Chapter 17Working Stress Design

NBC 2016 (SP 7:2016) Volume 1

2016 · PDF page 1035

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17.1 General

17.1.1 General design requirements of Section 6(c) shall apply in this section.

17.1.2 Methods of structural analysis of Section 6(d) shall also apply to this section. The elastic analysis method shall be used in the working stress design.

17.1.3 The working stress shall be calculated applying respective partial safety factors for loads, specified in Table 4 for the limit states of serviceability.

17.1.4 In load combinations involving wind or seismic loads, the permissible stresses in steel structural members may be increased by 33 percent. For anchor bolts and construction loads this increase shall be limited to 25 percent. Such an increase in allowable stresses should not be considered if the wind or seismic load is the major load in the load combination (such as acting along with dead load alone).

17.2 Tension Members

17.2.1 Actual Tensile Stress

The actual tensile stress, $f_{\mathrm{t}}$ on the gross area of cross-section, $A_{\mathrm{g}}$ of plates, angles and other tension members shall be less than or equal to the smaller value of permissible tensile stresses, $f_{\mathrm{at}}$ , as given below:

Actual tensile stress, $f_{\mathrm{t}} = T_{\mathrm{s}} / A_{\mathrm{g}}$

The permissible stress, $f_{\mathrm{at}}$ is smallest of the values as obtained below:

a) As governed by yielding of gross section:

f _ {\mathrm{at}} = 0. 6 f _ {\mathrm{y}}

b) As governed by rupture of net section

Plates under tension:

f _ {\mathrm{at}} = 0. 6 9 T _ {\mathrm{dn}} / A _ {\mathrm{g}}

Angles under tension:

f _ {\mathrm{at}} = 0. 6 9 T _ {\mathrm{dn}} / A _ {\mathrm{g}}

c) As governed by block shear:

f _ {\mathrm{at}} = 0. 6 9 T _ {\mathrm{db}} / A _ {\mathrm{g}}

where

\begin{array}{r c l} T _ {\mathrm{s}} & = & \text {actual tension under working (service)} \\ & & \text {load,} \end{array}

$A_{\mathrm{g}} =$ gross area,

$T_{dn} =$ design strength in tension of respective plate/angle calculated in accordance with 12.3, and

$T_{db} =$ design block shear strength in tension of respective plate/angle calculated in accordance with 12.4.

17.3 Compression Members

17.3.1 Actual Compressive Stress

The actual compressive stress, $f_{\mathrm{c}}$ at working (service) load, $P_{\mathrm{s}}$ of a compression member shall be less than or equal to the permissible compressive stress, $f_{\mathrm{ac}}$ as given below:

17.4 Members Subjected to Bending

17.4.1 Bending Stresses

The actual bending tensile and compressive stresses, $f_{bt}$ , $f_{bc}$ at working (service) load moment, $M_s$ of a bending member shall be less than or equal to the permissible bending stresses, , respectively, as given herein. The actual bending stresses shall be calculated as:

17.5 Combined Stresses

17.5.1 Combined Bending and Shear

Reduction in allowable moment need not be considered under combined bending and shear.

17.5.2 Combined Bending and Axial Force

Members subjected to combined axial compression and bending shall be so proportioned to satisfy the following requirements:

a) Member stability requirement:

\frac {f _ {\mathrm{c}}}{f _ {\mathrm{acy}}} + 0. 6 K _ {\mathrm{y}} \frac {C _ {\mathrm{my}} f _ {\mathrm{bcy}}}{f _ {\mathrm{abcy}}} + K _ {\mathrm{LT}} \frac {f _ {\mathrm{bcz}}}{f _ {\mathrm{abcz}}} \leq 1. 0;

17.6 Connections

17.6.1 All design provisions of Section 6(k), except for the actual and permissible stress calculations, shall apply.

17.6.2 Actual Stresses in Fasteners

17.6.2.1 Actual stress in bolt in shear, $f_{sb}$ should be less than or equal to permissible stress of the bolt, $f_{asb}$ as given below:

The actual stress in bolt in shear, $f_{s b} = V_{s b} /$

Section 6 (n) Design and Detailing for Earthquake Loads

actual tension under working (service)load,

ac

Actual compressive stress, $f_{\mathrm{c}} = P_{\mathrm{s}} / A_{\mathrm{e}}$

The permissible compressive stress, $f_{\mathrm{ac}} = 0.60f_{\mathrm{cd}}$

where

$A_{\mathrm{e}} =$ effective sectional area as defined in 13.3.2, and

$f_{cd}$ = design compressive stress as defined in 13.1.2.1 (for angles, see 13.5.1.2), calculated without the partial safety factor, $\gamma_{m0}$ .

17.3.2 Design Details

Design of the compression members shall conform to 13.3.

17.3.3 Column Bases

The provisions of 13.4 shall be followed for the design of column bases, except that the thickness of a simple column base, $t_{\mathrm{s}}$ shall be calculated as:

t _ {\mathrm{s}} = \sqrt {3 w \left(a ^ {2} - 0 . 3 b ^ {2}\right) / f _ {\mathrm{bs}}}

where

w = uniform pressure from below on the slab base due to axial compression;

$a, b =$ larger and smaller projection of the slab base beyond the rectangle circumscribing the column, respectively; and

$f_{\mathrm{bs}} =$ permissible bending stress in column base equal to $0.75f_{\mathrm{y}}$

17.3.4 Angle Struts

Provisions of 13.5 shall be used for design of angle struts, except that the limiting actual stresses shall be calculated in accordance with 17.3.1.

17.3.5 Laced and Battened Columns

The laced and battened columns shall be designed in accordance with 13.6 and 13.7, except that the actual stresses shall be less than the permissible stresses given in 17.3.1.

s

f_{abt}, f_{abc}

f _ {\mathrm{bc}} = M _ {\mathrm{s}} / Z _ {\mathrm{ec}} \quad \text {and} \quad f _ {\mathrm{bt}} = M _ {\mathrm{s}} / Z _ {\mathrm{et}}

The permissible bending stresses, $f_{\mathrm{abc}}$ or $f_{\mathrm{abt}}$ shall be the smaller of the values obtained from the following:

a) Laterally supported beams and beams bending about the minor axis:

i) Plastic and compact sections:

f _ {\mathrm{abc}} \text {or} f _ {\mathrm{abt}} = 0. 6 6 f _ {\mathrm{y}}

ii) Semi-compact sections:

f _ {\mathrm{abc}} \text {or} f _ {\mathrm{abt}} = 0. 6 0 f _ {\mathrm{y}}

b) Laterally unsupported beams subjected to major axis bending:

\begin{array}{l} f _ {\mathrm{abc}} = 0. 6 0 M _ {\mathrm{d}} / Z _ {\mathrm{ec}} \\ f _ {\mathrm{abt}} = 0. 6 0 M _ {\mathrm{d}} / Z _ {\mathrm{et}} \end{array}

c) Plates and solid rectangles bending about minor axis:

f _ {\mathrm{abc}} = f _ {\mathrm{abt}} = 0. 7 5 f _ {\mathrm{y}}

where

$Z_{ec}, Z_{et} =$ elastic section modulus for the cross-section with respect to extreme compression and tension fibres, respectively;

$f_{\mathrm{y}}$ = yield stress of the material; and

$M_{d}$ = design bending strength of a laterally unsupported beam bent about major axis, calculated in accordance with 14.2.2.

17.4.2 Shear Stress in Bending Members

The actual shear stress, $\tau_{\mathrm{b}}$ at working load, $V_{\mathrm{s}}$ of a bending member shall be less than or equal to the permissible shear stress, $\tau_{\mathrm{ab}}$ given below:

Actual shear stress, $\tau_{b} = V_{\mathrm{s}} / A_{\mathrm{v}}$

The permissible shear stress is given by:

a) When subjected to pure shear:

\tau_ {\mathrm{ab}} = 0. 4 0 f _ {\mathrm{y}}

b) When subjected to shear buckling (see 14.4.2.1):

\tau_ {\mathrm{ab}} = 0. 7 0 V _ {\mathrm{n}} / A _ {\mathrm{v}}

where

$V_{\mathrm{n}} =$ deesign shear strength as given in 14.4.2.2 (a), and

$A_{v}$ = shear area of the cross-section as given in 14.4.1.

17.4.3 Plate Girder

Provisions of 14.3, 14.4, 14.5, 14.6 and 14.7 shall apply, for the design of plate girder, except that the allowable stresses shall conform to 17.4.1 and 17.4.2.

17.4.4 Box Girder

In design of box girder the provisions of 14.8 shall apply, except that the allowable bending stresses shall conform to 17.4.1.

acy

fc

+

0.6KyfabcyCmyfbcy+

KLTfabczfbcz≤

1.0;

\frac {f _ {\mathrm{c}}}{f _ {\mathrm{acz}}} + 0. 6 K _ {\mathrm{y}} \frac {C _ {\mathrm{my}} f _ {\mathrm{bcy}}}{f _ {\mathrm{abcy}}} + K _ {\mathrm{z}} \frac {C _ {\mathrm{mz}} f _ {\mathrm{bcz}}}{f _ {\mathrm{abcz}}} \leq 1. 0

where

$C_{my}, C_{mz} = \text{equivalent uniform moment factor as per Table 18,}$

$f_{c}$ = applied axial compressive stress under service load,

$f_{\mathrm{bcy}}, f_{\mathrm{bcz}} =$ applied compressive stresses due to bending about the major $(y)$ and minor $(z)$ axis of the member, respectively,

$f_{acy}, f_{acz}$ = allowable axial compressive stress as governed by buckling about minor (y) and major (z) axis, respectively,

$f_{abcy}, f_{abcz} =$ allowable bending compressive stresses due to bending about minor (y) and major (z) axes of the cross-section (see 17.4),

K _ {\mathrm{y}} \quad = \quad 1 + (\lambda_ {\mathrm{y}} - 0. 2) n _ {\mathrm{y}} \leq 1 + 0. 8 n _ {\mathrm{y}},

K _ {\mathrm{z}} \quad = 1 + (\lambda_ {\mathrm{z}} - 0. 2) n _ {\mathrm{z}} \leq 1 + 0. 8 n _ {\mathrm{z}},

K _ {\mathrm{LT}} \quad = 1 - \frac {0 . 1 \lambda_ {\mathrm{LT}} n _ {\mathrm{y}}}{\left(C _ {\mathrm{mLT}} - 0 . 2 5\right)} \geq

1 - \frac {0 . 1 n _ {\mathrm{y}}}{\left(C _ {\mathrm{mLT}} - 0 . 2 5\right)},

PART 6 STRUCTURAL DESIGN — SECTION 6 STEEL

where

$n_{y}, n_{z}$ = ratio of actual applied axial stress to the allowable axial stress for buckling about the y and z axis, respectively,

$C_\mathrm{mLT} =$ equivalent uniform moment factor; and

$\lambda_{LT}$ = non-dimensional slenderness ratio (see 14.2.2).

b) Member strength requirement:

At a support the values $f_{\mathrm{abcy}}$ and $f_{\mathrm{abcz}}$ shall be calculated using laterally supported member and shall satisfy:

\frac {f _ {\mathrm{c}}}{0 . 6 f _ {\mathrm{y}}} + \frac {f _ {\mathrm{bcy}}}{f _ {\mathrm{abcy}}} + \frac {f _ {\mathrm{bcz}}}{f _ {\mathrm{abcz}}} \leq 1. 0

17.5.3 Combined Bending and Axial Tension

Members subjected to both axial tension and bending shall be proportioned so that the following condition is satisfied:

\frac {f _ {\mathrm{t}}}{f _ {\mathrm{at}}} + \frac {f _ {\mathrm{bty}}}{f _ {\mathrm{abty}}} + \frac {f _ {\mathrm{btz}}}{f _ {\mathrm{abtz}}} \leq 1. 0

where

$f_{abty}, f_{abtz} =$ permissible tensile stresses under bending about minor (y) and major (z) axis when bending alone is acting, as given in 17.4.1.

17.5.4 Combined Bearing, Bending and Shear Stresses

Where a bearing stress is combined with tensile or compressive stress, bending and shear stresses under the most unfavourable conditions of loading, the equivalent stress, $f_{e}$ obtained from the following formula, shall not exceed $0.9f_{y}$

f _ {\mathrm{e}} = \sqrt {f _ {\mathrm{b}} ^ {2} + f _ {\mathrm{p}} ^ {2} + f _ {\mathrm{b}} f _ {\mathrm{p}} + 3 \tau_ {\mathrm{b}} ^ {2}}

where

\tau_ {\mathrm{b}} = \text {actual shear stress},

f _ {\mathrm{t}} = \text {actual tensile stress,}

$f_{\mathrm{b}} =$ actual bending stress,

f _ {\mathrm{y}} = \text {yield stress, and}

f _ {\mathrm{p}} = \text {actual bearing stress}.

The value of permissible bending stresses $f_{\mathrm{bcy}}$ and $f_{\mathrm{bcz}}$ to be used in the above formula shall each be lesser of the values of the maximum allowable stresses $f_{\mathrm{abc}}$ and in bending about appropriate axis.

f_{sb} = V_{sb} / A_{sb}

The permissible stress in bolt in shear, $f_{asb} = 0.60 V_{nsb} / A_{sb}$

where

$V_{\mathrm{sb}} =$ actual shear force under working (service) load,

$V_{\mathrm{nsb}} =$ nominal shear capacity of the bolt as given in 16.3.3, and

$A_{\mathrm{sb}} =$ nominal plain shank area of the bolt.

17.6.2.2 Actual stress of bolt in bearing on any plate, $f_{\mathrm{pb}}$ should be less than or equal to the permissible bearing stress of the bolt/plate, $f_{\mathrm{apb}}$ as given below:

Actual stress of bolt in bearing on any plate, $f_{pb} = V_{sb} / A_{pb}$

The permissible bearing stress of the bolt/plate, $f_{apb} = 0.60 V_{npb} / A_{pb}$

where

$V_{npb}$ = nominal bearing capacity of a bolt on any plate as given in 16.3.4, and

$A_{\mathrm{pb}} =$ nominal bearing area of the bolt on any plate.

17.6.2.3 Actual tensile stress of the bolt, $f_{\mathrm{tb}}$ should be less than or equal to permissible tensile stress of the bolt, $f_{\mathrm{atb}}$ as given below:

Actual tensile stress of the bolt, $f_{\mathrm{tb}} = T_{\mathrm{s}} / A_{\mathrm{sb}}$

The permissible tensile stress of the bolt, $f_{atb} = 0.60 T_{nb}/A_{sb}$

where

$T_{\mathrm{s}} =$ tension in bolt under working (service) load,

$T_{nb} =$ design tensile capacity of a bolt as given in 16.3.5, and

A _ {\mathrm{sb}} = \text {nominal plain shank area of the bolt.}

17.6.2.4 Actual compressive or tensile or shear stress of a weld, $f_{\mathrm{w}}$ should be less than or equal to permissible stress of the weld, $f_{\mathrm{aw}}$ as given below:

The permissible stress of the weld, $f_{\mathrm{aw}} = 0.6f_{\mathrm{wn}}$

where

$f_{wn} =$ nominal shear capacity of the weld as calculated in 16.5.7.1.1.

17.6.2.5 If the bolt is subjected to combined shear and tension, the actual shear and axial stresses calculated in accordance with 17.6.2.1 and 17.6.2.3 do not exceed

the respective permissible stresses $f_{\mathrm{asb}}$ and $f_{\mathrm{atb}}$ and the expression given below should satisfy:

\left[ \frac {f _ {\mathrm{sb}}}{f _ {\mathrm{asb}}} \right] ^ {2} + \left[ \frac {f _ {\mathrm{tb}}}{f _ {\mathrm{atb}}} \right] ^ {2} \leq 1. 0

where

\begin{array}{r l} f _ {\mathrm{sb}}, f _ {\mathrm{tb}} & = \text {actual shear and tensile stresses,} \\ & \text {respectively; and} \end{array}

$f_{asb}, f_{atb} = \text{permissible shear and tensile stresses respectively.}$

17.6.3 Stresses in Welds

17.6.3.1 Actual stresses in the throat area of fillet welds shall be less than or equal to permissible stresses, $f_{aw}$ , as given below:

f _ {\mathrm{aw}} = 0. 4 f _ {\mathrm{y}}

17.6.3.2 Actual stresses in the butt welds shall be less than the permissible stress as governed by the parent metal welded together.

+

≤

fb

fp

+

3

τb2

abc

f_{\mathrm{abt}}