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DOE OSTI2023

Topology driven and soft phonon mode enabled Na-ion diffusion in quaternary chalcogenides, Na 3 ZnGaX 4 (X = S, and Se)

The compounds Na 3 ZnGaX 4 (X = S, Se) are potential solid electrolyte materials in sodium-based batteries, which have certain advantages over oxide materials and have shown significant ionic conductivity at ambient temperature. In this paper, we bring out atomic-level features of the diffusion process in these new materials using the microscopic techniques of inelastic neutron scattering (INS), quasielastic neutron scattering (QENS), and ab initio molecular dynamics (AIMD) simulations. The insights obtained from these techniques are unique and not available from other macroscopic experiments. Neutron scattering experiments have been performed at temperatures from 100 to 700 K. The simulations have been carried out up to 900 K. We have calculated the phonon spectra and the space–time correlation functions and found good agreement with the results of the neutron scattering experiments. The simulations enable detailed analysis of the atomic-site dependent dynamical information. We observe low-energy phonon modes of ~6 meV involving the vibrations of certain Na atoms in the lattice. This reveals that the Na at 32g Wyckoff sites (Na2) has sufficiently shallow potential among the two available crystallographic sites. This shallow potential facilitates diffusion. Furthermore, the specific structural topology of the network of interconnected zig-zag chains of the Na2 atomic sites provides the low-barrier energy pathways for diffusion. A small fraction of vacancy defects appears essential for diffusion. We further observe that the Na2 atoms undergo jump-like diffusion to the vacant next or the 2nd next neighbour sites at ~4 Å. While the QENS experiments reveal the jump-like diffusion and its time scale, detailed analysis of the AIMD simulations shows that the jumps appear mostly along zig-zag chains of the Na2 sites in the tetragonal ab-plane, as well as between the chains along the c-axis. In conclusion, the net diffusion is essentially 3-dimensional, with little anisotropy despite the anisotropy of the tetragonal crystal structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Comparison of Energy Storage and Arbitrage Options for Nuclear Power

Nuclear power is the most reliable source of clean energy and plays a crucial role in decarbonization efforts and national energy security. Achievement of Net-Zero targets depends on the deployment of new Nuclear Power Plants (NPPs) – both advanced reactors and large-scale Light-Water Reactors (LWRs) – as well as continuing operations at existing LWR plants. The Light-Water Reactor Sustainability (LWRS) program seeks to extend the lifetime of existing NPPs and improve their economic performance through research into plant modernization, Flexible Plant Operation and Generation (FPOG), risk-informed systems analysis, materials research, and physical security. The FPOG pathway investigates alternative revenue streams for LWRs. When electricity prices are driven low by an oversupply of renewable energy, steam and electricity from an NPP can be used to make value-added products while taking advantage of the low energy price; alternatively, this cheap energy can be stored chemically, electrically, or thermally, and used to regenerate-generate electricity at a later time when energy demand, and therefore the wholesale price of electricity, is higher in an economic concept called arbitrage. The purpose of this report is to investigate energy storage technologies that can store 500 MW of electricity from an LWR for a wide spectrum of durations.

13 HYDRO ENERGY↗

DOE OSTI2025

Development and Preliminary Analysis of a U.S. Geothermal Heat Pump Installation Database

This paper seeks to addresses the significant gap in the literature regarding the installation and adoption of geothermal heat pump (GHP) systems in the United States. While the "2021 U.S. Geothermal Power Production and District Heating Market Report" published by the National Renewable Energy Laboratory (NREL) focused on direct-use geothermal district heating systems, it did not include an analysis of GHP installations (Robins et al. 2021). To bridge this gap, NREL has compiled a novel database currently containing 70,470 records of GHP installations, primarily sourced from state well permits and small-scale studies. Our methodology emphasizes the collection, cleaning, and standardization of data, addressing challenges such as inconsistent reporting formats and privacy concerns. Despite limitations in data on capacity, costs, and performance, our preliminary geospatial analysis reveals insights into the distribution of GHP systems across urban and rural areas and climate zones. The paper highlights the importance of publicly accessible data for advancing GHP technology adoption with a discussion of existing data sources and their limitations, advocating for improved collaboration between NREL and industry stakeholders.

data collection↗

DOE OSTI2023

Regional variability in the environmental controls of precipitation regimes in the tropics

The environmental factors that control precipitation regimes in Boreal winter rainfall in the tropics and their regional variabilities are examined using a simple statistical analysis and a machine learning model. Radar-derived precipitation from field campaigns at Darwin Australia, Manaus Brazil, and the Equatorial Indian Ocean, along with the corresponding large-scale environmental variables from ERA5 reanalysis, are used. The dependence of marginal distributions of frequencies of these regimes on five environmental variables are calculated. The variables are hourly column integrated precipitable water (PW), convective available potential energy (CAPE), convective inhibition (CIN), and lower and upper tropospheric wind shear. The simple machine learning model that predicts the probability of transition from suppressed to an active regime as a function of the environmental variables is designed and optimized for a potential application as a trigger function for convection parameterizations. To the first order the analysis shows an abrupt increase in the probability of an active regime near PW > 60 mm and CIN of <100 J kg -1 . The key differences in the frequencies of active regimes among the regions are found to be related to the fact that over Darwin there is strong variability in PW while CIN is generally low. Over Amazon, on the other hand, both PW and CIN are quite variable. Over the DYNAMO domain the comparatively frequent low PW is compensated for by consistently low CIN resulting in a moderate frequency of an active regime.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Techno-economic analysis and life cycle assessment for electrochemical ammonia production using proton conducting membrane

Green ammonia production is facing increasing interest on a global scale as a hydrogen carrier for power generation as well as fertilizer for food production. The conventional Haber-Bosch method for ammonia synthesis is energy demanding, requires high purity hydrogen, and is based on fossil fuels. A preliminary techno-economic model for electrochemical ammonia synthesis at near ambient pressure using feed rates of 32 metric ton/day for hydrogen and 135 metric ton/day for nitrogen is presented in this study. Various pathways using different methods for nitrogen generation and hydrogen production were investigated to gain insight into added energy savings per metric ton of ammonia. Electrochemical synthesis using electrolysis for hydrogen and cryogenic nitrogen was found to be a potentially viable pathway for green ammonia. The profitability metrics including discounted cash flow rate of return, net present value and discounted payback period were estimated to be 8%, $40 MM, and 4–6 years respectively for this pathway. The cost of electricity, conversion rate, and conversion efficiency dominate the tonnage cost of ammonia and were used to assess the feasibility of the model. A life cycle assessment was also conducted to assess the environmental impact of a well to product ammonia process.

08 HYDROGEN↗

DOE OSTI2024

Exploration of mass splitting and muon/tau mixing parameters for an eV-scale sterile neutrino with IceCube

We present the first three-parameter fit to a 3+1 sterile neutrino model using 7.634 years of data from the IceCube Neutrino Observatory on $ν$ μ + $\overline{ν}$ μ charged-current interactions in the energy range 500–9976 GeV. Our analysis is sensitive to the mass-squared splitting between the heaviest and lightest mass state (Δm$^{2}_{41}$), the mixing matrix element connecting muon flavor to the fourth mass state (|U μ4 | 2 ), and the element connecting tau flavor to the fourth mass state (|U $\tau$4 | 2 ). Predicted propagation effects in matter enhance the signature through a resonance as atmospheric neutrinos from the Northern Hemisphere traverse the Earth to the IceCube detector at the South Pole. The remaining sterile neutrino matrix elements are left fixed, with |U e4 | 2 = 0 and δ 14 = 0, as they have a negligible effect, and δ 24 = π is set to give the most conservative limits. The result is consistent with the no-sterile neutrino hypothesis with a probability of 4.3%. Profiling the likelihood of each parameter yields the 90% confidence levels: 2.4eV 2 < Δm$^{2}_{41}$) < 9.6eV 2 , 0.0081< |U μ4 | 2 < 0.10, and |U $\tau$4 | 2 < 0.035, which narrows the allowed parameter-space for |U $\tau$4 | 2 . However, the primary result of this analysis is the first map of the 3+1 parameter space exploring the interdependence of Δm$^{2}_{41}$, |U μ4 | 2 , and |U $\tau$4 | 2 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1978

Development of Low-cost, High Energy-per-unit-area Solar Cell Modules

The development of two hexagonal solar cell process sequences, a laserscribing process technique for scribing hexagonal and modified hexagonal solar cells, a large through-put diffusion process, and two surface macrostructure processes suitable for large scale production is reported. Experimental analysis was made on automated spin-on anti-reflective coating equipment and high pressure wafer cleaning equipment. Six hexagonal solar cell modules were fabricated. Also covered is a detailed theoretical analysis on the optimum silicon utilization by modified hexagonal solar cells.

Jones, G. T.↗

DOE OSTI2021

Pipe Parity Analysis of Seawater Desalination in the United States: Exploring Costs, Energy, and Reliability via Case Studies and Scenarios of Emerging Technology

As climate change-induced variables exacerbate water scarcities, the use of seawater reverse osmosis (SWRO) membrane desalination technology for treating seawater could potentially provide a long-term drought-proof source of drinking water. This study carried out a technoeconomic assessment (TEA) for three SWRO desalination plants in the U.S. and one in Israel to set baselines for the cost and energy consumption for seawater desalination. In addition, a breakeven curve for implementing SWRO desalination was estimated in relation to the cost of water conservation measures to meet drought-induced reduction of the traditional water supply. The results show that the cost of SWRO water production scales with the plant capacity while energy intensity is not dramatically different across the plants. The higher cost in some U.S. plants is due to high capital investment, including land acquisition and permitting. Variations in plant capacity utilization have the greatest impact on the levelized cost of water (LCOW) over the plant service life, suggesting the importance of reducing fouling and maintenance-related downtime. Scenario analysis of fixed labor cost reduction through process automation indicates investments in automation and sensing technology could result in long-term savings. Breakeven analysis shows the decision to adopt SWRO is highly dependent on the local cost associated with water conservation to meet water supply reduction. Moreover, a small reduction in SWRO cost can influence a shift toward the adoption of SWRO over water conservation measures. Incorporation of future water demand, water conservation potential, and water stress data around the nation indicates SWRO desalination could be an important contributor to the future municipal drinking water portfolio in the U.S.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Eulerian and Lagrangian second-order statistics of superfluid 4 He grid turbulence

Here, we use particle-tracking velocimetry to study Eulerian and Lagrangian second-order statistics of superfluid 4 He grid turbulence. The Eulerian energy spectra at scales larger than the mean distance between quantum vortex lines behave classically with close to Kolmogorov-1941 scaling and are almost isotropic. The Lagrangian second-order structure functions and frequency power spectra, measured at scales comparable with the intervortex distance, demonstrate a sharp transition from nearly classical behavior to a regime dominated by the motion of quantum vortex lines. Employing the homogeneity of the flow, we verify a set of relations that connect various second-order statistical objects that stress different aspects of turbulent behavior, allowing a multifaceted analysis. We use the two-way bridge relations between Eulerian energy spectra and second-order structure functions to reconstruct the energy spectrum from the known second-order velocity structure function and vice versa. The Lagrangian frequency spectrum reconstructed from the measured Eulerian spectrum using the Eulerian-Lagrangian bridge differs from the measured Lagrangian spectrum in the quasiclassical range, which calls for further investigation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Improvement of Atmospheric Objective Analysis Over Sloping Terrain and Its Impact on Shallow-Cumulus Clouds in Large-Eddy Simulations

Surface topography strongly impacts the regional atmospheric circulation dynamically and thermodynamically. Over the Great Plains in the United States, the gently tilted slope is an important factor that impacts clouds, convection and regional circulations. This study enhances an atmospheric constrained variational analysis by using a terrain-following sigma vertical coordinate and applies to the data collected at the Southern Great Plain (SGP) site of the Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program. Sensitivity studies are performed to examine the impact of the terrain effects on the derived large-scale atmospheric forcing fields and the simulated shallow-cumulus clouds in large-eddy simulation (LES) driven by the forcing. We found that the terrain impacts on the large-scale forcing fields are mainly at lower levels and are strongly controlled by up/downslope winds. The response of the derived forcing to the slope of the terrain is monotonic, but the response of the simulated shallow-cumulus clouds is more complex and depends on several factors. Overall, the terrain impact is small over SGP due to the small slope angle. However, the flat-surface assumption may cause larger biases in the large-scale forcing fields at locations with steeper terrain. The new sigma-coordinate algorithm, with its consideration of surface slope, should be more suitable to derive large-scale objective analysis over regions with steep terrain for application to force single-column models, cloud resolving models and LES models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2021

Liana optical traits increase tropical forest albedo and reduce ecosystem productivity

Lianas are a key growth form in tropical forests. Their lack of self-supporting tissues and their vertical position on top of the canopy make them strong competitors of resources. A few pioneer studies have shown that liana optical traits differ on average from those of colocated trees. Those trait discrepancies were hypothesized to be responsible for the competitive advantage of lianas over trees. Yet, in the absence of reliable modelling tools, it is impossible to unravel their impact on the forest energy balance, light competition, and on the liana success in Neotropical forests. To bridge this gap, we performed a meta-analysis of the literature to gather all published liana leaf optical spectra, as well as all canopy spectra measured over different levels of liana infestation. We then used a Bayesian data assimilation framework applied to two radiative transfer models (RTMs) covering the leaf and canopy scales to derive tropical tree and liana trait distributions, which finally informed a full dynamic vegetation model. According to the RTMs inversion, lianas grew thinner, more horizontal leaves with lower pigment concentrations. Those traits made the lianas very efficient at light interception and significantly modified the forest energy balance and its carbon cycle. While forest albedo increased by 14% in the shortwave, light availability was reduced in the understorey (−30% of the PAR radiation) and soil temperature decreased by 0.5°C. Those liana-specific traits were also responsible for a significant reduction of tree (−19%) and ecosystem (−7%) gross primary productivity (GPP) while lianas benefited from them (their GPP increased by +27%). This study provides a novel mechanistic explanation to the increase in liana abundance, new evidence of the impact of lianas on forest functioning, and paves the way for the evaluation of the large-scale impacts of lianas on forest biogeochemical cycles.

Félicien Meunier↗

DOE OSTI2025

DESI-DR1 $3 \times 2$-pt analysis: consistent cosmology across weak lensing surveys

We present a joint cosmological analysis of projected galaxy clustering observations from the Dark Energy Spectroscopic Instrument Data Release 1 (DESI-DR1), and overlapping weak gravitational lensing observations from three datasets: the Kilo-Degree Survey (KiDS-1000), the Dark Energy Survey (DES-Y3), and the Hyper-Suprime-Cam Survey (HSC-Y3). This combination of large-scale structure probes allows us to measure a set of $3 \times 2$-pt correlation functions, breaking the degeneracies between parameters in cosmological fits to individual observables. We obtain mutually-consistent constraints on the parameter $S_8 = σ_8 \sqrt{Ω_{\rm m}/0.3} = 0.786^{+0.022}_{-0.019}$ from the combination of DESI-DR1 and DES-Y3, $S_8 = 0.760^{+0.020}_{-0.018}$ from KiDS-1000, and $S_8 = 0.771^{+0.026}_{-0.027}$ from HSC-Y3. These parameter determinations are consistent with fits to the Planck Cosmic Microwave Background dataset, albeit with $1.5-2σ$ lower values in the $S_8-Ω_{\rm m}$ plane. We perform our analysis with a unified pipeline tailored to the requirements of each cosmic shear survey, which self-consistently determines cosmological and astrophysical parameters. We generate an analytical covariance matrix for the correlation data including all cross-covariances between probes, and we design a new blinding procedure to safeguard our analysis against confirmation bias, whilst leaving goodness-of-fit statistics unchanged. Our study is part of a suite of papers that present joint cosmological analyses of DESI-DR1 and weak gravitational lensing datasets.

Porredon, A. [Madrid, CIEMAT; Edinburgh U., Inst. ↗

DOE OSTI2026

Innovations in underground hydrogen storage with multiphysics simulations, optimization, and monitoring: A review

Underground Hydrogen Storage (UHS) is a promising solution for large-scale energy storage and a critical component in advancing low-carbon energy system. Ensuring the safety and efficiency of UHS necessitates a comprehensive understanding of multiphysical interactions driven by cyclic pore fluid pressure fluctuations and coupled physicochemical processes. Here, this review examines the key geomechanical responses in UHS, including rock property variations under cyclic loading, fracture evolution and propagation, reservoir stress sensitivity, and fault stability. It also explores the impact of geochemical and microbial reactions on geomechanical characteristics. We provide an in-depth analysis of Thermal-Hydraulic-Mechanical-Chemical (THMC) coupled numerical simulations, highlighting their potential for future multi-scale modeling. Limitations of current machine learning (ML) approaches in addressing UHS challenges are highlighted, emphasizing the need for innovative ML-based methodologies. Operational strategies for hydrogen injection and production are reviewed, focusing on safety, efficiency, and economic viability. The necessity for multi-objective optimization (MOO) to balance storage efficiency, risk mitigation, and cost-effectiveness is also discussed. Current monitoring technologies are evaluated to ensure safe and efficient UHS operations. Finally, this review identifies critical knowledge gaps and underscores the importance of advancing geomechanical understanding under multiphysics-coupling. We highlight the need for ML-driven multiphysics theories, enhanced modeling techniques, and robust optimization strategies to improve UHS performance. This study serves as a comprehensive reference for future research and the large-scale implementation of UHS systems.

25 ENERGY STORAGE↗

DOE OSTI2025

Temperature Evolution of the Activation Barriers Leads to Meyer−Neldel Rules for Structural Relaxation and Transport in Polymers

Understanding activation barriers controlling structural relaxation in glass-forming liquids, molecular transport, and ionic conductivity in amorphous polymers is a grand challenge of fundamental scientific and materials engineering interest across disciplines. Over decades, intriguing but puzzling empirical correlations between the elementary time scale of activated barrier crossing and the apparent Arrhenius activation energy, the so-called Meyer−Neldel (MN) rules, have been discovered in diverse liquids and glasses. Here, in this study, we formulate and successfully apply a new experimental analysis and an explicitly dynamical theoretical framework which provides an understanding of the origin, validity, and failure of such correlations, that bridge and unify the three fields of structural relaxation, molecular transport, and ionic conductivity in liquids and quenched glasses. Distinct quasi-universal laws are predicted in equilibrated liquids and nonequilibrium glasses, consistent with experiments. Our analysis reveals that even if the relaxation appears Arrhenius over a limited temperature range, the physical activation barrier is generally temperature-dependent in polymeric systems even below glass transition temperature. In addition, we show that the approximate validity of classical MN rules hinges on a linear temperature dependence of this barrier and the temperature range probed in experiments. Our findings are relevant for controlling the activation barrier in functional soft polymeric materials relevant to molecular separations, barrier coatings, and charge transport, and also provide new constraints on the theoretical understanding of the mechanism underlying slow activated dynamics in glass-forming condensed matter.

Meyer-Neldel rules↗

DOE OSTI2023

Exclusion and Verification of Remote Nuclear Reactors with a 1-kiloton Gd -Doped Water Detector

To date, antineutrino experiments built for the purpose of demonstrating a nonproliferation capability have typically employed organic scintillators situated as close to the core as possible (typically at a distance of a few meters to tens of meters) and have not exceeded a few tons in size. One problem with this approach is that proximity to the reactor core requires accommodation by the host facility. Water Cherenkov detectors located offsite, at distances of a few kilometers or greater, may facilitate nonintrusive monitoring and verification of reactor activities over a large area. As the standoff distance increases, the detector target mass must scale accordingly. This paper quantifies the degree to which a kiloton-scale gadolinium-doped water Cherenkov detector can exclude the existence of undeclared reactors within a specified distance, and remotely detect the presence of a hidden reactor in the presence of declared reactors, by verifying the operational power and standoff distance using a Feldman-Cousins-based likelihood analysis. A 1-kton scale (fiducial) water Cherenkov detector can exclude gigawatt-scale nuclear reactors up to tens of kilometers within a year. In conclusion, when attempting to identify the specific range and power of a reactor, the detector energy resolution is not sufficient to delineate between the two.

42 ENGINEERING↗

DOE OSTI2024

Assessing correlated truncation errors in modern nucleon-nucleon potentials

We test the BUQEYE model of correlated effective field theory (EFT) truncation errors on Reinert, Krebs, and Epelbaum's semilocal momentum-space implementation of the chiral EFT (𝜒⁢EFT ) expansion of the nucleon-nucleon (NN) potential. This Bayesian model hypothesizes that dimensionless coefficient functions extracted from the order-by-order corrections to NN observables can be treated as draws from a Gaussian process (GP). We combine a variety of graphical and statistical diagnostics to assess when predicted observables have a 𝜒⁢EFT convergence pattern consistent with the hypothesized GP statistical model. Our conclusions are that, first, the BUQEYE model is generally applicable to the potential investigated here, which enables statistically principled estimates of the impact of higher EFT orders on observables. Second, parameters defining the extracted coefficients such as the expansion parameter 𝑄 must be well chosen for the coefficients to exhibit a regular convergence pattern—a property we exploit to obtain posterior distributions for such quantities. Third, the assumption of GP stationarity across lab energy and scattering angle is not generally met; this necessitates adjustments in future work. We provide a workflow and interpretive guide for our analysis framework, and show what can be inferred about probability distributions for 𝑄, the EFT breakdown scale Λ 𝑏 , the scale associated with soft physics in the 𝜒⁢EFT potential 𝑚 eff , and the GP hyperparameters. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other 𝜒⁢EFT NN potentials.

Bayesian methods↗

DOE OSTI2022

Formation and Reconnection of Electron Scale Current Layers in the Turbulent Outflows of a Primary Reconnection Site

We simulate with 3D particle in cell, the spontaneous formation of turbulent outflows in an initially laminar 3D reconnecting current layer. We observe the formation of many secondary current layers and reconnection sites in the outflow. The approach we follow is to study each individual feature within the turbulent outflow. To identify all clusters of current in the outflow we use a clustering technique widely used in unsupervised machine learning: density-based spatial clustering of applications with noise. Once the clusters are identified we measure their size and compute reconnection indicators to establish which are undergoing reconnection. With this analysis we establish that the size of the current clusters reaches all the way from its initial system scale down to subelectron skin depth scale. We observe that the smaller current clusters are more prone to reconnecting and to releasing energy. We then find the process of reconnection of the smaller current cluster to be of the recently observed electron-only type that leaves the ions essentially unaffected.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Effects of Accident Thermal Loading on In-Plane Shear Behavior of Steel-Plate Composite Walls

Structural walls in safety-related nuclear facilities are required to be designed for seismic and accident thermal (due to postulated high-energy pipe break events) loading combination. Current U.S. and international codes provide limited guidance for analysis and design of walls for this loading combination. This paper describes the experimental results and observations from tests conducted on a laboratory-scale (1:4 to 1:5) test unit representing steel-plate composite (SC) walls subjected to combined in-plane (seismic) and accident thermal loading. The test unit was subjected to surface temperatures of up to 450°F in combination with cyclic in-plane loading. Results of similar experiments recently conducted in Japan are also summarized (with surface temperatures up to 570°F). Surface heating combined with the low thermal conductivity and high specific heat of concrete resulted in nonlinear thermal gradients through the thickness of the specimens. These nonlinear thermal gradients and the associated self- or internal restraint led to extensive concrete cracking. This concrete cracking reduced the initial and secant stiffness of the specimens. The initial stiffness of the heated specimens reduced to 30 to 40% of the initial stiffness of the control (unheated) specimen. The secant stiffness of the heated specimens reduced up to 50% of the secant stiffness of the control (unheated) specimen. However, the in-plane shear strength of the heated SC specimens was still approximately 10 to 30% greater than the nominal in-plane shear strength calculated, for the limit state of steel plate von Mises yielding, using AISC N690 equations and measured material properties. Evaluation of the experimental results and observations suggests that the in-plane shear strength of SC walls subjected to typical accident surface temperatures (up to 570°F) can be estimated conservatively using the current provisions of AISC N690. The stiffness for accident thermal loading combinations can be considered to reduce from cracked composite stiffness at ambient temperature to fully cracked—that is, steel-only stiffness as the surface temperature increases up to typical accident value.

Construction & Building Technology↗