Radial Stress Distribution Research Articles

Evaluation of Wellbore Stability by Small Parameter Perturbation Nonlinear Elastoplastic Model

Abstract Wellbore instability is a frequent occurrence during drilling and a popular research topic among petroleum workers. Most of the previous studies simplified the hardening stage and ignored or classified it into the elastic stage. Engineering practice shows that the total stress–strain process of rock can more truly reflect the bearing and deformation characteristics of rock. This study establishes a total stress–strain constitutive model by combining the perturbation index equation with the linear elastic equation. Additionally, the physical model of rock around the well is presented using the total deformation theory for the plastic zone. The stress field of the rock surrounding the well is analyzed based on the physical model of the rock surrounding the well, taking into account the influence of rock strength and geostress state. The relationship between rock strength, geostress state, drilling fluid density, and plastic radius is given. The calculation method of drilling fluid density limit is also given. The practical application demonstrates that the stability of a borehole wall can be evaluated by analyzing the size and direction of the plastic radius, as well as the distribution of radial, tangential, and shear stress for various combinations of stress states and rock strengths. The maximum shear stress is always found in the softening zone, which is also the region where wellbore instability is most likely to happen. Therefore, the area within the softening radius is regarded as an unstable area, and the softening radius can be used to determine the range of wellbore instability.

Numerical Simulation and Experimental Study of Carbon Fiber-Reinforced Polymer Single-Bar Extrusion Anchorage Structure.

The reliable anchorage of carbon fiber-reinforced polymer (CFRP) tendons is a critical issue influencing the stable bearing capacity of bridge cables. This study introduces a novel CFRP single-strand extrusion anchoring structure, where the strand is compressed at its end. By integrating this with internal cone filler wrapping, we create a CFRP multi-strand cable composite anchoring system. This innovative design not only minimizes the overall dimensions of the anchoring system but also significantly improves its anchoring efficiency coefficient. An axisymmetric model was developed using ANSYS finite element software. The radial stress distribution and anchorage efficiency coefficient in the anchorage zone of Φ7 CFRP bar and Φ13.6 extrusion die were analyzed with varying parameters, such as chamfering, outer diameter, and length of the extrusion sleeve, and were validated through static load anchorage tests. The results indicate that the highest anchoring efficiency is achieved when four extrusion sleeves with a chamfer angle of 5°, an outer diameter of Φ14.4, and a length of 15 mm are connected in series, reaching a coefficient of 61.04%. Furthermore, this study proposes an anchorage structure where multiple extrusion sleeves are connected in series and sequentially compressed to overcome the limitations of increasing anchorage length for enhancing the anchorage coefficient. The test results demonstrate that with equal total anchorage length, connecting four 15 mm extrusion sleeves in series enhances the anchorage efficiency coefficient by 24.98% compared to a single 60 mm extrusion sleeve structure.

Analytical solution on magneto-electro-elasto-hygrothermal coupling in rotating functionally graded piezoelectric/piezomagnetic cylinders on Winkler elastic foundation

This study focuses on the multi-field coupling phenomena in a rotating functionally graded piezoelectric/piezomagnetic (FGPEPM) hollow cylinder under magneto-electro-elasto-hygrothermal loading. The cylinder is assumed to be infinitely long and on a Winkler elastic foundation. The hygrothermo parameter, magneto-electro-elastic properties, hygrothermal expansion, and density within the FGPEPM cylinder follow power laws with different gradient indexes along its thickness. Analytical solutions for the distributions of radial displacement, stresses, electric potential, magnetic potential, temperature, and moisture are derived by solving magneto-electro-elasto-hygrothermal coupling differential equations with appropriate boundary conditions. Validation against the existing analytical results for simplified models confirms the effectiveness of the present analytical solution. Numerical analyses further explore the effects of gradient indexes, rotational velocity, and elastic foundation stiffness on the multi-field coupling behavior of the FGPEPM cylinder. The findings provide valuable insights for designing multi-field coupling characteristics for FGPEPM materials.

Elastic-plastic response of tunnel in GZZ-based constitutive model

Investigating the stress redistribution characteristics after tunneling is critical for designing and constructing deeply buried tunnels. Three-dimensional stresses are more prominent in deep than in shallow tunnels, resulting in nonlinear strength. The generalized Zhang–Zhu (GZZ) criterion captures the nonlinear strength well. Therefore, this study established a 2D plane-strain numerical model using a GZZ-based constitutive model. The effects of the axial stress and rock properties on the stress redistribution and plastic zone are discussed. The initial axial stresses changed the axial stress distribution after excavation and had little effect on the radial and tangential stress distributions. The size of the plastic zone decreases with decreasing geological strength index and increasing rock mass mi . However, with increasing dilation coefficient, the stress distributions remained almost unchanged, whereas the radial deformation gradually increased.

Analytical approach on stress analysis in a functionally graded piezoelectric annular disk with varying compressibility and varying density under internal pressure

When a crystal is subjected to mechanical stress, it exhibits piezoelectricity, also known as the piezoelectric effect, which is the emergence of an electrical potential across the crystal's sides. A few examples of piezoelectric materials include quartz, Rochelle salt, lead zirconate titanate (PZT4) and zinc oxide (ZnO). Piezoelectricity has many applications in regards to electrical transducers and signal devices. In this paper, the analytical solution is obtained for elastic-plastic stresses in a thin rotating disc formed of functionally graded piezoelectric material with varying compressibility and varying density for distinct angular velocity with internal pressure using Seth's transition theory. The distribution of the mechanical and electrical components can be precisely controlled by applying functionally graded piezoelectric materials (FGPMs). Transition theory assumes that a mid-zone (transition state) exists between elastic state and plastic state. A nonlinear Governing equation of the problem is formulated using equilibrium equation by substituting the values of stresses. For evaluation of transitional stresses, transition function R is assumed in terms of radial stresses and equations are solved analytically by considering the transition (critical points) of the differential equation. The investigation focuses on how the rotational velocity and internal pressure affects the radial and circumferential distribution of stresses. With the help of graphs and mathematical calculations, it is observed that both variable density and variable compressibility have significant effect on the performance of a functionally graded piezoelectric materials. Therefore, it can be concluded that an annular disc made up of functionally graded piezoelectric materials is safer than that of homogeneous piezoelectric materials for engineering design purposes.

A novel anchor method for large tonnage CFRP cable: Anchorage design and full-scale experiment

This study introduces a novel three-segment CFRP cable anchorage to address stress concentration challenges in CFRP cable anchors. The anchorage features a continuously varying inner cone angle along the anchor length to prevent excessive radial stress on the CFRP cable. The radial stress distribution is theoretically analyzed, followed by a numerical simulation design using the Tsai-Wu failure criterion and the anchor system's equivalent stiffness as evaluation indices. The results demonstrate a 47.06 % and 45.73 % reduction in the radial stress peak of the novel anchorage compared to the inner cone and inner cone + straight cylinder anchorage, respectively. Importantly, beyond an anchor length 23 times the equivalent diameter of the CFRP tendon, increasing length has a marginal impact on anchor efficiency but diminishes equivalent stiffness. Positive effects are observed by increasing the inner cone segment proportion and adjusting the inner cone angle within the 2° to 4° range. Conversely, increasing the bonding medium thickness reduces anchor efficiency and equivalent stiffness. Experimental verification indicates the anchor system achieving 99.83 % anchor efficiency. Moreover, the axial strain of CFRP tendons in the anchor zone exhibits a linear trend along the anchor length, with test stresses at corresponding positions consistent with FE calculation results.

Effect of damage accumulation on the asymptotic behavior of stresses ahead the crack tip

The subject of this study is the analysis of mechanical fields associated with a crack tip under creep conditions, taking into account the phenomenon of damage accumulation. The objective of the study is to perform finite element modeling, using the SIMULIA Abaqus software package, of uniaxial tension of a plate with a central horizontal crack under creep conditions, taking into account damage accumulation. For numerical simulation of creep, the Bailey-Norton power law is used. The power law of creep with the help of the user procedure UMAT (User Material) of the SIMULIA Abaqus package was supplemented with the Kachanov-Rabotnov kinetic equation of damage accumulation in a related formulation. In the calculation scheme of finite elements, the crack tip was modeled as a mathematical notch and as a notch with a finite radius of curvature. As a result of the calculations, the distributions of stresses, strains, and continuity under creep conditions were obtained, taking into account the accumulation of damage over time. Radial distributions of continuity, stresses, and strains are plotted over time at various distances from the crack tip. The subject of the study was the consideration of the asymptotic of the stress distribution. As a result of the study, it is shown that in the elastic region the asymptotic corresponds to the distribution under the elastic regime, and in the creep zone the asymptotics of Hutchinson, Rice and Rosengren (HRR-solution) is satisfied for different exponents nof the power law of creep.
 A comparison is made of the radial stress distributions in modeling without taking into account damage and in the case of taking into account damage accumulation. It is shown that the presence of damage significantly changes the asymptotics of the stress field in the vicinity of the crack tip.

Mechanical response analysis of the wide-chord hollow fan blade considering the fluid–structure interaction

The aero-engine wide-chord hollow fan blade with a cavity stiffener structure can effectively reduce the weight and greatly increase the rotational speed. However, during the high-speed rotation process of the hollow fan, there is a strong coupling effect between the solid domain of the blade and the incoming air. This effect leads to a certain deformation of the rotor blade, which has a large impact on the structural strength of the blade. Aiming at the problem of the fluid–structure interaction in its operation, the finite-element method was used to simulate the two-layer structure of the TC4 titanium alloy wide-chord hollow fan blade. The centrifugal force and fluid–structure coupling effect were considered when carrying out the research on the structural mechanical characteristics of the blade. The results show that the maximum equivalent stress of the blade considering the fluid–structure coupling effect is 508 MPa at the rotational speed of 2,900 r/min, which is approximately 18% higher than the maximum stress when only the centrifugal force is considered. This phenomenon indicates that the effect of aerodynamic force on the blade stress cannot be ignored. The stress concentration area of the blade is located in the third stiffener from the leading edge and near the root of the blade, and the aerodynamic force has a more significant effect on the radial stress distribution of the blade. Further analysis of the equivalent stress distribution along the blade tip direction shows a trend of first increasing and then decreasing. The maximum equivalent stress appears at a distance of 30 mm up to the bottom of the stiffener.

Pile Driving and the Setup Effect and Underlying Mechanism for Different Pile Types in Calcareous Sand Foundations

The mechanical response and deformation characteristics in calcareous sand foundations during pile driving and setup were studied using model tests combined with the technical methods of tactile pressure sensors and close-range photogrammetry. Different types of piles were considered, including a pipe pile, square pile and semi-closed steel pipe pile. The test results show that during pile driving, the pile tip resistance of different piles increases with an increase in the pile insertion depth, and an obvious fluctuation is also obtained due to the particle breakage of the calcareous sand and energy dissipation. Different degrees of particle breakage generated by different type piles make the internal stress variations different, as with the pile tip resistance. The pile tip resistance of model pile A, which simulates a pipe pile, is the highest, followed by model pile B, the simulated square pile. Model pile C, which simulates a semi-closed steel pipe pile, has the smallest pile tip resistance because its particle breakage is the most obvious and the pile tip energy cannot be continuously accumulated. The induced deformation such as sag or uplift on the surface and the associated influence range for the calcareous sand foundation are the smallest for model pile C, followed by model pile B and then model pile A. Model pile A has the most obvious pile driving effect. During the pile setup process after piling, the increase in the total internal stress of model pile B is the largest, and the improvement of the potential bearing capacity is the most obvious, followed by model pile A and model pile C. During the pile setup, the induced uplift deformation in pile driving is recovered and the potential bearing capacity increases due the redistribution and uniformity of the vertical and radial stress distributions in the calcareous sand foundation. Considering the potential bearing capacity of different model piles, the influence range of pile driving, foundation deformation and the pile setup effect, it is suggested to use a pointed square pile corresponding to model pile B in pile engineering in calcareous sand foundations.

Unified theoretical solutions for describing the crack-tip stress fields of mode-II cracked specimens under the fully plastic condition

Potential novel singular solutions to the crack-tip stress fields beyond the asymptotic solution frame are discussed in this study. It is believed that one of them is not only suitable for the crack-tip stress fields of mode-I cracked specimens but also for those of mode-II cracked specimens. The crack-tip stress fields of mode-II cracked specimens are investigated based on the singular solution and the stress factor of mode-II cracked specimen derived from energy density equivalence principle. Further, special functions for describing the coefficients of normalized stress distributions of mode-II cracked specimens are proposed. The method to determine the parameters in the theoretical solutions are introduced. To give an example, one set of parameters for compact shear specimen under plane-strain conditions are determined by the finite element analysis of a few typical materials and geometries conditions. Finally, comparisons of radial and circumferential stress distributions and contour lines of equivalent stress are completed for the compact shear specimens and Arcan-shaped shear specimens of power-law plastic materials under plane-strain and plane-stress conditions. And the results show that the applicability and reliability of the proposed unified theoretical solutions are verified.

Using 2DVD technology to explore droplet characteristic variations of sprinkler irrigation as affected by a maize canopy

Canopy cover influences the water distribution and droplet characteristics of sprinkler irrigation, creating uncertainty in the design optimization of sprinkler irrigation systems. To evaluate the effects of canopy cover on water distribution and droplet characteristics of sprinkler irrigation, the radial distribution of droplet diameters, velocities, impact angles, shear stresses, and kinetic energies were investigated by an indoor experiment using a two-dimensional video disdrometer (2DVD) with Nelson R33LP low-pressure sprinklers at three operating pressures (100, 200, and 300 kPa), three nozzle diameters (4.4, 4.8, and 5.2 mm), and two growing stages of the maize canopy. Additionally, the water application rates were measured by catch-can devices for each treatment. The results show that small droplets passing through the canopy converge into larger-diameter droplets and large droplets passing through the canopy break up into smaller-diameter droplets. The canopy cover significantly affected droplet kinetic energy and velocity and reduced shear stress by 2.48–96.09 %, which could minimize the risk of soil erosion. Meanwhile, an increase in the leaf area index (LAI) reduced the kinetic energy by 0.26–99.00 %. Canopy cover also had an obvious effect on the irrigation uniformity coefficients (CU). The CU without the canopy exhibited a significant linear correlation with the CU with the canopy. When the irrigation CU without the canopy was 62.00 %, the maize canopy at the jointing stage improved it by 16.62 %, and when the CU without the canopy was 88.47 %, the maize canopy cover at the jointing stage reduced it by 4.68 %. An increase in operating pressure improved the uniformity of the sprinkler by 0.57–151.58 % and reduced shear stress by 2.80–95.11 %. An increasing nozzle size increased the application rate and specific power. This study provides technical support for the design of sprinkler irrigation systems.

Monitoring corrosion-induced concrete cracking adjacent to the steel-concrete interface

Substantial research effort has been devoted on linking corrosion-induced cracking of concrete with the internal corrosion damage level. Still, numerical models of the corrosion and cracking process require internal parameters, that cannot be directly evaluated from experimental data. Therefore, this study provides a novel experimental method for monitoring the effects of steel corrosion adjacent to the steel-concrete interface. This non-destructive method is suited for small-scale laboratory-made specimen, and was designed to provide missing information required for subsequent calibration of numerical models. Hollow steel bars were cast into concrete and subjected to accelerated corrosion using the impressed current technique. The deformations of the hollow steel bars were measured using distributed strain sensing in an optical fibre, attached to the inner surface of the hollow steel bars. After the corrosion period, X-ray Computed Tomography scans were performed to evaluate concrete cracking and corrosion level. The results reveal a non-uniform distribution of strain around the perimeter of the steel, indicating a non-uniform radial stress distribution. The non-uniformity correlated very well with the position of the corrosion-induced cracks; with extension hoop strains in the steel at the location of these cracks and contraction hoop strains in between. Further, the corrosion level varied around the perimeter, with higher values near cracks. The combination of non-destructive monitoring techniques used in this study on small-scale laboratory-made specimens show great potential to reveal new insights on how the corrosion pattern, corrosion-induced cracking of the concrete cover and stress (indirectly measured through the strain in the steel) interact throughout the corrosion process.

Analysis of the Magneto-Thermal Bidirectional Coupling Strength of Macro and Micro Integration for Self-Starting Permanent Magnet Hysteresis Synchronous Motors

High-speed permanent magnet synchronous motors (PMSMs) are usually started with the hybrid low-speed open-loop and high-speed closed-loop control mode. However, low-speed open-loop control produces large starting current, or even current overload, resulting in demagnetization and motor damage. Therefore, there is an urgent need to develop a high-speed permanent magnet synchronous motor with self-starting ability at low speed, that is, a permanent magnet hysteresis motor (PMHM). This paper takes the permanent magnet ring hysteresis column rotor structure as the research object. Firstly, the performance of this type of rotor is improved using the micro level of effective layer material AlNiCo, and the mechanical properties of AlNiCo are calculated. Secondly, based on the thick-walled cylinder theory, the analytical model for calculating the strength of the composite rotor considering the temperature effect is deduced, and the tangential and radial stress distribution for each part of the rotor under no-load and load conditions are obtained. Then, the electromagnetic losses and temperature field distribution of the rotor are obtained using the magneto-thermal bidirectional coupling finite element method. Finally, strength of the thermal rotor is analyzed by substituting the temperature rise curve function and AlNiCo parameters at the operating temperature. The comparison of the stress calculation results of the semi-analytical solution and the finite element method showed that the error between both of them is less than 5%, which verified that the semi-analytical solution can accurately analyze the thermal stress distribution of the rotor during high-speed rotation.

Radial deformation and stress distribution of grinding wheel on surface grinding

Radial deformation and stress distribution of grinding wheel on surface grinding

Analytical Modeling of Shrink-Fitted FGM Thick-Walled Cylinder

One off the most powerful assembly technique is the shrink-fitting process.It is found in many fields such us mechanics, petroleum, military industries as well as in nuclear power plants etc. This article developed an analytical formulation of shrink-fitted Functionally Graded Material axisymmetric thick-walled cylinder based on the linear plane elasticity theory. The stresses and displacement fields in the thick cylindrical shells are calculated using the laws of linear elasticity. The resulting displacements and stresses are analyzed, and particularly the residual contact pressure and her relationship with the interference values. The results show that the variation of the FGM material composition has a clear effect on the fit pressure in the intersection area of the two fitted cylinders. The value of this pressure affects the distribution of radial and tangential stresses in the FGM cylinder walls. Subsequently, we highlighted the influence of the interference value, on the residual contact pressure which increases with the increase of the interference value. The stresses are modeled for a case study using MATLAB software. keywords. shrink-fit, FGM, Interference, residual stress, Elasticity.

Molecular dynamics simulation of hollow and porous amorphous silicon nanowires coated with amorphous aluminum oxide

Silicon causes structural changes and residual stresses during the process of lithium-ion penetration. Aluminum oxide coatings with an optimal thickness can prevent the structural variations and failure of the anode, though it will affect the ionic conductivity. In this research, the mechanical and electrochemical properties of the aluminum oxide-coated silicon nanowires are investigated by the molecular dynamics simulations. The results of the simulations show that the capacity increases, and the dimensional stability is maintained to a suitable extent by applying the void space or creating porosity in the coated nanowires. Furthermore, the volumetric changes for the base sample decrease from 56.3% to 10.25% and 19.1% for porous and hollow Si nanowires samples, respectively. Nevertheless, the capacity is increased from 1015.3 to 1063.8, 1219.6, and 1573.3 mAhg−1 for porous, closed, and open-hole samples, respectively. The radial distribution of the residual stresses and elemental mapping are also measured to investigate the effect of porosity and void space on the amorphous nanowires.

Analysis of Flow and Runner Dynamic Response Characteristics under Pump Conditions of Variable-Speed Pump Turbine

Pumped storage power stations can ensure the safe operation of the grid, as well as utilize clean energy sources to establish a low-carbon, safe, and efficient energy system. As pump turbines, the core components of pumped storage power plants, become more and more popular, the technical requirements for hydraulic design begin to improve year by year. However, when the unit operates far beyond the optimal range, the variable-speed pump turbine can overcome the shortcomings of the fixed-speed unit and solve the problem of unstable operation under partial load. The pressure pulsation of the unit in the pump condition is investigated by numerical simulation, analyzing the hydraulic thrust, and studying the dynamic response characteristics of the runner at a maximum speed of 456.5 rpm. Comparing the pressure pulsation amplitude of various components in the entire flow passage, the highest values of pressure pulsation were found in the runner and vaneless space. The axial hydraulic thrust has a fluctuation range between 174t and 198t and 0t to 40t for radial force. As per the structural analysis, it has been observed that the runner demonstrates uneven patterns in both its axial and radial deformations, with deformation mainly concentrated in radial displacement and stress distribution mainly concentrated on the blades near the crown. The dynamic stress amplitude of the runner at monitoring point S1 (located on the runner blade near the crown) is 37 MPa. This stress has a dominant frequency of 4.8fn, while the monitoring point S2 (located on the runner blade near the band) is 4 MPa, and the dominant frequency is 1.8fn. Using these findings, the design of the variable-speed pump turbine’s runner can be optimized, and the unit’s stable and secure operation can be guided accordingly.

COMPARATIVE ANALYSIS OF THE ANALYTICAL AND NUMERICAL METHODS FOR CALCULATING THE STRESS-STRAIN STATE OF THE NEAR-WELLBORE ZONE BASED ON THE ELASTIC MODEL TAKING INTO ACCOUNT THE MAIN STRUCTURAL ELEMENTS OF THE WELL

Link for citation: Popov S.N., Chernyshov S.E., Krivoshchekov S.N. Comparative analysis of the analytical and numerical methods for calculating the stress-strain state of the near-wellbore zone based on the elastic model taking into account the main structural elements of the well. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 5, рр.94-102. In Rus. The relevance of the research is caused by the scientific interest in calculating the near-wellbore zone stress-strain state to improve the development of oil and gas fields, to predict the casing stability and the safety of the cement stone. The main aim: based on a comparative analysis of the methods of analytical and numerical simulation of stress calculation near a vertical well using an elastic model, determine the distribution of radial and tangential stresses, compare the accuracy of their calculation by different methods and identify the advantages and disadvantages of each of them. Objects: near-wellbore zone of the terrigenous reservoir of the Achimov deposits of one of the fields of the Khanty-Mansiysk autonomous region. Methods: analytical and numerical finite element methods for stress-strain state calculating of the near-wellbore zone, taking into account the main structural elements of the well and using a linear elastic model. Results. The paper considers the analytical relationships used to calculate the radial and tangential stresses in the casing, cement stone and reservoir rock, as well as the equations used in numerical finite element modeling of stresses near a vertical well. The authors have developed a finite element scheme of the near-wellbore zone, including its main structural elements. The paper introduces the results of calculation of the main components of the stress tensor in the structural elements of the well depending on the radial coordinate for the bottom hole pressure of 20, 40 and 60 MPa. The authors carried out the comparative analysis of the stress calculations results by the methods used. It is shown that the largest discrepancy between the analytical and numerical methods was 2 % that corresponds to radial stresses for the calculation option with a bottom hole pressure of 20 MPa. On average, the discrepancies were: for radial stresses – 0,04 %, for tangential stresses – 0,72 %. It is concluded that when using the model of a linearly elastic medium and under boundary conditions in the form of fixing the model in the upper and lower parts along the normal to the surface, and also without taking into account the pressure distribution in the depression funnel of the model, it is sufficient to use the analytical method of calculation. If it is supposed to use combined boundary conditions, a poroelastic model, taking into account viscoplastic deformations, then it is most preferable to use the numerical simulation method.

원전용 밸브 패킹응력 해석을 위한 모델링 연구

The valve used in nuclear power plant must be qualified by the known experimental equation, which is the requirement of ASME QME-1 standard. Up to now, the stress on packing is assumed to be constant in design and experimental analysis. This paper deals with the development of analysis model for the packing stress. In the analysis model, the stress is calculated with the love function, whose eigen function is deduced by applying the separation method of axial and radial variables to biharmonic equation with boundary conditions. And the unkown parameters of love function are calculated by applying the remaining boundary conditions. The distribution of radial and axial stress are not constant and the big variation of stress is found at the inner and outer face. The radial stress after boundary layer of radial stress is 45% of gland packing stress. Considering the discussion that the double packing stress makes the radial stress in the packing as same as the fluid pressure, it is proper that the industrial design guide has been used to select the gland packing stress as twice as much as fluid pressure. And the force on stem can be calculated by applying shear stress of packing on stem area. Later, the load factor, which is used in the experimental analysis for consideration of stress distribution, must be related to the real stress distribution by this research result.

An analytical formulation of unidirectional composite curved beam with out-of-plane fiber waviness under bending

A closed-form analytical solution is developed for analyzing laminated composite curved beam with out-of-plane fiber waviness under bending. Timoshenko beam theory was adopted in derivation where the effects of shear deformation was considered for moderately thick beam. Explicit expressions for evaluating equivalent axial and bending stiffness are formulated based upon the modified lamination theory and taking the structural deformation characteristics of narrow section beam into consideration. Stress distribution at any given location calculated by the proposed method is investigated. Significant increase of radial normal stress and shear stresses are observed when out-of-plane fiber waviness is introduced. The comparisons between present analytical results and numerical data indicate that the present methodology have ability to capture radial normal, circumferential normal, and shear stress distributions of composite curved beam with out-of-plane fiber waviness and the level of stress predicted is satisfactory with numerical results.