TABLE OF CONTENTS

• Summary
• Neara
  • Enable Feature
  • Configure Feature
  • Implementation Details
    • Static Analysis
      • Span M(z,cat)
      • Pole M(z,cat)
    • FEA
  • Validate Feature
    • Static Analysis
      • Validate Span M(z,cat)
      • Validate Pole M(z,cat)
    • FEA
• AS/NZS7000:2016 Theory
  • Synoptic M(z,cat)
  • Downdraft M(z,cat)

Summary

M(z,cat) is a multiplier applied to the regional wind speed to take into account the terrain category and the height above ground. Terrains where there are few obstructions will have higher wind speeds as will structure and spans higher above the ground. At the end of this document are useful reference formulas from AS/NZS7000:2016. 

Neara

Enable Feature

M(z,cat) is a feature that is specific for Australia and New Zealand and hence Neara needs to apply a configuration setting to enable this feature. To test if this feature has been enabled go to Project -> Design Settings and see if the option Default Mzcat Terrain Category is there. If it is not please contact Neara to have this enabled.

Configure Feature

The first step to using M(z,cat) is to set up environments with either synoptic or downdraft conditions in the Height Factor column as can be seen below. Note any environment without synoptic or downdraft in the Height Factor column will not apply M(z,cat).The Gust Factor column to the left of the Height Factor column enables SRF/TSRF.

Next each span needs to have a terrain category assigned to it. To do this create a custom report with Spans (for help creating custom reports see How To Create Custom Reports).  

Next in the report fill in the terrain category for each span. Note there are options for bulk editing and filtering to make this task easier. 

Clicking on a category will bring a drop down of available options. 

Note there is a D - Project Default setting. This is configured in the Project -> Design Settings with the Default Mzcat Terrain Category setting.

Implementation Details

There are two different implementations of M(z,cat). The first is for static analysis and the second is for FEA. In static analysis the decision was made to use a single wind multiplier for the entire strain section due to the ruling span. However in FEA the wind speed multipliers are calculated on a span by span basis. Hence there could be some discrepancies between static analysis and FEA.

Static Analysis

The implementation of M(z,cat) within static analysis uses a single wind speed multiplier for the entire strain section which the highest M(z,cat) value for the strain section. Note this means that a tee structure with different strain sections attached could have different M(z,cat) values applied to each section.  

Span M(z,cat)

Within Neara the M(z,cat) is calculated using the following steps.

Step 1: Average Height Above Ground

The average height above ground is calculated for each span in strain section. For each span 10 samples are taken starting at 5% along the span and finishing at 95% along the span. 

Step 2: M(z,cat) for Every Span

Both synoptic and downdraft M(z,cat) is then calculated for each span in a strain section. Downdraft m(z,cat) is independent of the terrain category. Synoptic uses linear interpolation of both category and height from Table 4.1 AS/NZS1170.2:2011. 

Example calculation of synoptic M(z,cat):

A Terrain Category (TC) of 2.5 and average span height of 28m would be the linear interpolation of the 20m entries for TC2 (1.08) and TC3 (0.94) => (1.08 + 0.94) / 2 = 1.01 and the 30m entries TC2 (1.12) and TC3 (1.00) => (1.12 + 1.00) / 2 = 1.06. The calculation would be: 1.01 + (28 - 20) * (1.06 - 1.01) / (30 - 20) = 1.05.

Step 3: Select Largest M(z,cat) Multiplier

The final step is to select the highest synoptic and downdraft M(z,cat) multiplier for each strain section and then use these for all relevant calculations in the strain section. 

Pole M(z,cat)

For synoptic wind, the worst case terrain category of spans connected to the structure will be used. However for downdraft wind the terrain category is not taken into account (as per the equation). 

For both synoptic and downdraft half of the structure height above ground will be used in the equation to calculate M(z,cat). For synoptic linear interpolation is used between categories and height entries. 

FEA

This section still needs to be written.

Validate Feature

This section covers examples of how to validate the M(z,cat) implementation. 

Static Analysis

Validate Span M(z,cat)

To validate the value of M(z,cat) calculated for a span create a custom report with Spans -> Environments (for help creating custom reports see How To Create Custom Reports).  

The field Wind Speed Multiplier is the overall multiplication of all the multipliers; M(z,cat) being one of them. For the moment Neara has only implemented M(z,cat) so the other factors are set to 1. Note the wind speed multipliers apply to the wind speed, not the wind pressure (wind pressure is proportion to wind speed squared).

Consider the below example with a span between two mountains each 100m tall and a valley between them. The terrain category is set to 2. A filter has been applied to the environments to only show the results for the synoptic and downdraft case. For the example below the downdraft M(z,cat) is 0.79 which by rearranging equation B2 in AS/NZS7000:2016 (H = 150 - 100xM(z,cat)) would mean the average height above ground here was about 71m which looks correct (noting that the height above ground is less than 100m near the structures).

Also for the synoptic the value is 1.21 which is the linear interpolation between the 50m and 75m, 1.18 and 1.22 (Table 4.1 from AS/NZS 1170.2:2011). That is 1.18 + (1.22 - 1.18)*(71-50)/(75-50) = 1.21. 

To validate how it applies M(z,cat) to the wind speed consider this example where there is a straight line between two mountains. The span lengths are 143.62m and 353.38m and synoptic M(z,cat) of 1.256285 and 1.125562 respectively. There is a single conductor with diameter 27mm at the top of all the poles. We will consider the loading on the middle pole due to the conductors (no wind on pole to simplify example). The environment is set up with a wind pressure of 1000 Pa and there are no load factors applied. 

Firstly the higher M(z,cat) value of 1.256285 will be used. Note that the multiplier applies to the wind speed not the wind pressure and hence in the calculation the pressure is converted to a wind speed and then back to a pressure again. 

The hand calculation for the tip load would be:

Since in the model the conductor has been moved to the top of the pole the force calculated in the hand calc can be compared with the tip load. In the screen shot below the tip load calculated by Neara is calculated as 10.59kN which is the same result as the hand calc.

Validate Pole M(z,cat)

For this test three environments have been set up with wind only on the poles (no wind on the conductors).

Test 1: Tip Load With No M(z,cat)

A pole has also been set up which is 10m out of the ground with a diameter of 0.5m (no taper). The tip load on this pole is calculated with the following formula:

Hence using the data provided the tip load should be:

This matches the "max" environment which has no M(z,cat) applied.

Test 2: Synoptic M(z,cat)

To now test the Synoptic case the pole is 40m tall, diameter is 1m and has a span either side of the pole with no angle. The terrain category on one side is 2 and the other side of 3 as shown below. 

In this case the worst of the terrain categories would be selected which is TC2. This along with half the pole height; 20m would be used to look up the synoptic M(z,cat) for the pole which in this case would be 1.08. Hence the tip load on the pole should be:

This matches the result in Neara as can be seen below:

Test 3: Downdraft M(z,cat)

For the downdraft case the pole would need to be over 100m to get a reduction in the wind pressure due to a down draft. This is due to half the pole height being used in the formula. Hence for the purpose of validation the pole will be set to 150m tall and 1m in diameter. The reference height would be 75m (half the pole height) and hence the downdraft M(z,cat) would be calculated as:

This matches the calculation in Neara as can be seen below:

FEA

This section is still to be written.

AS/NZS7000:2016 Theory

M(z,cat) is a multiplier applied to the regional wind speed to take into account the terrain category and the height above ground. Terrains where there are few obstructions will have higher wind speeds as will structure and spans higher above the ground.

AS/NZS1170.2:2021 defines how to calculate M(z,cat) for synoptic winds and AS/NZS7000:2016 defines how to calculate M(z,cat) for downdraft winds. 

Synoptic M(z,cat)

AS/NZS1170.2:2021 defines the following terrain categories:

Terrain Category 1 (TC1) - Very exposed open terrain with very few or no obstructions, and all water surfaces (e.g. flat, treeless, poorly grassed plains; open ocean, rivers, canals, bays and lakes) 

Terrain Category 2 (TC2) - Open terrain, including grassland, with well-scattered obstructions having heights generally from 1.5m to 5m, with no more than two obstructions per hectare (e.g. farmland and cleared subdivisions with isolated trees and uncut grass).

Terrain Category 2.5 (TC2.5) - Terrain with some trees or isolated obstructions, terrain isolated obstructions, terrain in developing outer urban areas with scattered houses, or large acreage developments with more than two and less than 10 buildings per hectare.

Terrain Category 3 (TC3) - Terrain with numerous closely spaced obstructions having heights generally from 3 m to 10 m. The minimum density of obstructions shall be at least the equivalent of 10 house-size obstructions per hectare (e.g. suburban housing, light industrial estates or dense forests).

Terrain Category 4 (TC4) - Terrain with numerous large, high (10 m to 30 m tall) and closely-spaced constructions, such as large city centres and well-developed industrial complexes.

M(z,cat) is calculated using the height above ground, the terrain category and Table 4.1 from AS/NZS 1170.2:2011 shown below. For the intermediate categories linear interpolation is used.  

Table 4.1 AS/NZS1170.2:2011

Downdraft M(z,cat)

AS/NZS7000:2016 appendix B defines the downdraft M(z,cat) using the following formula: