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

NBC 2016 (SP 7:2016) Volume 1

2016 · PDF page 867

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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.

B-1.3 Assumptions for Design of Members

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.

B-2.1.1 Direct Tension

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:

Grade of Concrete	M10	M15	M20	M25	M30	M35	M40	M45	M50 and Above
Tensile Stress N/mm $^{2}$	1.2	2.0	2.8	3.2	3.6	4.0	4.4	4.8	5.2

The tensile stress shall be calculated as:

\frac {F _ {\mathrm{t}}}{A _ {\mathrm{e}} + m A _ {\mathrm{st}}}

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.

B-2.3 Increase in Permissible Stresses

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.

Table 25Permissible Stresses in Concrete (Clauses B-1.3, B-2.1, B-2.1.2, B-2.3 and B-4.2) All values in N/mm².

Sl No.	Grade of Concrete	Permissible Stress in Compression		Permissible Stress in Bond (Average) for Plain Bars in Tension
Sl No.	Grade of Concrete	Bending $\sigma_{\text{cbc}}$ (3)	Direct $\sigma_{\text{cc}}$ (4)	$\tau_{\text{bd}}$ (5)
(1)	(2)	Bending $\sigma_{\text{cbc}}$ (3)	Direct $\sigma_{\text{cc}}$ (4)	$\tau_{\text{bd}}$ (5)
i)	M 10	3.0	2.5	—
ii)	M 15	5.0	4.0	0.6
iii)	M 20	7.0	5.0	0.8
iv)	M 25	8.5	6.0	0.9
v)	M 30	10.0	8.0	1.0
vi)	M 35	11.5	9.0	1.1
vii)	M 40	13.0	10.0	1.2
viii)	M 45	14.5	11.0	1.3
ix)	M 50	16.0	12.0	1.4
x)	M 55	18.0	13.5	1.5
xi)	M 60	20.0	15.0	1.6
NOTES
1 The values of permissible shear stress in concrete are given in Table 27.
2 The bond stress given in col 4 shall be increased by 25 percent for bars in compression.

B-3 Permissible Loads in Compression Members

B-3.1 Pedestals and Short Columns with Lateral Ties

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:

P = \sigma_ {\mathrm{cc}} A _ {\mathrm{c}} + \sigma_ {\mathrm{sc}} A _ {\mathrm{sc}}

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.

B-3.2 Short Columns with Helical Reinforcement

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.

Table 26Permissible Stresses in Steel Reinforcement (Clauses B-2.2, B-2.2.1, B-2.3 and B-4.2)

Sl No.	Type of Stress in Steel Reinforcement	Permissible Stresses N/mm2
Sl No.	Type of Stress in Steel Reinforcement	Mild Steel Bars Conforming to Grade 1 of Accepted Standard [6-5A(42)]	Medium Tensile Steel Conforming to Accepted Standard [6-5A(42)]	High Yield Strength Deformed Bars Conforming to Accepted Standard [6-5A(36)] (Grade Fe 415)
(1)	(2)	(3)	(4)	(5)
i)	Tension ( $\sigma_{st}$ or $\sigma_{sv}$ )
	a) Up to and including 20 mm	140	Half the guaranteed yield	230
	b) Over 20 mm	130	stress subject to a maximum of 190	230
ii)	Compression in column bars ( $\sigma_{sc}$ )	130	130	190
iii)	Compression in bars in a beam or slab when the compressive resistance of the concrete is taken into account	The calculated compressive stress in the surrounding concrete multiplied by 1.5 times the modular ratio or $\sigma_{sc}$ whichever is lower
iv)	Compression in bars in a beam or slab where the compressive resistance of the concrete is not taken into account:
	a) Up to and including 20 mm	140	Half the guaranteed yield	190
	b) Over 20 mm	130	stress subject to a maximum of 190	190
NOTES
1 For high yield strength deformed bars of Grade Fe 500 the permissible stress in direct tension and flexural tension shall be 0.55 $f_y$ . The permissible stresses for shear and compression reinforcement shall be as for Grade Fe 415.
2 For welded wire fabric conforming to accepted standard [6-5A(43)], the permissible value in tension $\acute{o}_{st}$ is 230 N/mm2.
3 For the purpose of this standard, the yield stress of steels for which there is no clearly defined yield point should be taken to be 0.2 percent proof stress.
4 When mild steel conforming to Grade II of accepted standard [6-5A(42)] is used, the permissible stresses shall be 90 percent of the permissible stresses in col 3, or if the design details have already been worked out on the basis of mild steel conforming to Grade 1 of accepted standard [6-5A(42)]; the area of reinforcement shall be increased by 10 percent of that required for Grade 1 steel.

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

B-3.3 Long Columns

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:

C _ {\mathrm{r}} = 1. 2 5 - \frac {l _ {\mathrm{ef}}}{4 8 b}

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:

C _ {\mathrm{r}} = 1. 2 5 - \frac {l _ {\mathrm{ef}}}{1 6 0 i _ {\min}}

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

B-3.4 Composite Columns

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:

P = \sigma_ {\mathrm{cc}} A _ {\mathrm{c}} + \sigma_ {\mathrm{sc}} A _ {\mathrm{sc}} + \sigma_ {\mathrm{mc}} A _ {\mathrm{m}}

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

B-4.1 Design Based on Uncracked Section

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:

\text {a)} \quad \frac {\sigma_ {\mathrm{cc,cal}}}{\sigma_ {\mathrm{cc}}} + \frac {\sigma_ {\mathrm{cbc,cal}}}{\sigma_ {\mathrm{cbc}}} \leq 1

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 $P$ , $A_{\mathrm{c}}$ and $A_{\mathrm{sc}}$ are defined in B-3.1 and $m$ is the modular ratio.

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

B-4.2 Design Based on Cracked Section

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:

\tau_ {\mathrm{v}} = \frac {V}{b d}

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:

\tau_ {\mathrm{v}} = \frac {V \pm \frac {M \tan \beta}{d}}{b d}

where

$\tau_{\mathrm{v}}, V, b$ and $d$ are the same as in B-5.1.

$M =$ bending moment at the section, and

$\beta =$ angle between the top and the bottom edges of the beam.

The negative sign in the formula applies when the bending moment M increases numerically in the same direction as the effective depth d increases, and the positive sign when the moment decreases numerically in this direction.