Field measurements in two tunnels in Edmonton, Alberta

1980 ◽  
Vol 17 (1) ◽  
pp. 20-33 ◽  
Author(s):  
S. Thomson ◽  
F. El-Nahhas
Keyword(s):  
Body Movement ◽  
Small Diameter ◽  
Ground Surface ◽  
Beam Theory ◽  
Field Measurements ◽  
Element Analysis ◽  
Overburden Pressure ◽  
Pressure Cell ◽  
Horizontal Diameter ◽  
Overburden Thickness

Observations of the deformation of the temporary lining of two tunnels are presented. The Whitemud Creek tunnel was 6.05 m in diameter and was bored through Upper Cretaceous clay shale. The 170 Street tunnel was bored through till and had a diameter of 2.56 m.In the Whitemud Creek tunnel, the vertical diameter decreased by 10–15 mm and the horizontal diameter decreased by 6 mm. Movement was essentially complete in about 3 months. There was a rigid body movement upward of the lining system probably due to unloading of the soil in the invert area. Deformation moduli indicate a softening of the soil around the tunnel, which is consistent with the deformation observations. A finite-element analysis suggests that this softened zone is as important with regard to lining deformation as increasing K0 from 0.67 to 1.0In the 170 Street tunnel, the ground surface showed significant movement despite the small diameter and considerable overburden thickness. The vertical and horizontal diameter decreases were about one half of those of the Whitemud Creek tunnel and were essentially complete in 4–5 weeks. Soil pressures calculated from the observations showed a wide variation. Values derived from lagging deflection yielded a maximum of 63% of overburden pressure whereas pressure cell readings were 3.3% of overburden.It appears that the space between the lagging and the moled surface of the soil is an important factor affecting the magnitude of stresses in the temporary lining. Diameter changes are considered to be the easiest and most reliable observation of tunnel linings. The deflection of the lagging is also simple to observe but may not satisfy simple beam theory. Pressure cell results were disappointing and their use is debatable.

Natural frequency analysis of a functionally graded rotor-bearing system with a slant crack subjected to thermal gradients

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arnab Bose ◽  
Prabhakar Sathujoda ◽  
Giacomo Canale
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Power Law ◽  
Beam Theory ◽  
Functionally Graded ◽  
Thermal Gradients ◽  
Element Analysis ◽  
Rotor Bearing ◽  
Natural Frequency Analysis ◽  
Bearing System

Abstract The present work aims to analyze the natural and whirl frequencies of a slant-cracked functionally graded rotor-bearing system using finite element analysis for the flexural vibrations. The functionally graded shaft is modelled using two nodded beam elements formulated using the Timoshenko beam theory. The flexibility matrix of a slant-cracked functionally graded shaft element has been derived using fracture mechanics concepts, which is further used to develop the stiffness matrix of a cracked element. Material properties are temperature and position-dependent and graded in a radial direction following power-law gradation. A Python code has been developed to carry out the complete finite element analysis to determine the Eigenvalues and Eigenvectors of a slant-cracked rotor subjected to different thermal gradients. The analysis investigates and further reveals significant effect of the power-law index and thermal gradients on the local flexibility coefficients of slant-cracked element and whirl natural frequencies of the cracked functionally graded rotor system.

scholarly journals Comparison of Mechanical Impedance Methods for Vibration Simulation

1996 ◽  
Vol 3 (3) ◽  
pp. 223-232 ◽  
Author(s):  
Jeffrey A. Gatscher ◽  
Grzegorz Kawiecki
Keyword(s):  
Mechanical Impedance ◽  
Field Measurements ◽  
Cumulative Damage ◽  
Vibration Test ◽  
Element Analysis ◽  
Impedance Measurements ◽  
Testing Strategies ◽  
Impedance Testing ◽  
Vibration Simulation ◽  
Test Requirements

The work presented here explored the detrimental consequences that resulted when mechanical impedance effects were not considered in relating vibration test requirements with field measurements. The ways in which these effects can be considered were evaluated, and comparison of three impedance methods was accomplished based on a cumulative damage criterion. A test structure was used to simulate an equipment and support foundation system. Detailed finite element analysis was performed to aid in computation of cumulative damage totals. The results indicate that mechanical impedance methods can be effectively used to reproduce the field vibration environment in a laboratory test. The establishment of validated computer models, coupled with laboratory impedance measurements, can eliminate the overtesting problems inherent with constant motion, infinite impedance testing strategies.

scholarly journals Dynamic Analysis of Honeycomb Sandwich Beam with Multiple Debonds

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
B. Saraswathy ◽  
R. Ramesh Kumar ◽  
Lalu Mangal
Keyword(s):  
Analytical Solution ◽  
Transient Analysis ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Beam Length ◽  
Honeycomb Core ◽  
Element Analysis ◽  
Fast Fourier Transform Analysis ◽  
Honeycomb Sandwich ◽  
Nonlinear Transient

Analytical formulation for the evaluation of frequency of CFRP sandwich beam with debond, following the split beam theory, generally underestimates the stiffness, as the contact between the honeycomb core and the skin during vibration is not considered in the region of debond. The validation of the present analytical solution for multiple-debond size is established through 3D finite element analysis, wherein geometry of honeycomb core is modeled as it is, with contact element introduced in the debond region. Nonlinear transient analysis is followed by fast Fourier transform analysis to obtain the frequency response functions. Frequencies are obtained for two types of model having single debond and double debond, at different spacing between them, with debond size up to 40% of beam length. The analytical solution is validated for a debond length of 15% of the beam length, and with the presence of two debonds of same size, the reduction in frequency with respect to that of an intact beam is the same as that of a single-debond case, when the debonds are well separated by three times the size of debond. It is also observed that a single long debond can result in significant reduction in the frequencies of the beam than multiple debond of comparable length.

Modeling of a One-Sided Bonded and Rigid Constraint Using Beam Theory

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Peter J. Ryan ◽  
George G. Adams ◽  
Nicol E. McGruer
Keyword(s):  
Boundary Conditions ◽  
Microelectromechanical Systems ◽  
Three Dimensional ◽  
Beam Theory ◽  
Rotational Stiffness ◽  
Element Analysis ◽  
Transverse Loads ◽  
Rigid Constraint ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

In beam theory, constraints can be classified as fixed/pinned depending on whether the rotational stiffness of the support is much greater/less than the rotational stiffness of the freestanding portion. For intermediate values of the rotational stiffness of the support, the boundary conditions must account for the finite rotational stiffness of the constraint. In many applications, particularly in microelectromechanical systems and nanomechanics, the constraints exist only on one side of the beam. In such cases, it may appear at first that the same conditions on the constraint stiffness hold. However, it is the purpose of this paper to demonstrate that even if the beam is perfectly bonded on one side only to a completely rigid constraining surface, the proper model for the boundary conditions for the beam still needs to account for beam deformation in the bonded region. The use of a modified beam theory, which accounts for bending, shear, and extensional deformation in the bonded region, is required in order to model this behavior. Examples are given for cantilever, bridge, and guided structures subjected to either transverse loads or residual stresses. The results show significant differences from the ideal bond case. Comparisons made to a three-dimensional finite element analysis show a good agreement.

Analysis and Optimization of Bellows With General Shape

1998 ◽  
Vol 120 (4) ◽  
pp. 325-333 ◽  
Author(s):  
B. K. Koh ◽  
G. J. Park
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Beam Theory ◽  
Inequality Constraints ◽  
Shell Element ◽  
Scalar Function ◽  
Programming Algorithm ◽  
Multiple Objective ◽  
Axially Symmetric ◽  
Element Analysis

A bellows is a component in piping systems which absorbs mechanical deformation with flexibility. Its geometry is an axially symmetric shell which consists of two toroidal shells and one annular plate or conical shell. In order to analyze the bellows, this study presents the finite element analysis using a conical frustum shell element. A finite element analysis program is developed to analyze various bellows. The formula for calculating the natural frequency of bellows is made by the simple beam theory. The formula for fatigue life is also derived by experiments. A shape optimal design problem is formulated using multiple objective optimization. The multiple objective functions are transformed to a scalar function with weighting factors. The stiffness, strength, and specified stiffness are considered as the multiple objective function. The formulation has inequality constraints imposed on the natural frequencies, the fatigue limit, and the manufacturing conditions. Geometric parameters of bellows are the design variables. The recursive quadratic programming algorithm is utilized to solve the problem.

Do We Need a Safe Excavation Pressure for Dented Pipelines: How Should it Be Defined?

2018 ◽  
Author(s):  
Muntaseer Kainat ◽  
Doug Langer ◽  
Sherif Hassanien
Keyword(s):  
Fracture Mechanics ◽  
Boundary Conditions ◽  
Structural Reliability ◽  
Limit State ◽  
Stress And Strain ◽  
Operating Pressure ◽  
Fitness For Purpose ◽  
Element Analysis ◽  
Overburden Pressure ◽  
Conflicting Objectives

Pipeline operators’ utmost priority is to achieve high safety measures during the lifecycle of pipelines including effective management of integrity threats during excavation and repair processes. A single incident pertaining to a mechanical damage in a gas pipeline has been reported previously which resulted in one fatality and one injury during investigation. Some operators have reported leaking cracks while investigating rock induced dents. Excavation under full operating pressure can lead to changes in boundary conditions and unexpected loads, resulting in failure, injuries, or fatalities. In the meantime, lowering operating pressure during excavation can have a significant impact on production and operational availability. The situation poses two conflicting objectives; namely, maximizing safety and maximizing operational availability. Current pipeline regulations require that operators have to ensure safe working conditions by depressurizing the line to a level that will not cause a failure during the repair process. However, there are no detailed guidelines on how an operator should determine a safe excavation pressure (SEP) level, which could lead to engineering judgment and subjectivity in determining such safety level. While the pipeline industry relies on well-defined fitness for purpose analyses for threats such as crack and corrosion, there is a gap in defining a fitness for purpose for dents and dents associated with stress riser features in order to set an SEP. Stress and strain based assessment of dents can be used in this matter; however, it requires advanced techniques to account for geometric and material nonlinearity. Additionally, loading and unloading scenarios during excavation (e.g. removal of indenter, overburden pressure, etc.) drive a change in the boundary conditions of the pipe that could lead to leakage. Nevertheless, crack initiation or presence within a dent should be considered, which requires the incorporation of crack geometry and application of fracture mechanics in assessing a safe excavation pressure. Recently, there have been advancements in stress and strain based finite element analysis (FEA) of dents coupled with structural reliability analysis that can be utilized to assess SEP. This paper presents a reliability-based approach to determine a safe excavation pressure for dented liquid pipelines. The approach employs nonlinear FEA to model dents interacting with crack features coupled with uncertainties associated with pipe properties and in-line-inspection information. A fracture mechanics-based limit state is formulated to estimate the probability of failure of dents associated with cracks at different levels of operating pressure during excavation. The application of the developed approach is demonstrated through examples within limited scope. Recommended enhancements and future developments of the proposed approach are also discussed.

scholarly journals NASTRAN Analysis of a Turbine Blade and Comparison With Test and Field Data

1975 ◽  
Author(s):  
J. M. Allen ◽  
L. B. Erickson
Keyword(s):  
Turbine Blade ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Mode Shapes ◽  
Stress Distributions ◽  
Free Standing ◽  
Element Analysis ◽  
Metallographic Examination ◽  
Stiffening Effect ◽  
Generalized Beam Theory

A NASTRAN finite element analysis of a free standing gas turbine blade is presented. The analysis entails calculation of the first four natural frequencies, mode shapes, and relative vibratory stresses, as well as deflections and stresses due to centrifugal loading. The stiffening effect of the centrifugal force field was accounted for by using NASTRAN’s differential stiffness option. Natural frequencies measured in a rotating test correlated well with computed results. Areas of maximum vibratory stress (fundamental mode) coincided with the three zones of crack initiation observed in a metallographic examination of a fatigue failure. Airfoil stress distributions were found to be significantly different from that predicted by generalized beam theory, especially near the airfoil-platform junction.

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