The study addresses the difficulties in the preliminary design of test benches for extra-long wind turbine blades, where efficient load prediction approaches are lacking. The international testing standard IEC 61400 defines the required test items and loading configurations for full-scale blade certification, but it offers no quantitative calculation methods for test loads and no dedicated design specifications for large-scale blade test benches. In current practice, benches are largely designed according to generic structural guidelines for buildings. Most existing commercial benches are rated only for blades matching turbine units of 10 to 18 MW, while the design loads of blades themselves normally require fluid-structure interaction calculations in professional software such as Bladed or HAWC2, which involve complicated procedures and long computation cycles.

The core difficulty is that ultra-long blades are still under development. Their geometric profiles, composite layup schemes and cross-sectional configurations remain undetermined, which prohibits refined shell-element simulation of the kind used for mature blade designs. A single refined shell model of a blade can contain more than one million elements, leading to lengthy computation times. The team, led by Peixiang Liu and colleagues, therefore built a simplified analysis model that characterizes each blade with just four spanwise distributed parameters: linear mass density, flapwise bending stiffness, edgewise bending stiffness and torsional stiffness. Together these determine blade self-weight, center-of-gravity position, gravitational bending moment, principal bending deformations, low-order vibration modes and the global torsional response. The authors note that this four-parameter representation is not intended to describe local stresses, cross-sectional distortion, buckling or ply-level failure, which require refined shell or solid models.

To validate the simplification, the researchers took an 86-meter blade as a test case and computed its equivalent cross-sectional properties using the finite element software ANSYS. Linear mass density was obtained by segmental analysis, with each cross-section’s density determined by averaging the weight of two equidistant truncated segments on either side. Stiffnesses were calculated by fixing one end of a blade segment and applying a unit rotation angle at the other end. All three stiffness measures reach their maxima at the root and decline rapidly toward the tip, with milder decreases beyond five meters from the root.

Modal analysis with BEAM188 beam elements then showed how closely the simplified model tracks the full shell model. Across segment lengths of 0.5, 1, 2 and 3 meters, all predicted natural frequencies were slightly higher than the shell model values, but every error remained below 5 percent, and the errors shrank as segment length increased. The first and third vibration modes correspond to flapwise motion and the second to edgewise motion. With 3-meter segments, the deviations in the first three natural frequencies were all within 3 percent. The team selected a 1-meter element length as a compromise, noting that the 0.5-meter model roughly doubles the element count and computational cost while producing larger frequency errors, whereas the 1-meter model keeps the first three frequency errors within 5 percent while still adequately representing the steep property variations near the root.

The next step was to make the model predictive rather than descriptive. The researchers normalized the four parameters into a dimensionless spanwise coordinate, with zero at the blade root and one at the tip, and fitted the distributions with a four-parameter double exponential function, y = ae^bx + ce^dx. The two decay rates capture the rapid decrease near the root and the more gradual variation farther along the span, and soft boundary constraints keep the fitted curves physically plausible. Separate reference models were constructed for blades with glass fiber reinforced polymer spar caps and carbon fiber reinforced polymer spar caps, using a typical 86-meter GFRP blade and a typical 120-meter CFRP blade as fitting objects. Because carbon fiber offers higher longitudinal specific stiffness, a CFRP spar cap can deliver the required bending stiffness at lower mass than a comparable glass fiber design, reducing the gravitational root moment and helping to control blade-tip deflection. The 120-meter boundary serves only as a classification limit for the available datasets, not as a universal threshold for material selection.

To anchor the extrapolation in real data, the team collected self-weight data for approximately 70 wind turbine blades and fitted a quadratic relationship between blade length and total mass, with the reference root linear mass density back-calculated from the total. Stiffness data proved harder to gather and available samples are limited, but they provide a reference basis for prediction. Root stiffnesses are predicted with a cubic polynomial shared by the flapwise and edgewise directions, whose values differ little, and a quadratic polynomial for torsional stiffness. Applying this machinery with blade length as the sole input, the study predicts that a 180-meter CFRP spar-cap blade would have a root linear mass of about 6,465 kilograms per meter, a total mass of 111.05 tonnes, a center of gravity 50.77 meters from the root, and first three natural frequencies of 0.2308, 0.4136 and 0.6890 hertz. The corresponding 200-meter blade would weigh 138.51 tonnes, with a root linear mass of about 7,282 kilograms per meter and first three frequencies of 0.2190, 0.3924 and 0.6535 hertz. The predicted vibration mode pattern matches that of conventional-length blades, which the authors interpret as supporting the model’s accuracy for dynamic characteristics.

The second half of the framework converts these blade parameters into test bench design loads. Full-scale blade testing comprises two core working conditions, ultimate static loading and cyclic fatigue loading, and the corresponding loads serve as the controlling design indicators for the bench structure and loading system. Conventional schemes require complete aerodynamic load time series from turbine manufacturers and refined fluid-structure interaction calculations, which are inaccessible in the preliminary design stage. Instead, the researchers performed statistical analysis on collected test load data from more than 70 commercial blades, using the gravitational bending moment as a unified conversion benchmark because it integrates blade mass, spanwise mass distribution and moment arm, and can be calculated directly from the predicted linear mass density distribution without detailed aerodynamic or wind-field data. Under a 50 percent guarantee rate, the statistical results show that the ultimate static load is approximately 4.41 times the gravity moment, while the fatigue load equals 0.567 times the ultimate static load, equivalent to 2.50 times the gravity moment.

Applying the conversion to the prospective ultra-long blades yields concrete preliminary estimates. The ultimate static load for a 180-meter blade reaches 243,812 kilonewton-meters, with a fatigue load of 138,201 kilonewton-meters. For a 200-meter blade, the ultimate static load is 338,729 kilonewton-meters and the fatigue load is 192,023 kilonewton-meters. The authors are explicit about the limitations: these 180-meter and 200-meter configurations are prospective designs developed for preliminary bench planning, no full-scale test data currently exist for them, and the predicted loads cannot yet be experimentally validated. The statistical coefficients are also constrained by the limited sample size, and differences in rated turbine power are not incorporated, so the authors suggest minor revisions combined with turbine power ratings in practical engineering application.

Even with those caveats, the method offers a practical route to the early-stage decisions that matter most for future testing infrastructure. Test benches must be designed with redundancy to accommodate larger blades in coming years, yet the airfoil profiles and structural dimensions of next-generation ultra-long blades have not been finalized, and no unified quantitative thresholds exist for core bench design indicators such as stiffness, strength, natural frequency and ultimate deformation. The new framework requires only blade length as input, combines prediction formulas for root parameters with the normalized double exponential distributions, and outputs quantitative estimates of natural frequencies and gravity moments, from which ultimate and fatigue design loads follow. The authors position the predicted values as suitable for preliminary scheme comparison and primary structural design rather than certification-level assessment, and the method’s accuracy is affected by sample size.

Subject of Research: A beam element based method for predicting design loads of test benches for ultra-long wind turbine blades

Article Title: Load equivalent analysis method of large test bench for wind turbine blade based on beam element model

Article References: Liu, P., Meng, W., Meng, X., Cui, X., & Feng, P. (2026). Load equivalent analysis method of large test bench for wind turbine blade based on beam element model. Case Studies in Construction Materials, 25, Article e06654. https://doi.org/10.1016/j.cscm.2026.e06654

Image Credits: AI Generated

DOI: 10.1016/j.cscm.2026.e06654

Keywords: wind turbine blades, test benches, beam element model, structural testing, design loads, fatigue load, static load, CFRP spar caps, natural frequencies, IEC 61400, offshore wind energy, load prediction