated by the theory of cracked section in which the tensile resistance of concrete is ignored. If the calculated stresses are within the permissible stress specified in Tables 25, 26 and 27 the section may be assumed to be safe.

NOTE — The maximum stress in concrete and steel may be found from tables and charts based on the cracked section theory or directly by determining the no-stress line which should satisfy the following requirements:

a) The direct load should be equal to the algebraic sum of the forces on concrete and steel,

b) The moment of the external loads about any reference line should be equal to the algebraic sum of the moment of the forces in concrete (ignoring the tensile force in concrete) and steel about the same line, and

c) The moment of the external loads about any other reference lines should be equal to the algebraic sum of the moment of the forces in concrete (ignoring the tensile force in concrete) and steel about the same line.

B-4.3 Members Subjected to Combined Direct Load and Flexure

Members subjected to combined direct load and flexure shall be designed by limit state method as in 38.5 after applying appropriate load factors as given in Table 18.

B-5 Shear

B-5.1 Nominal Shear Stress

The nominal shear stress $\tau_{\mathrm{v}}$ in beams or slabs of uniform depth shall be calculated by the following equation:

where

$V =$ shear force due to design loads,

b = breadth of the member, which for flanged sections shall be taken as the breadth of the web, and

$d =$ effective depth.

B-5.1.1 Beams of Varying Depth

In the case of beams of varying depth, the equation shall be modified as:

B-5.2.1 The permissible shear stress in concrete in beams without shear reinforcement is given in Table 27.

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

NOTE — $A_{s}$ is that area of longitudinal tension reinforcement which continues at least one effective depth beyond the section being considered except at supports where the full area of tension reinforcement may be used provided the detailing conforms to 25.2.2 and 25.2.3.

B-5.2.1.1 For solid slabs the permissible shear stress in concrete shall be $k\tau_{\mathrm{c}}$ where $k$ has the value given below:

NOTE - This does not apply to flat slabs for which 30.6 shall apply.

B-5.2.2 Shear Strength of Members Under Axial Compression

For members subjected to axial compression P, the permissible shear stress in concrete $\tau_{c}$ given in Table 27, shall be multiplied by the following factor:

$\delta = 1 + \frac{5P}{A_{\mathrm{g}}f_{\mathrm{ck}}}$, but not exceeding 1.5.

where

$P =$ axial compressive force, in N;

$A_{\mathrm{g}} =$ gross area of the concrete section, in $\mathrm{mm}^2$; and

$f_{ck}$ = characteristic compressive strength of concrete.

B-5.2.3 With Shear Reinforcement

When shear reinforcement is provided the nominal shear stress $\tau_{\mathrm{cmax}}$ in beams shall not exceed $\tau_{\mathrm{c}}$ given in Table 28.

B-5.2.3.1 For slabs, $\tau_{\mathrm{v}}$ shall not exceed half the value of given in Table 28.

B-5.3 Minimum Shear Reinforcement

When $\tau_{\mathrm{v}}$ is less than $\tau_{\mathrm{c}}$ given in Table 27, minimum shear reinforcement shall be provided in accordance with 25.5.1.6.

When $\tau_{\mathrm{v}}$ exceeds $\tau_{\mathrm{c}}$ given in Table 27, shear reinforcement shall be provided in any of the following forms:

a) Vertical stirrups,

b) Bent-up bars along with stirrups, and

c) Inclined stirrups.

Where bent-up bars are provided, their contribution towards shear resistance shall not be more than half that of the total shear reinforcement.

Shear reinforcement shall be provided to carry a shear equal to $V - \tau_{\mathrm{c}}bd$. The strength of shear reinforcement $V_{\mathrm{s}}$ shall be calculated as below:

a) For vertical stirrups:

b) For inclined stirrups or a series of bars bent-up at different cross-sections:

c) For single bar or single group of parallel bars, all bent-up at the same cross-section:

where

$A_{sv} =$ total cross-sectional area of stirrup legs or bent-up bars within a distance

$s_{v}$ = spacing of the stirrups or bent-up bars along the length of the member,

$\tau_{\mathrm{c}} =$ design shear strength of the concrete,

b = breadth of the member which for flanged beams, shall be taken as the breadth of the web b_w,

$\sigma_{sv}$ = permissible tensile stress in shear reinforcement which shall not be taken greater than 230 N/mm $^{2}$ ,

$\alpha =$ angle between the inclined stirrup or bent-up bar and the axis of the member, not less than $45^{\circ}$, and

d = effective depth.

NOTE — Where more than one type of shear reinforcement is used to reinforce the same portion of the beam, the total shear resistance shall be computed as the sum of the resistance for the various types separately. The area of the stirrups shall not be less than the minimum specified in 25.5.1.6.

B-5.5 Enhanced Shear Strength of Sections Close to Supports

Shear failure at sections of beams and cantilevers without shear reinforcement will normally occur on plane inclined at an angle $30^{\circ}$ to the horizontal. If the angle of failure plane is forced to be inclined more steeply than this [because the section considered (X–X) in Fig. 24 is close to a support or for other reasons], the shear force required to produce failure is increased.

The enhancement of shear strength may be taken into account in the design of sections near a support by increasing design shear strength of concrete, $\tau_{c}$ to $2d\tau_{c}/a_{v}$ provided that the design shear stress at the face of support remains less than the values given in Table 28. Account may be taken of the enhancement in any situation where the section considered is closer to the face of a support of concentrated load than twice the effective depth, d. To be effective, tension reinforcement should extend on each side of the point where it is intersected by a possible failure plane for a distance at least equal to the effective depth, or be provided with an equivalent anchorage.

If shear reinforcement is required, the total area of this is given by:

This reinforcement should be provided within the middle three quarters of $a_{\mathrm{v}}$. Where $a_{\mathrm{v}}$ is less than $d$, horizontal shear reinforcement will be more effective than vertical.

B-5.5.3 Enhanced Shear Strength Near Supports (Simplified Approach)

The procedure given in B-5.5.1 and B-5.5.2 may be used for all beams. However, for beams carrying generally uniform load or where the principal load is located further than $2d$ from the face of support, the shear stress may be calculated at a section a distance $d$ from the face of support. The value of $\tau_{\mathrm{c}}$ is calculated in accordance with Table 27 and appropriate shear reinforcement is provided at sections closer to the support, no further check for such section is required.

B-6 Torsion

In structures where torsion is required to maintain equilibrium, members shall be designed for torsion in accordance with B-6.2, B-6.3 and B-6.4. However, for such indeterminate structures where torsion can be eliminated by releasing redundant restraints, no specific design for torsion is necessary provided torsional stiffness is neglected in the calculation of internal forces. Adequate control of any torsional cracking is provided by the shear reinforcement as per B-5.

NOTE — The approach to design in this clause for torsion is as follows:

Torsional reinforcement is not calculated separately from that required for bending and shear. Instead the total longitudinal reinforcement is determined for a fictitious bending moment which is a function of actual bending moment and torsion; similarly web reinforcement is determined for a fictitious shear which is a function of actual shear and torsion.

B-6.1.1 The design rules laid down in B-6.3 and B-6.4 shall apply to beams of solid rectangular cross-section. However, these clauses may also be applied to flanged beams by substituting $b_{w}$ for b, in which case they are generally conservative; therefore specialist literature may be referred to.

B-6.2 Critical Section

Sections located less than a distance $d$, from the face of the support may be designed for the same torsion as computed at a distance $d$, where $d$ is the effective depth.

B-6.3 Shear and Torsion

Equivalent shear, $V_{\mathrm{e}}$ shall be calculated from the formula:

where

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

$T =$ torsional moment, and

$b =$ breadth of beam.

The equivalent nominal shear stress, $\tau_{\mathrm{ve}}$, in this case shall be calculated as given in B-5.1, except for substituting $V$ by $V_{\mathrm{e}}$. The values of $\tau_{\mathrm{ve}}$ shall not exceed the values of given in Table 28.

B-6.3.2 If the equivalent nominal shear stress $\tau_{ve}$ does not exceed $\tau_{c}$ , given in Table 27, minimum shear reinforcement shall be provided as specified in 25.5.1.6.

B-6.3.3 If $\tau_{\mathrm{ve}}$ exceeds $\tau_{\mathrm{c}}$ given in Table 27, both longitudinal and transverse reinforcement shall be provided in accordance with B-6.4.

B-6.4 Reinforcement in Members Subjected to Torsion

B-6.4.1 Reinforcement for torsion, when required, shall consist of longitudinal and transverse reinforcement.

The longitudinal reinforcement shall be designed to resist an equivalent bending moment, $M_{\mathrm{el}}$, given by:

where

$M =$ bending moment at the cross-section, and

where $T$ is the torsional moment, $D$ is the overall depth of the beam and $b$ is the breadth of the beam.

B-6.4.2.1 If the numerical value of $M_{\mathrm{t}}$ as defined

in B-6.4.2 exceeds the numerical value of the moment M, longitudinal reinforcement shall be provided on the flexural compression face, such that the beam can also withstand an equivalent moment $M_{e2}$ given by $M_{e2} = M_{t} - M$ , the moment being taken as acting in the opposite sense to the moment M.