### REFERENCE MANUAL

**STRESS ANALYSIS**

Self-supporting monopoles may be treated as a vertical cantilever beam subjected to horizontal wind pressures and the self-weight. It may be analysed by beam theory for the purpose of determining the resulting longitudinal stresses. The only error introduced in the analysis of the stack shell by beam theory, as opposed to shell analysis, is the assumption that plane sections remain plane such that the stresses are proportional to the distances from the neutral axis. However, the error introduced by this assumption is small and conservative.

[Troitsky M.S.1990,* ‘Tubular Steel Structures – Theory and Design’, *p. 5-9]

**LAP JOINTS**

The minimum length of any telescopic (i.e. slip type) field splices for all structures shall be 1.5 times the inside diameter of the exposed end of the female section.

[American Association of State Highway and Transportation Officials 2013, *‘Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals’, *Section 5.14.9]

**DRAG FACTOR FOR CIRCULAR/18-SIDED/20-SIDED MONOPOLES**

Projections such as ladders and pipes from the side of the circular cylinder will promote flow separation for wind directions for which the project is at, or about, 90° from the windward generator. For those wind directions a drag coefficient of 1.2 should be used in the vicinity of the projection, irrespective of the value obtained for the “clean” cylinder. This value should be adopted along the axis of the cylinder for a length equal to one cylinder diameter, either side of the projection.

[Australasian Wind Engineering Society 2002, *‘Wind Loading Handbook for Australia and New Zealand’*, p. 67]

**VORTEX SHEDDING**

The character of the vortex shedding forces for circular cylinders depends on the Reynolds number. While shedding tends to be organized at sub-critical (Re < 3 x 10^{5}) and trans-critical (Re > 3 x 10^{6}) Reynolds numbers, it tends to be irregular in the critical range (3 x 10^{5} ≤ Re ≤ 3 x 10^{6}) unless the structural motion is sufficiently large to organise the fluctuating flow around the body. This phenomenon, referred to as “lock in”, becomes important for lightly damped members.

Vortex shedding tends to occur with steady continuous winds at a critical velocity. The velocity need not be very high, but it has been found that significant vibration does not occur unless the velocity is greater than 5 m/s. The periodic frequency of the vortex shedding can lock in on the natural frequency of the pole, resulting in very large alternating forces acting transverse to the wind flow direction. Occasionally, the vibration is so severe that fatigue cracks will appear.

Although vortex shedding can “lock in” and continue as the velocity increases or decreases slightly, if the velocity changes by more than 20 percent, the vortex shedding will stop. Gusty variable winds, such as might occur in a severe storm typically will not cause vortex shedding. In fact, if the wind velocity is greater than 15 m/s, the wind is generally too turbulent for vortex shedding to occur. In summary, the winds that are dangerous for vortex shedding are steady winds in the velocity range 5 to 15 m/s.

[Giosan, I, *‘Vortex Shedding Induced Loads on Free Standing Structures’*, p. 6]

The Strouhal number (St) is a dimensionless number relating vortex shedding frequency (n_{cr}) to wind speed (V_{cr}) and cross-sectional width (d).

For circular cross-sections, the Strouhal number varies with flow velocity and therefore the Reynolds number (R_{e}). Experimental investigation has shown that the Strouhal number changes between sub-critical, critical, and trans-critical ranges, though a constant value of 0.2 can be assumed for practical application to the analysis of structures.

CHECKPOLE assumes the following values depending on the cross-sectional shape:

CROSS-SECTION |
STROUHAL NUMBER |

Circular/18-sided/20-sided | 0.20 |

Square | 0.12 |

6-sided/8-sided/10-sided/12-sided/14-sided/16-sided | 0.16 |