Annex E(Clause 4.4.3.3)

NBC 2016 (SP 7:2016) Volume 1

2016 · PDF page 525

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Effect of a Cliff or Escarpment on Equivalent Height Above Ground ( $k\{3\}$ Factor)

E-1 The influence of the topographic feature is considered to extend $1.5 L_{e}$ upwind and $2.5 L_{e}$ downwind of the summit of crest of the feature where $L_{e}$ is the effective horizontal length of the hill depending on slope as indicated below (see Fig. 23):

\begin{array}{c} \text {Slope} \\ 3 ^ {\circ} < \theta_ {\mathrm{s}} \leq 1 7 ^ {\circ} \\ \theta_ {\mathrm{s}} > 1 7 ^ {\circ} \end{array}

\begin{array}{c} L _ {\mathrm{e}} \\ L \\ Z / 0. 3 \end{array}

where

$L =$ actual length of the upwind slope in the wind direction,

$Z =$ effective height of the topography feature, and

$\theta_{s} =$ upwind slope in the wind direction.

In case, the zone in downwind side of the crest of the feature is relatively flat ( $\theta_{s} < 3^{\circ}$ ) for a distance exceeding $L_{e}$ , then the feature should be treated as an escarpment. Otherwise the feature should be treated as a hill or ridge. Examples of typical features are given in Fig. 23.

1 No difference is made, in evaluating $k_{3}$ between a three dimensional hill and two dimensional ridge.

2 In undulating terrain, it is often not possible to decide whether the local topography to the site is significant in terms of wind flow. In such cases, the average value of the terrain upwind of the site for a distance of $5\mathrm{km}$ should be taken as the base level from wind to assess the height, $Z$ , and the upwind slope $\theta$ , of the feature.

E-2 Topography Factor, $K\{3\}$

The topography factor $K_{3}$ is given by the following:

K _ {3} = 1 + C s _ {0}

Wind Force on Circular Sections

F-1 The wind force on any object is given by:

F = C _ {\mathrm{f}} A _ {\mathrm{e}} \rho_ {\mathrm{d}}

where

$C_{}$ force coefficient;

∘

θs>17∘

1

+

Cs0

where $C$ has the following values:

Slope	C
$3^{\circ} < \theta_{s} \leq 17^{\circ}$	1.2 (Z/L)
$\theta_{s} > 17^{\circ}$	0.36

and $s_{0}$ is a factor derived in accordance with E-2.1 appropriate to the height, H above mean ground level and the distance, X, from the summit or crest relative to the effective length, $L_{e}$

E-2.1 The factor, $s_0$ should be determined from:

a) Figure 24 for cliffs and escarpments, and

b) Figure 25 for ridges and hills.

NOTE — Where the downwind slope of a hill or ridge is more than $3^{\circ}$ , there will be large regions of reduced accelerations or even shelter and it is not possible to give general design rules to cater for these circumstances. Values of $s_{0}$ from Fig. 25 may be used as upper bound values.

23A General Notations

FIG. 23 DEFINITION OF TOPOGRAPHICAL DIMENSIONS

PART 6 STRUCTURAL DESIGN — SECTION 1 LOADS, FORCES AND EFFECTS

Chart

FIG. 24 FACTOR $S_{0}$ FOR CLIFF AND ESCARPMENT

Chart

FIG. 25 FACTOR $S_0$ FOR RIDGE AND HILL

ANNEX F

[Clauses 4.5.4.2.2, 4.5.4.3.2 (c) and 4.5.4.3.3]

C_{f} =

$A_{e}$ = effective area of the object normal to the wind direction; and

$\rho_{\mathrm{d}} =$ design pressure of the wind.

For most shapes, the force coefficient remains approximately constant over the whole range of wind speeds likely to be encountered. However, for objects of circular cross-section, it varies considerably.

For a circular section, the force coefficient depends on the way in which the wind flows around it and is dependent upon the velocity and kinematic viscosity of the wind and diameter of the section. The force coefficient is usually quoted against a non-dimensional parameter, called the Reynolds number, which takes into account of the velocity and viscosity of the flowing medium (in this case the wind), and the member diameter.

Reynolds number, $R_{\mathrm{e}} = \frac{D\overline{V}_{\mathrm{d}}}{\nu}$

where

D = diameter of the member,

$\overline{V}_{\mathrm{d}} =$ design hourly mean wind speed, and

v = kinematic viscosity of the air which is $1.46 \times 10^{-5}$ m $^{2}$ /s at 15°C and standard atmospheric pressure.

Since in most natural environments likely to be found in India, the kinematic viscosity of the air is fairly constant, it is convenient to use $D\overline{V}_{\mathrm{d}}$ as the parameter instead of Reynolds number and this has been done in this Section.

The dependence of a circular section's force coefficient on Reynolds number is due to the change in the wake developed behind the body.

At a low Reynolds number, the wake is as shown in Fig. 26 and the force coefficient is typically 1.2. As Reynolds number is increased, the wake gradually changes to that shown in Fig. 27, that is, the wake width $d_{\mathrm{w}}$ decreases and the separation point, denoted as $sp$ , moves from front to the back of the body.

FIG. 26 WAKE IN SUB-CRITICAL FLOW

FIG. 27 WAKE IN SUPER-CRITICAL FLOW

As a result, the force coefficient shows a rapid drop at a critical value of Reynolds number followed by a gradual rise as Reynolds number is increased still further.

The variation of $C_{f}$ with parameter $D\overline{V}_{d}$ is shown in Fig. 5 for infinitely long circular cylinders having various values of relative surface roughness ( $\varepsilon/D$ ) when subjected to wind having an intensity and scale of turbulence typical of built-up urban areas. The curve for a smooth cylinder ( $\varepsilon/D = 1 \times 10^{-5}$ ) in a steady air stream, as found in a low-turbulence wind tunnel, is also shown for comparison.

It can be seen that the main effect of free-stream turbulence is to decrease the critical value of the parameter. For subcritical flows, turbulence can produce a considerable reduction in $C_{f}$ below the steady air-stream values. For supercritical flows, this effect becomes significantly smaller.

If the surface of the cylinder is deliberately roughened, such as by incorporating flutes, riveted construction, etc, then the data given in Fig. 5 for appropriate value of $\varepsilon / D > 0$ shall be used.

NOTE — In case of uncertainty regarding the value of e to be used for small roughness, $\varepsilon / D$ shall be taken as 0.001.

PART 6 STRUCTURAL DESIGN — SECTION 1 LOADS, FORCES AND EFFECTS

Effect of a Cliff or Escarpment on Equivalent Height Above Ground ( k{3}k\{3\}k{3} Factor)

E-2 Topography Factor, K{3}K\{3\}K{3}

Wind Force on Circular Sections

Effect of a Cliff or Escarpment on Equivalent Height Above Ground ( $k\{3\}$ Factor)

E-2 Topography Factor, $K\{3\}$