Why is it important to check the criteria of the Equivalent Static Method?

This article stresses the importance of verifying the Equivalent Static Method (ESM) when analysing telecom towers, as heavier 5G antennas often exceed its limits. Factors like equipment weight, placement, and shielding accuracy can determine whether static or spectral analysis is needed. Shapemaker automates this verification, ensuring safety while simplifying the process.

Andrzej Baczkowicz
Andrzej Baczkowicz
Aug 26, 2025
3
min read
Why is it important to check the criteria of the Equivalent Static Method?

In the practice of steel structural analysis of telecommunication towers in Europe, the methodology described in standard EN 1993-3-1 – Design of steel structures Part 3-1: Towers, masts and chimneys –Tower and masts is commonly applied. This standard represents the dynamic effects of wind through static loads, using a procedure known as the Equivalent Static Method (ESM).
Such an approach constitutes a significant simplification of the actual physical process, which is inherently far more chaotic and unpredictable.

However, not every tower satisfies the applicability conditions of this method, and before carrying out the calculations, it is necessary to verify whether the ESM criteria are fulfilled.

Many engineers omit this step, since historically it has been rare for a structure to fail the requirement, whereas verifying the criteria can be demanding. In recent years, however, the substantial increase in the weight of 5G antennas compared to earlier generations has meant that these criteria are not always satisfied, making it essential to first verify whether the design standard methodology is applicable.

In Shapemaker, this verification is integrated into every analysis and is fully automated, requiring no additional user input.

If the condition is not fulfilled, Eurocode requires the use of more advanced methods – for example, spectral analysis.

This article provides a detailed explanation of the verification procedure and discusses strategies to improve the likelihood of meeting the ESM requirements.

ESM applicability criterion – equation B.12 (EN 1993-3-1)

The criteria for ESM are expressed as:

\[\frac{7m_{T}}{\rho_{s}c_{fT}A_{T}\sqrt{d_{B}\tau_{o}}}(\frac{5}{6}-\frac{h_{T}}{h})<1\]

where:

\(m_{T}\) - is the total mass of the panels making up \(c_{f,T}\) (in kg)

\(\rho_{s}\) - is the density of the material of the tower structure (in kg/m3)

\(c_{fT}A_{T}\) - is the sum of the panel wind forces (including ancillaries), commencing from the top of the tower, such that \(c_{fT}A_{T}\) is just less than one-third of the overall summation \(c_{f}A_{T}\) for the whole tower (in m2)

\(d_{B}\) - is the depth in the direction of the wind, equal to:

  • base \(d\) for rectangular towers (in m)
  • 0.75 × base width for triangular towers (in m)

\(\tau_{o}\) - is a volume/resistance constant taken as 0,001 m

\(h_{T}\) - is the total height of the panels making up \(c_{fT}\), but not greater than h/3 (in m)

\(h\) - is the height of the tower (in m)

Verifying whether equation B.12 is satisfied is not always straightforward. Equipment on towers is rarely arranged symmetrically, meaning that for each wind direction, the result of the criterion may differ. This makes the process time-consuming if carried out manually.

Investigation of a 36 m lattice tower

Consider a 36 m lattice tower with solid round main legs and angle bracing. At the top, a head-frame supports operators 1, 2, and 3, while operators 4 and 5 are located just below.

Tower diagram created automatically in Shapemaker

The antenna configuration includes:

  • 15 GSM antennas of size 2622 × 300 × 152 mm, 15 kg each,
  • 32 RRU modules of size 553 × 397 × 150 mm, 32 kg each, installed behind the GSM antennas,
  • 4 MW Dishes Ø 0.6–1 m, 21-40 kg each,
Ancillaries configuration

All antennas are installed at the top, most of them on the head-frame.
Additionally, the tower carries a ladder (15 kg/m) and two cable trays (30 kg/m each, including clamps).

The site is located in a wind zone with a basic wind speed of 22.5 m/s, terrain category IV (city), and no terrain orography effects.

Antenna replacement scenario

Let us now consider the case where each tenant replaces their GSM antennas (15 kg each) with new 5G antennas (33 kg each)of identical size, ensuring that the projected area remains unchanged.

The resulting change in the ESM criterion value has been calculated in two cases:

1. Without shielding effects, assuming a fully exposed wind area:

2. With Automatic shielding toggled on, where ancillary items provide mutual shielding when installed in proximity:

    Note:
    Values highlighted in red indicate those that fail to satisfy the ESM criteria or represent instances where structural members are subjected to overload.

Results and observations

The analysis indicates that equipment co-location and replacement with heavier devices can shift a tower from a situation where a simple static analysis is sufficient to one requiring spectral analysis, provided that the projected areas are calculated accurately with mutual shielding taken into account.

Conversely, when a less precise method is used to estimate the projected area of ancillary equipment (ignoring shielding), the ESM criteria may still be met; however, overall member utilisation can increase, potentially leading to overstressed conditions in some cases.

An increase of 54 kg per set of three antennas resulted in a 1–2 % rise in the ESM criterion factor.

This case demonstrates that, with Shapemaker, where automated shielding and ESM verification are performed by default, the tower can safely support the upgraded antennas for one tenant, whereas the conservative approach results in overutilization even under the existing scenario, without any antenna upgrades.

Takeaway

Before carrying out a complex spectral analysis, it is important to consider that:

  • Weight Effects
    • Heavier equipment relative to its wind area produces a higher risk of failing the criterion.
    • When the ESM index nears 1.0, even small weight increases (a few kg per antenna) can flip results from safe to unsafe.
    • Always use precise weights in the first analysis to avoid surprises later.
  • Positioning Effects
    • Installing antennas lower on the tower (where service requirements allow) improves the ESM criterion by increasing \(h_T\)
    • Concentrating equipment at the top of the tower raises the risk of failure.
    • Paradoxically, sometimes increasing the exposed area (e.g., by not stacking RRUs behind GSM antennas) reduces the criterion value and keeps the tower within static method limits.
  • Modelling Assumptions
    • Ignoring shielding can make the ESM criterion look satisfied but may increase member utilisation, hiding overstressed conditions.
    • Accurate projected areas (with shielding effects included) are essential for safe and reliable results.

In short, the Equivalent Static Method is simple and efficient, but its applicability depends on careful attention to weight, placement, and modelling accuracy. As 5G antennas replace lighter GSM units, checking compliance with EN 1993-3-1 is no longer optional - it’s essential.

Shapemaker makes the verification effortless, but engineers should still understand the underlying mechanics – especially since small design choices can determine whether a tower remains within the scope of the static method or requires a full dynamic spectral analysis.

Eurocode 3 - EN 1993-3-1 – Design of steel structures Part 3-1: Towers, masts and chimneys –Tower and masts

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