Moment resistance of steel pipes subjected to combined loads

The first part of this paper provides a review of recent investigations on steel pipes subjected to combined loads. Attention is given to studies involving both numerical and experimental components aimed at quantifying the modified moment resistance of pipes subjected to internal pressure and axial force. The comparison of experimental and finite element results indicate that the nonlinear shell finite element analysis is a reliable tool for predicting moment capacities of pipes. The second part of the paper reports two additional full-scale tests recently conducted at the University of Ottawa aimed at expanding the existing experimental database to pipes subjected to more complex load combinations involving twisting moment and shear (in addition to axial force, internal pressure, and bending). The finite element analysis for both tests is shown to provide excellent predictions of pipe moment capacity. The third part of the paper is a systematic parametric study based on the FEA model verified in previous and present investigations, aimed to assess the ability of pipe sections to attain their modified elastic and/or plastic moment resistance as predicted by analytically derived interaction equations. The parameters investigated are the applied torsion, internal pressure, axial force, and the diameter-to-thickness ratio of the pipe.     

A comparative study of usefulness for pad reinforcement in cylindrical vessels under external load on nozzle

The main purpose of this paper is to perform a comparative study of strength behavior for cylindrical shell intersections with and without pad reinforcement under out-of-plane moment loading on nozzle. Three pairs of full-scale test vessels with different d/D ratios were designed and fabricated for testing and analysis. A three-dimensional nonlinear finite element numerical analysis was also performed. The maximum elastic stress for each vessel under per unit moment on nozzle is provided. The plastic limit moment on nozzle is obtained by load–displacement and load–strain curves for each test vessel. The results indicate that the effect of pad reinforcement on decreasing maximum elastic stress and increasing plastic limit load is obviously effective. The study results will serve as the available data for understanding the usefulness of pad reinforcements and as the basis for developing an advanced design method by limit analysis for pad-reinforced cylindrical vessels under external loads on nozzle.     

Limit and burst pressures for a cylindrical shell intersection with intermediate diameter ratio

This paper provides results of inelastic stress analysis for a vessel–nozzle intersection with intermediate diameter ratio (d/D=0.526) under increasing internal pressure loading from experimental and non-linear finite element methods. The determination of the limit load due to internal pressure is performed by an experimental study for comparison with finite element analysis. The spread of plastic area for the analytical model vessel is provided. Also a burst test of the model vessel is carried out to provide some data to justify the existing design method and the basis for developing an advanced design guideline for shell intersections under internal pressure loading.     

Stress analysis in cylindrical pressure vessels with loads applied to the free end of a nozzle

This paper contains a stress analysis of a cylindrical pressure vessel loaded by axial and transverse forces on the free end of a nozzle. The nozzle is placed such that the axis of the nozzle does not cross the axis of the cylindrical shell. The method of finite elements was applied to determine the state of stress in the cylindrical shell. The values obtained for stress in the nozzle region were used to determine the following: envelopes of maximum stress values; maximum values on these envelopes; and distances between maximum values on envelopes and the outer edge of the nozzle. Algebraic functions were determined, which enable easy and simple determination of these numerous stress values. The stress values obtained from the algebraic function were within −12.5 and +12.8% of those from finite elements. The difference between stresses deduced from strain gauge readings on experimental and calculated stresses was a maximum of 12%.     

A three-dimensional finite element analysis of a steam generator channel-head-complex—Comparison of theory and experiment

The purpose of this investigation is to compare three-dimensional stress and displacement distributions determined analytically and experimentally: the geometry chosen was a steam generator channel-head-complex. The analytical procedure employed a three-dimensional elastic finite element approach, using linear, quadratic, cubic and mixed isoparametric hexahedral elements. The experimental procedure employed frozen stress photo-elastic models.Three different types of loading: internal pressure, nozzle moment and nozzle thrust, were considered and calculated stresses and displacements at selected points were compared with results generated by a photoelastic analysis.¹ The comparison showed generally close agreement between these two sets of results.     

Simplified Thermoelastoplastic Models for Determination of Global and Local Stress in Coke Drums

Coke drums as major pressure vessels in delayed coking process experience cyclic thermal and mechanical loading during operation. The elastic-plastic behavior of coke drums including global and local (hot and cold spot) stress distribution has been analyzed using finite element analysis (FEA) method in our previous study. Here, instead of using FEA simulations, simplified theoretical models (STM) for global and local stress determination are developed. The global stress model is developed based on a single cladded shell element with temperature and pressure loading cycle. The local stress model is built on an axisymmetric circular cladded plate experiencing a non-uniform temperature distribution history. With the same input data, stress and strain values estimated by the STM are consistent with those from the FEA. An ease-of-use software package with built-in STMs is developed. It is the objective of this paper to show that STM can be a very time- and cost-saving analysis tool for general industrial users compared to professional commercial FEA software.     

An analysis of bottom entry nozzles for atmospheric storage tanks

In this paper, we describe the analysis of soil settlement in the vicinity of a bottom entry nozzle of an atmospheric storage tank for several practical loadings. These are the pressure of the liquid stored in the tank, the body force of the rock and soil foundation, and an external moment applied to the nozzle where it emerges from the foundation. The foundation is modelled as a three-dimensional elastic medium which can support no tensile stress and is composed of two materials (rock and soil) with an elastic cylindrical shell embedded in the rock phase. The solution is accomplished with a general-purpose finite element program (ICES—STRUDL II). The overall conclusion reached is that bottom entry nozzles are acceptable for tankage installed on reasonably good soil.     

Fatigue behaviour of oblique nozzles on cylindrical shells submitted to internal pressure and axial forces

In detailed analytical checks against fatigue failure, the local notch stress approach can be considered as one of the most advanced methods for predicting the fatigue behaviour of a mechanical structure. However, it is based on a detailed strength analysis, including macroscopic notch effects, of the real structure, e.g., at weld seams. In this paper, the fatigue behaviour of oblique nozzles on cylindrical shells submitted to internal pressure, axial force and combined loading is analysed according to these principles. Detailed three-dimensional, parametric, finite element models based on brick elements are applied to describe the mechanical behaviour of the structure for a wide range of relevant geometrical parameters. The results of the serial finite element analyses are approximated analytically and thus can be offered to potential users to determine the stresses at arbitrary points of the nozzle-to-vessel junction and to predict the most probable location of fatigue failure.     

Stresses at the junctions of axisymmetric shells under axially varying load

This paper deals with the investigation of stresses and deformations in the neighborhood of junctions of axisymmetric shells, made of segments of different geometries and subjected to different edge restraints and axially varying internal pressure. The method of investigation involves solution of a set of six first order highly nonlinear differential equations seeking the state of deformation of the shell at which, for a given pressure, the potential energy in the deformed shell is a relative minimum. The basic concept of the multisegment integration, as developed by Kalnins and Lestingi (On nonlinear analysis of elastic shells of revolution, J. Appl Mech. 1967;34:59–64), has been utilized for obtaining the solutions of the governing equations. Solutions for various problems are obtained for increasing loading, starting from a low value. The soundness of the method and the correctness of the computer program used in the analysis are verified by comparing the results with that of the corresponding analytical results available in the literature. Results are presented in the form of curves for stresses and deformations for varying loads and varying shell parameters which can be used for locating the critical zones and determining suitable values of shell parameters. The results include both stresses and deformations in their nondimensional forms based on both the linear and nonlinear theories.     

Thermo-mechanical simulation for nozzle header of once-through steam generator by experiment and finite element method

The thermo-mechanical behaviour of the nozzle header of a steam generator developed for an integral reactor was investigated using experimental and finite element methods. The nozzle feedwater header suffers from severe thermal transient loadings during the operation of the nuclear reactor. The nozzle header is exposed to the low temperature inlet feedwater and the high temperature outlet superheated steam and the other side of the nozzle header contacts with the high temperature primary coolant. The temperature gradients result in high thermal stresses in the nozzle header. The thermal transient loading has been simulated in a test loop. The input and thermo-hydraulic parameters of the primary and the secondary system were. Strain gauges and thermocouples attached to the highly stressed region monitored the thermo-mechanical behaviour of the nozzle header. In parallel with the experimental study, the transient behaviour of the nozzle header was simulated by utilizing a commercial finite element code. The fluid temperature and pressure obtained from the test loop were used as inputs to the finite element analysis. As a result of this investigation, the thermo-mechanical load carrying capacity of the developed steam generator nozzle header was proved numerically and experimentally.     

On the shakedown analysis of nozzles using elasto-plastic FEA

The performed shakedown calculations of a dished end with a nozzle in the knuckle region with varying internal pressure load, and two cylinder–cylinder intersections with constant moment load and varying internal pressure load are example cases for the application of the check against progressive plastic deformation as stated in the new European UFPV standard, Annex 5.B: “Direct route for design by analysis” (DBA). To calculate the shakedown limits, Melan's (lower bound) shakedown theorem is used. In this context, the usage of the deviatoric maps of stress states to obtain proper self-equilibrating stress fields is shown. Furthermore, some problems and corresponding possible solutions for performing the shakedown check using a finite element model with shell elements are stated and shown in the examples.     

Stress concentration factors for intersecting cylindrical shells under mechanical loading

Based on an efficient finite element algorithm for the calculation of the stress field at the intersection region of rotationally symmetric component shells, the case of circular cylindrical shells intersecting at arbitrary inclination angles are considered under conditions of general mechanical loading upon the branch pipe.

As examples, stress concentration factors are calculated and presented for different diameter and thickness ratios of two cylindrical shells intersecting at 30° and 90° angles under an axial force, and in- and out-of-plane bending moment loadings acting on the intersecting cylinder.     

Stress concentration in cone–cylinder intersection

The finite element method and shell theory were employed to investigate cone–cylinder shell intersections. The developed special-purpose computer program Sais (stress analysis in intersecting shells) was used for elastic stress analysis of branch connections. A comparison of calculated results with experimental data is presented. A parametric study of non-radial models of the cone–cylinder shell intersection subjected to internal pressure loading was performed. The intersections of thin and middle thickness shells were analysed. The results are presented in graphical form. Non-dimensional geometric and angular parameters are considered to analyse the effects of changing these parameters on stress ratios in the shell intersection.     

Local and global collapse pressure of longitudinally flawed pipes and cylindrical vessels

Limit loads can be calculated with the finite element method (FEM) for any component, defect geometry, and loading. FEM suggests that published long crack limit formulae for axial defects under-estimate the burst pressure for internal surface defects in thick pipes while limit loads are not conservative for deep cracks and for pressure loaded crack-faces. Very deep cracks have a residual strength, which is modelled by a global collapse load. These observations are combined to derive new analytical local and global collapse loads. The global collapse loads are close to FEM limit analyses for all crack dimensions.     

Limit analysis based on elastic compensation method of branch pipe tee connection under internal pressure and out-of-plane moment loading

A new method of calculating the limit load of a structure via a sequence of incompressible elastic finite element calculations with variable Young's moduli converging to the rigid perfectly plastic problem is used to study the limit load of branch pipe tee connections. Several models of branch pipe tee connection are meshed with shell elements and submitted to internal pressure with end axial load effect or out-of-plane moment. Results are compared with lower and upper bound analytical solutions and experimental results reported in the literature. Computations with 20 noded cubic elements are also proposed to validate shell studies. The J integral is also calculated by a simplified method with the limit load, using an example of a defective branch pipe tee connection.     

Nonlinear stress analysis for thin spherical vessels with local non-axisymmetric imperfections

On a thin spherical shell with a local and non-axisymmetric imperfection, the magnitude of the strain concentration occurring around the imperfect region was investigated by means of a finite element method, and the quantitative determination method of it was theoretically studied. In a stress analysis of the thin shell structures, a large deformation analysis considering geometrical nonlinearity of the imperfect regions was practically necessary and important, as reported previously in detail (Ohtani et al., Int. J. Pres. Ves. & Piping, 45 (1991) 3–21). As a result of this analysis, it was seen that the imperfection induced a considerably high strain concentration, even if the amplitude of imperfection was very small, and that a tendency of strain concentration due to loading of internal pressure apparently showed a nonlinearity to the pressure. Furthermore, from a comparison of the present results for the local non-axisymmetric imperfection with the previous ones for the banded axisymmetric imperfection, which deformed uniformly on circumferential direction, it was found that a tendency of strain concentration due to this kind of local imperfection was basically similar to that of the uniform axisymmetric one. Therefore, it was clarified that the magnitude of strain in the local non-axisymmetric imperfection was calculated in practical accuracy by using the formulae presented in the previous paper for the axisymmetric one.     

Linear elastic stress intensity factors for cracks in nuclear pressure vessel nozzles under pressure and temperature loading

Stress intensity factors for two different nozzle geometries and different crack sizes are evaluated for pressure and thermal loading utilising three-dimensional elastic finite element models.The results are compared to available experimental data and a procedure is proposed to estimate the maximum of the stress intensity factor for arbitrary crack size and loading conditions.     

Limit and shakedown analysis of nozzle/cylinder intersections under internal pressure and in-plane moment loading

A simple technique called the elastic compensation method developed previously by Mackenzie & Boyle is used in combination with full three-dimensional finite-element analysis to obtain limit and shakedown interaction diagrams for nozzle/cylinder intersections subject to combined internal pressure and in-plane nozzle moment loading. The results are compared with solutions from the literature and also with detailed elasto-plastic thin shell finite-element analysis. It is found that the simple elastic compensation procedure can provide good estimates of plastic failure mechanisms for complex three-dimensional structures. A detailed discussion of various issues which arose relates to finite-element modelling and the measures taken to improve the results are also documented.     

Plastic limit loads of nozzles in cylindrical vessels under out-of-plane moment loading

The purpose of this paper is to study the plastic limit moment of nozzles in cylindrical vessels with different d/D ratios under out-of-plane moment loading. Three full size test models were designed and fabricated. A 3D nonlinear finite element numerical simulation was also performed. A twice-elastic-slope plastic moment on the nozzles was obtained approximately by use of load–displacement and load–strain curves. The results show that plastic loads determined by test and numerical simulation methods are in good agreement. The results can serve as a basis for developing an advanced design guideline by limit analysis for cylindrical vessels with a nozzle under external loads.