4th International Conference on Structural Health Monitoring and Engineering Structures (SHM&ES 2025)

Table of Contents

1. Structural Mechanics

   1. Frontmatter

   2. An Analytical Approach to Free Vibration Analysis of Beams Considering Lateral Shear Strain Based on Displacement and Shear Force Variables

      Thanh Thuy Vu

      Abstract

      This study presents an approach to the free vibration analysis of beams, accounting for lateral shear strain through two independent variables: displacement \(y\) and shear force \(Q\). The model builds upon the author’s previously developed theory, A New Beam Theory Considering Horizontal Shear Strain, and yields vibration functionals expressed in terms of variables \(y\) and \(Q\). This study employs the virtual load method, combined with the Lagrange multiplier method, to derive the characteristic polynomial for determining the natural frequencies. Additionally, the parameter optimization method is used to solve the eigenvalue problem under various boundary conditions. The proposed approach accurately captures the influence of lateral shear strain, which significantly affects the structural response of deep beams, short columns, and thick plates. Furthermore, this approach effectively eliminates the shear locking phenomenon, commonly encountered in analyses of structures considering shear strain.

   3. Experimental Study on the Combustion Properties of Glued Laminated Timber Structures

      Tien Thinh Do, Minh Dien Pham, Thuy Van T. Tran, Le Thuy Nguyen

      Abstract

      This study investigates the structural behavior of Glued Laminated Timber (GLT) through a comprehensive experimental program, including assessments of material properties, fire resistance, and mechanical performance. While GLT is widely used in countries like Japan, its application in Vietnam remains limited. Nonetheless, GLT offers key advantages such as a high strength-to-weight ratio, efficient use of wood resources, environmental sustainability, and architectural flexibility. To explore its potential in Vietnam’s construction sector, a two-story prototype structure was built entirely with GLT. This prototype serves as a test model to evaluate the real-world performance of engineered timber under local environmental conditions, providing a scientific basis for broader application in Vietnamese construction practices. Particular focus was placed on examining the combustion behavior of Japanese cedar GLT, with a series of standardized fire tests conducted to determine its compliance with Vietnam’s fire safety regulations and its overall suitability for application in modern building practices.

   4. A New Analytical Proposal for Evaluating Torsional Behavior of FRP-Strengthened Reinforced Concrete Beam Based on Modified-Softened-Variable-Angle-Truss Model

      Vinh Sang Nguyen, Anh Dung Nguyen, Ngoc Thang Nguyen, Van Toan Nguyen

      Abstract

      A new analytical method has been proposed to forecast the torsional behavior of reinforced concrete (RC) girder strengthened with fiber-reinforced polymer (FRP). The proposal was an enhanced modified-softened-variable-angle-truss model, considering the impact of FRP strengthening on concrete confinement alongside softened compressive and tensile behaviors in concrete. A database of 36 solid RC girders, strengthened with diverse FRP systems, was analyzed to evaluate the precision and dependability of the proposed model, considering an iterative trial-and-error algorithm. The results indicate agreement between experimental and analytical findings, confirming the RA-MSTMT-FRP model as a feasible method for forecasting torsional response.

   5. Numerical Investigation of Kinetic Pyrolysis in Fire-Exposed Compressed Spruce Panels

      T. T. Tran, T. B. Q. Vu, Thi-Hanh Nguyen, Hoang-Anh Nguyen, Gia-Huy Ngo

      Abstract

      This study presents a numerical investigation into the fire resistance of thermo-mechanically densified Spruce wood using a kinetic pyrolysis model. Unlike conventional approaches that rely on simplified or generalized thermal degradation models developed for untreated bulk wood, this research emphasizes the necessity of incorporating the specific thermal decomposition behavior of wood’s primary constituents (hemicellulose, cellulose, and lignin). The densification process significantly alters the wood’s internal structure by reducing its moisture content and porosity, thereby changing its fire response characteristics. To accurately simulate these effects, a user-defined subroutine (UMATHT) was implemented in Abaqus to model heat transfer and material degradation under various heat flux conditions. The results demonstrate that the kinetic pyrolysis model provides a more realistic and reliable prediction of the degradation process in densified wood, offering valuable insights for fire-oriented design and performance-based safety assessments in structures utilizing engineered wood materials.

   6. Analytical and FEM Load–Deflection Behavior of RC Beams Strengthened with a Combination of Fiber-Reinforced Cementitious Matrix and Fiber-Reinforced Polymer

      The Thanh Pham Nguyen

      Abstract

      This study focuses on establishing analytical and finite element models to determine the load–deflection behaviors that resulted by the combined strengthening effective of the combined of Fiber-Reinforced Cementitious Matrix composite and Fiber-Reinforced Cementitious Matrix composite. In the model, a Fiber-Reinforced Cementitious Matrix is bonded to the soffit of the RC beam and Fiber-Reinforced Polymer layers are bonded to the soffit of the FRCM layer. Theoretical formulas are attained and enhanced to identify the load–deflection behaviors. Besides, finite element models are created using ABAQUS C3D8 and T2D2 element types. The concrete damaged plasticity model is used to predict the behavior of concrete under strain loading. The deflection path curves at soffit of the beam determined through both the theoretical model and FEM are reasonable agreement, with error margin of 3.79–9.01% in comparation with those in FEM models. The scope of application of the theoretical formulation and FEM has been proposed. Implications for research on the development of the theoretical formulation have been suggested.

   7. Micromechanical Analysis of Variable Angle Tow Composites Considering Uncertainties in Constituents

      Trang Le, Luan Trinh, Daniela Butan, Paul Leahy, Paul Weaver

      Abstract

      Fibre reinforced polymers are commonly used for hydrogen tanks, which operate under a range of temperatures, pressures, and levels of hydrogen permeation. This working environment can affect the mechanical properties of the composite mostly through the matrix. This study investigates the impact of uncertainties in constituents on the homogenised properties of fibre reinforced composite at the ply-scale. The uncertainties of the mechanical properties of individual carbon fibres and epoxy resin are incorporated into micromechanical analysis models to investigate the probabilistic distribution of the mechanical characteristics of unidirectional (UD) composites and variable angle tow (VAT) composites. The elastic moduli of composites determined from Ansys Representative Volume Element (RVE) models are compared to those derived from the rules of mixtures (ROM), modified rule of mixtures (MROM), Bridging micromechanics model, Halpin–Tsai, Mori–Tanaka, and macroscale experiments to verify the precision of simulations. The RVE models effectively predict the variation of UD and VAT stiffness. In addition, Young’s modulus of the VAT ply shows the most sensitivity to the uncertainty of matrix and fibre where the fibre angles range from 0° to 20° for E_x. Monte Carlo simulations for the UD composites show that E₁ (Elastic modulus aligned with the fibre) is more sensitive to the uncertainty of fibre while E₂ (Elastic modulus transverse to the fibre direction) is more sensitive to matrix variations.

   8. Navier Solution for Static Behavior Analysis of Smart FGP Beams on Pasternak Elastic Medium and Subjected to Electro-Mechanical Loads

      Do Minh Duc, Le Cao Tuan, Tran Quang Hung, Tran Minh Tu

      Abstract

      In this report, smart functionally graded porous beams (smart FGP beams), consisting of a host FGP core bonded with two piezoelectric faces and contacting with a two-parameter Pasternak elastic medium foundation, are introduced. Importantly, static behavior analysis of such beams under electro-mechanical loads utilizing the Navier solution is presented for the first time. The equilibrium equations are derived based on the virtual work principle in conjunction with the sinusoidal shear deformation beam theory. The displacement and potential fields are analytically determined by Navier solution. The reliability of the proposed approach is validated by comparison with previous results of other authors. The deflection and axial stress of the beams under different combinations of electrical and mechanical loads are examined. Additionally, effects of porosity coefficients and elastic foundation parameters on the static characteristic of the smart FGP beams are investigated and commented.

   9. Numerical Analysis of Plant-Root-Reinforced Slope in Go Cong, Tien Giang, Vietnam

      Hung Quoc Nguyen, Bao Duy Nguyen, Hieu Duy Dinh, Thai Quoc Trinh, Viet Hoang Huu Nguyen, Nghia Trong Le, Kien Trung Nguyen

      Abstract

      This manuscript presents a numerical model to evaluate the stability of slopes located along the bank (Go Cong) with four different plant species, namely Eucalyptus, Stipa, Artemisia, and Rosmarinus. The analyses were performed using shear strength reduction method combined with finite element method implemented in the commercial Plaxis 2D software. In those analyses, plant-induced additional cohesion, which was a function of root depth and root tensile strength, was initially calculated and subsequently added into the original cohesion of bare soil. The Factor of Safety (FoS) was then calculated to examine the effectiveness of the plant species in improving the slope stability, in various scenarios of slope height and angle. Besides, parametric studies were conducted to investigate the increment of FoS due to vegetation reinforcement for several cases of internal friction angle and cohesion of bare soil.

   10. Theoretical Solution of the Timoshenko Beam Layed on the Foundation Subjected to Dynamic Load

       Thuy-Duоng Lе, Lе-Hung Trаn

       Аbstrасt

       This rеsеаrсh prеsеnts аn аnаlytiсаl frаmеwоrk fоr studying thе fоrсеd vеrtiсаl vibrаtiоns оf rаils in bаllаstеd trасks subjесtеd tо dynаmiс lоаding. Thе rаils аrе mоdеlеd аs infinitеly lоng, unifоrm bеаms fоllоwing Timоshеnkо bеаm thеоry, suppоrtеd by а pеriоdiс аrrаngеmеnt оf disсrеtе еlеmеnts. Еасh suppоrt is сhаrасtеrizеd аs а bеаm rеsting оn а visсоеlаstiс fоundаtiоn. By еmplоying thе frеquеnсy-dоmаin Grееn’s funсtiоn, а dirесt linеаr соrrеlаtiоn is dеrivеd bеtwееn slееpеr displасеmеnts аt thе rаil соntасt pоints аnd thе rеsulting rеасtiоn fоrсеs. This соrrеlаtiоn аllоws thе suppоrt systеm tо bе simplifiеd аs аn еquivаlеnt stiff-nеss spring. Inсоrpоrаting this rеlаtiоnship intо thе pеriоdiс rаil-suppоrt mоdеl, thе vеrtiсаl vibrаtiоn rеspоnsе оf bоth rаils is аnаlytiсаlly dеtеrminеd. Thе dеvеlоpеd mоdеl fасilitаtеs еffiсiеnt соmputаtiоn оf rаil dynаmiсs undеr diffеrеnt lоаding sсеnаriоs, еspесiаlly in аsymmеtriс саsеs. Furthеrmоrе, thе study соmpаrеs rаil rеspоnsеs оbtаinеd frоm twо distinсt bеаm thеоriеs. Еmphаsis is plасеd оn еxаmining rеsоnаnсе pеаks in frеquеnсy rеspоnsе spесtrа, оffеring а dееpеr undеrstаnding оf thе mесhаnisms driving rоlling nоisе gеnеrаtiоn.

   11. Investigate the Influenced Parameters for Exterior RC Joint Behavior by ABAQUS

       Viet-Phuong Nguyen, T. T. Tran

       Abstract

       Exterior reinforced concrete (RC) beam-column connection is one of the most crucial zones in a reinforced concrete moment resisting frame. The details of some parameters within this joint can affect to its behavior and greatly influences the strength and ductility of overall frame. In this research, parameter studies of three-dimensional models were studied by finite element ABAQUS software for exterior RC joint subjected to monotonic loading. These studies involving thirty specimens were conducted to investigate the influence of concrete strength, anchorage length, anchorage shape of reinforcement and stirrup occurence within the joint panel. The studied results indicated that the addition of beam or column stirrups within joint panel, the concrete strength and anchorage shape can affect the joint behavior in some specified cases. The influence of anchorage length is not considered when its value is less than the one given in TCVN 5574–2018.

   12. Numerical Modelling of Densified Wooden Nails in Timber Assemblies Using Abaqus

       N. Le Thuy, T. T. Tran, T. T. Thuy Van, N. Hong Son, N. T. Hanh, N. Hoang Anh

       Abstract

       This study presents a numerical investigation of densified wooden nails as a sustainable fastening solution in timber construction. Using Abaqus finite element software, a detailed model of a glulam timber assembly joined by densified beech nails was developed. The model accounts for material anisotropy, frictional interaction, and load-slip behavior observed in physical testing. Results demonstrate the ability of densified wooden nails to provide sufficient shear resistance and structural integrity while enabling compatibility with wood-based substrates. The numerical predictions are consistent with experimental findings and contribute to the broader application of bio-based fastening systems in both new construction and heritage restoration.

   13. Study on the Mechanical Properties of Glued Laminated Timber Members and Performance of Beam-Column Connections

       Tien Thinh Do, Anh Tuan Pham, Manh Toan Ngo, Thuy Van T. Tran, Le Thuy Nguyen

       Abstract

       This study presents mechanical properties of glued laminated timber members and performance of beam-column connections using Japanese cedar. As structural connections play a critical role in determining the overall stability and load transfer efficiency of timber frameworks, particular emphasis was placed on assessing both shear and tensile behaviors of connection systems. Full-scale tests were carried out to evaluate the load-bearing capacities of the connections under controlled laboratory conditions. The measured shear and tensile strengths were then compared to the nominal values provided by the manufacturer to verify compliance with design expectations. Results indicated that both connection types exhibited mechanical properties exceeding the prescribed limits, thereby confirming their structural reliability. These findings contribute to the body of knowledge supporting the application of engineered timber in modern construction and demonstrate the viability of Glued Laminated Timber systems for safe and efficient structural use in building environments, particularly in regions considering broader adoption of sustainable timber technologies.

   14. Effects of Rubber Aggregate and Fiber Carbon on Pervious Concretes

       Nguyen Thi Bich Thuy, Bui Anh Kiet, Tran Dang Truyen, Nguyen Anh Khanh, To Thanh Nhut

       Abstract

       The purpose of this paper is to investigate the effects of rubber aggregate and carbon fiber on basic properties of pervious concrete including compressive strength, porosity, and water permeability coefficient. The rubber aggregate is artificial aggregate made from the combining cement, fly ash, crushed rubber, and water with a ratio of 1:1:0.05:0.25. After 7 days of curing, the rubber aggregate is used to replace limestone by 0, 10, and 20% by volume, the carbon fiber to cement is 0.3%. The tested results show that the compressive strength of pervious concrete is enhanced 27.03% by using 10% of rubber aggregate, especially containing carbon fiber when compared to the controlled concrete. When the rubber aggregate content increases, the compressive strength tends to reduce. The porosity and compressive strength has a well correlation. The use of rubber aggregate leads to a lower water permeability coefficient. The mixture containing 10% rubber aggregate and carbon fiber shows the best properties with the highest compressive strength, the lowest porosity and water permeability coefficient. Therefore, the use rubber aggregate in the pervious concrete is suitable for road surface, sidewalk, or parking lot to avoid flooding in the rain season.

   15. Navier-Based Approach for Static and Vibration Analysis of FGP-Core Sandwich Plates with FG-CNTRC Cross-Ply Laminated Face Sheets

       Thanh-Tung Pham, Hoang-Nam Nguyen, Minh-Tu Tran, Viet-Tam Tran

       Abstract

       This paper examines the bending and free vibration behavior of a rectangular sandwich plate based on Reddy’s third-order shear deformation theory (RTSDT). The plate features a functionally graded porous material (FGP) core and cross-ply carbon nanotube-reinforced (CNT) face sheets. By applying the Navier solution, the governing equations are derived to determine the natural frequency and deflection of the simply supported sandwich plate. Systematic verification confirms the accuracy and reliability of the proposed model. Numerical studies reveal the influence of the porosity index of the FGP core, CNT distribution patterns, and the number of CNT layers on the plate’s deflection and fundamental frequency.

   16. Identifying Non-linear Output Frequency Response Functions Using Generalized Associated Linear Equations with Recursive and Coupled Computational Methods

       Wenbo Zhang, Yunpeng Zhu, Liangliang Cheng

       Abstract

       The non-linear output frequency response functions (NOFRF), as an extension of the linear frequency response function (FRF) in the non-linear case, has been applied to weakly non-linear system study and engineering structural health monitoring (SHM). The computation of NOFRFs requires first solving a series of linear ordinary difference equations, i.e., generalized associated linear equations (GALEs), and then obtaining the system's results of each order according to the definition of NOFRFs in the frequency domain. However, in practical applications, the solution of GALEs often requires the aid of numerical integration. Therefore, accurate numerical computation of GALE is the first task in system analysis using NOFRFs. In our study, two different numerical methods are proposed for solving the system of linear differential equations of GALEs. The first computational method involves solving the GALEs of each order using a Recursive Computational Method (RCM). The second approach transforms the problem of solving GALEs into state-space equations, which are then solved using the integral solver of numerical computation software (e.g., MATLAB). This method is referred to as the coupled computational method (CCM). Finally, we compare the results of the two methods for computing NOFRFs using a non-linear differential equation (NDE) model with a fourth-order nonlinear term as an example. The final results show that the two methods give consistent results for low order NOFRFs. However, for higher order NOFRFs, CCM produces more accurate results than RCM. This provides ideas for calculating NOFRFs by GALE in nonlinear systems and also provides an important theoretical basis for calculating NOFRFs in multiple-input multiple-output (MIMO) systems.

   17. Buckling Reliability of Composite Cylindrical Shells for Hydrogen Storage: Influence of Stacking Sequence and Material Property Variability

       Luan Trinh, Trang Le, Javier Sanz-Corretge, Thanh-Dam Pham, Van-Nguyen Dinh, Paul Leahy, Paul Weaver

       Abstract

       The buckling reliability of composite cylindrical shells under axial compression is examined, with particular attention to laminate stacking sequence and variability in material properties due to operational conditions such as hydrogen storage. Two laminate configurations, Z32 and Z33, are analysed using both analytical buckling formulations and finite element (Abaqus) simulations. The analytical model is implemented in MATLAB and validated against eigenvalue buckling predictions from Abaqus. To quantify the effect of material property variability, Monte Carlo simulations are conducted for three cases: (a) normally distributed variation in carbon fibre Young’s modulus, (b) variation in epoxy matrix modulus and (c) combined variability in both. Results show that while stacking sequence significantly influences the mean buckling load, matrix stiffness variability has a greater impact on reliability due to its higher coefficient of variation. The study highlights the need for robust stacking design and material control, especially for composite structures operating in temperature-sensitive environments. The presented framework enables efficient reliability assessment and informs safety factor selection for advanced lightweight composite designs.

   18. Static Analysis of Carbon Nanotube Reinforced Solid Plate by Using Isogeometric Analysis

       Binh Khanh Ngo, Khuong D. Nguyen

       Abstract

       This study examines the static behavior of carbon nanotube-reinforced composite solid plates under uniform transverse loading using three-dimensional isogeometric analysis. The implementation of the NURBS shape function helps avoid the shear locking phenomenon. To evaluate the accuracy and convergence of the method, this study examines several mesh densities and different orders of NURBS shape functions. Special attention is given to how the number of elements through the plate’s thickness affects the results. The results demonstrate that, similar to those of previous studies, results can be achieved with third-order NURBS functions and only a few elements in the thickness. These results reveal that 3D IGA can be an effective and accurate method for simulating CNTRC structures. Overall, the study provides practical guidance on selecting suitable discretization strategies when analyzing the mechanical behavior of CNT-reinforced plates.

   19. Limit State of Elastic Strip Under Combined Loading

       Vuong Pham Ngoc, S. Yu. Gridnev, Thuy Van Tran Thi, N. V. Minaeva, M. M. Korotkov

       Abstract

       This paper investigates the limit state of an elastic strip composed of a heterogeneous material with uneven side surfaces. Compressive forces are considered independently along the upper and lower boundaries as well as the lateral edges of the strip’s cross-section. A criterion based on the continuous dependence of the system’s response on initial data is proposed as a necessary condition for identifying the disruption of normal functioning. A violation of this continuity can lead to two types of limit states: the first involving a loss of stability, and the second characterized by excessive deformations and potential system failure. In the mathematical model, boundary conditions in the deformed configuration are incorporated, and the influence of rotation angles in the equilibrium equations is taken into account following the approaches of Novozhilov and Ishlinsky. A condition is derived that identifies the boundary region where the strip reaches a limit state, corresponding to the loss of stability of its equilibrium form. The impact of nonlinearity in the equilibrium equations within this critical region is also analyzed. The reliability of the results is supported by their agreement with established findings in the literature. Additionally, for various cross-sectional parameter values, regions are constructed where the stress–strain state remains approximately uniform.

   20. Load-Bearing Capacity of Reinforced Concrete Beams with Corroded Longitudinal Rebars

       Vu Hiep Dang, Phan Duy Nguyen, Nam Nguyen Van, The Anh Le

       Abstract

       Corrosion-induced deterioration of reinforced concrete (RC) structures poses a significant challenge worldwide. Studies aimed at accurately predicting the flexural performance of corroded RC beams are essential for assessing the limit state of structural elements. This study proposes predictive models for the load-bearing capacity of corroded slender RC beams using data from 145 beams tested in previous investigations. The database was analyzed using an artificial neural network (ANN) and an improved beam section model to identify critical parameters and develop a semi-empirical formula. The results indicate that the ANN model can effectively predict the ultimate flexural strength of beams with corroded longitudinal reinforcement, achieving an R-squared value of 0.9882. Parameter importance analysis enabled the development of a semi-empirical formula that can be conveniently applied by engineers. The beam section analysis-based formula also provides highly accurate predictions of load-bearing capacity, with an R-squared value of 0.9688. A comparison with previous formulas shows that the proposed models yield superior results.

   21. Modeling Truss Structures with Initial Length Imperfections Using Hybrid Finite Element Approach

       Thuy Van Tran Thi, Tien Dao Ngoc, Bich Quyen Vu Thi

       Abstract

       This study analyzed the dynamic response of truss structures with initial length imperfections under harmonic loading. A novel hybrid finite element method was developed, using both displacements and internal forces as unknowns in equations derived from the principle of virtual work. Imperfections introduced geometric nonlinearity, addressed through an incremental-iterative algorithm. Simulations showed accurate, efficient results for nodal displacements and internal forces. Even small imperfections significantly impacted dynamic behavior, highlighting their importance in nonlinear analysis and design.