Electrical Resistance Strain Gauges Research Articles

The Westminster Hall Roof: A Historiographic and Structural Study

The great hall roof of the medieval palace at Westminster, which now adjoins the British Houses of Parliament, was erected c. 1395 by Hugh Herland and stands as one of the great achievements of English monumental carpentry. When the roof was built to span the vast un-aisled interior of nearly 68 feet, it was 50 percent wider than any previously known hall in England. Hence, this unique framing of unprecedented scale has long been regarded as a technological tour de force uniting engineering skill and visual elegance. For the last century and a half, Herland's framing, combining a great arch with a "hammer-beam" bracket, has been discussed for its remarkable structure, and a number of ideas have been suggested by English and Continental experts concerning how the great weight of the roof is sustained and which members of the truss are structural as opposed to those which are mainly decorative. Yet, despite recent analyses by prominent engineers, there is no consensus of opinion as to how the frame actually carries its load. From a review of the major literature, which forms the first part of our study, a number of important questions arise concerning the nature of the timber frame, the function of its primary members, and, particularly, the precise structural relationship between the roof and its supporting masonry. In order to address and resolve the major structural and historiographical issues, we have undertaken a new and more complete study of the Westminster roof that combines archaeological and historical research with two types of interactive model analyses. The initial model was carefully constructed of timber at 1:10 scale to conform as closely as possible to a transverse frame of Herland's truss. This model, instrumented with electric-resistance strain gauges, was used to determine the general behavior of the truss under loading and with three kinds of support conditions, corresponding to the conflicting theories examined in the literature. Using the data from the timber-model testing as a guide, we then refined the analysis with a numerical (computer) model. Our results have clearly resolved the major questions raised by previous studies and indicate that the roof derives its primary support from the masonry wall at the level of the heraldic corbels, upon which rest the massive timber wall posts. The load of the roof is carried nearly halfway down the walls by the combined action of the heavy hammer posts and the great arch rib. We also found that the angel hammer beams are in tension and that they function, significantly, to take horizontal forces off the top of the wall. Moreover, these findings are consistent both historically and structurally with other examples of English carpentry that preceded Herland's brilliant design for Westminster Hall.

Strain-gage methods for measuring the opening-mode stress-intensity factor,K I

Measurements of strain near a crak tip with electrical-resistance strain gages do not usually provide a reliable measure ofK I because of local yielding, three-dimensional effects and limited regions for strain-gage placement. This paper develops expressions for the strains in a valid region removed from the crack tip, and indicates procedures for locating and orienting the gages to accurately determineK I from one or more strain-gage readings.

Gauged sleeve for controlled testing of rock

Electrical resistance strain gages, each 5 cm in length, were embedded at a depth of 1 mm, inside a Cil Monothane sleeve of thickness 2 mm. Cil Monothane A80 is a single component and non-toxic, he ...

Measurement of internal concrete strains using embedment strain gauges

Synopsis The use of embedment strain gauges—electric resistance strain gauges encapsulated in acrylic resin—for the measurement of internal concrete strain distributions infive tension specimens is described. Results are presented to illustrate the performance of the technique.

Determination of calibration constants for the hole-drilling residual stress measurement technique applied to orthotropic composites—Part I: Theoretical considerations

The hole-drilling technique for the measurement of residual stresses using electrical resistance strain gages has been widely used for isotropic materials and has been adopted by the ASTM as a standard method. A few attempts have been made to extend the technique to orthotropic composite materials. For thin isotropic plates, with a hole drilled through the thickness, the idealized hole-drilling calibration constants are obtained by making use of the well known Kirsch's solution. In this paper, an analogous attempt is made to theoretically determine the three idealized hole-drilling calibration constants for thin orthotropic materials by employing Savin's complex stress function approach. In Part II (to appear in the next issue), test results for a graphite-polyimide composite, with a very high degree of orthotropy, are given and compared with the theoretical results.

Glass reinforced plastic pipe bend subjected to vacuum and flexure

Tests were carried out on a right-angled GRP pipe bend constructed from E-glass and polyester resin by hand lay-up. The glass was in the form of chopped strand mat and the content was 1.2 kg m −2. The internal pipe diameter and the mean bend radius were nominally 250 mm. Straight lengths of pipe were attached to the bend for experimental purposes. Electrical resistance strain gauges and displacement transducers were used extensively to obtain measurements when the bend was subjected to vacuum only, in-plane flexure with and without vacuum and out-of-plane flexure with and without vacuum. Derived stress distributions and displacements were compared with theoretical estimates. The pipe bend under vacuum was finally tested to fracture when subjected to inplane flexure (tending to reduce the bend radius). It was clear that in designing GRP bends of certain geometries, vacuum alone and vacuum combined with flexure should be taken into consideration in applications where it is possible for vacuum to occur.

The use of electrolevel transducers for strain measurements in triaxial tests on weak rock

A new family of submersible local strain measuring devices has recently been developed. The gauges are designed to be mounted on the membrane of specimens undergoing triaxial testing without any special sample preparation. They permit accurate measurements of axial strain in tests where bedding, tilt and other errors can invalidate the conventional external recordings of strains over the vital early stages of a stress-strain curve. The transducers operate over a wide range of strain and can be used equally for drained or undrained experiments. The first test programme carried out with the new gauges included a number of experiments with samples of intact chalk. The results of three of these tests, and a description of the new transducers, are presented to illustrate how some of the developments can be of use in the testing of rocks in cases where the established techniques are not convenient. The devices offer advantages over electrical resistance strain gauges in some applications. The ease with which they can be mounted particularly suggests their use with fragile samples and by measuring strain over the central two thirds, representative results can be obtained with weathered or heterogeneous rocks. The gauges can also be used to study post-peak behaviour with brittle materials, provided that neither transducer becomes isolated on a single large piece of loose rock. It can also be seen that the technique is convenient in tests in which the fully saturated behaviour of porous samples is to be investigated. These features were particularly useful in observing the pre- and post-peak behaviour of the chalk samples. (TRRL)

On the Stress Concentration in a Strip with a Row of Circular Holes Subjected to In-plane-bending

The stress concentration problem of a strip with a finite row of circular holes subjected to in-plane-bending is solved numerically. It is assumed that the holes have equal diameters and are placed on a center line of the strip at equal intervals. A numerical method is adopted in which a general form of stress function expressed in the polar coordinates and its transformed equation in the rectangular coordinates are recurrently used; the former is used in the method of Fourier analysis to satisfy the boundary conditions on the circular edges, and the latter is used in the method of Fourier transform to satisfy the boundary conditions on the rectilinear edges. Stress concentration factors are calculated and summarized in some diagrams. The calculated results coincide well with solutions obtained by the finite element method and experimental data obtained by electrical resistance strain gages.

The work hardening of dual-phase steels at small plastic strains

The work hardening at small plastic strains in dual-phase steels has been studied as a function of the microstructure and the volume fraction of the hard phase (phase II) in a series of fully characterized steels with between 0 and 100 vol.% of phase II. Three series of steels were examined: banded, homogenized, and homogenized and tempered at 200°C. In all the steels the ferrite was free of fine precipitate particles and the martensite contained 0.37 wt.% C and negligible amounts of retained austenite. The elastic limits of the steels (the stress at a strain of less than 5 × 10 −5 and the stress-strain curves at small plastic strains were measured using balanced electrical resistance strain gauges of high sensitivity. The internal stresses were assessed from measurements of the Bauschinger strains as a function of the volume fraction of phase II and, in the untempered homogenized steel with 26 vol.% of phase II, as a function of the plastic prestrain. The cyclic hardening characteristics of the steels were determined by continuing the cyclic tests at a constant strain amplitude for 10 cycles or more. In all the dual-phase steels the elastic limit is equal to or less than the elastic limit of annealed ferrite, an effect which is attributed to the presence of local internal elastic stresses in the ferrite resulting from the strains produced by the martensitic transformation. The rapid work hardening in the dual-phase steels with a ferrite matrix is due to the heterogeneous deformation of the ferrite at plastic strains of less than about 3.5 × 10 −2, a heterogeneity which is due to the large variations in dislocation density within the ferrite. Heterogeneous deformation of the ferrite is a factor also in the initial deformation of steels with a martensitic matrix but, in this case, the high local elastic stresses are more important. The long-range elastic stresses in the ferrite of steels with a ferrite matrix are small at zero plastic strain, increase with increasing plastic strain and level off to a constant value at large strains. The contribution of these stresses to the hardening at small plastic deformations (less than 5 × 10 −3) is not significant but at larger deformations it can account for a measurable fraction of the hardening. The origins of the short- and long-range elastic stresses are discussed in some detail. There is no long-range internal stress in the martensite as is shown by the absence of permanent softening in the Bauschinger test. The cyclic hardening and softening of the dual-phase steels and of the constituent phases are described and discussed, as are the effects on all the properties considered here produced by low temperature tempering.

The application of resistance strain gauges to the study of metal-hydrogen systems

Tests and various applications of bonded electric resistance strain gauges in research on metal-hydrogen systems are reported.

An experimental study of the ratchetting and creep of thick flanged tubes subjected to steady axial mechanical loading and transient thermal loading

The aims of the investigation were to obtain experimental data against which finite element predictions can be assessed and to see whether the lead alloy used was suitable as a “ratchetting” model material. Thermal ratchetting tests were performed on lead alloy flanged tube components. In some of the tests, dwell periods were allowed between successive thermal shocks. Electrical resistance strain gauges were used to measure the ratchet and creep strains in plain tube and stress concentration regions. It was found that both the plain tube and peak fillet ratchet strains increased with increasing mechanical and thermal load for short dwell periods. However, the ratio of the peak fillet to plain tube ratchet strains reduced with increasing mechanical and thermal load. Also, the ratio of the peak fillet to plain tube ratchet strains increased with increasing dwell period. The data obtained from the lead alloy model component tests were found to correlate with data from a number of different components made from various materials, indicating that the material may be useful as a “ratchetting” model material.

Predicting the thermal ratchetting and creep behaviour of a component with a stress concentration

Finite element and ‘upper bound’ predictions of ratchetting and creep are compared with experimental data from two axially loaded shouldered tubes subjected to axisymmetric cyclic temperature variations. The shouldered tubes were machined from chill-cast bars of a lead alloy material. Electrical resistance strain gauges were used to measure the ratchet and creep strain. The results show that ratchet strains can accumulate significantly faster in stress concentration regions when compared with plain tube regions. Acceptable predictions were obtained for the ratchet strains. The discrepancies between the predicted and measured dwell period strains were due to neglecting the material plasticity-creep interactions. Some simple methods for estimating the strains are suggested.

Experimental theramal ratchetting data for a component with a stres concentration

The result from eleven tests of lead alloy model shouldered tubes, subjected to constant axial mechanical loads and cyclic, axisymmetric thermal shocks are described. Dwell periods between 0.5 h and 24 h allowed creep to occur between the thermal shocks. Electrical resistance strain gauges were used to measure ratchet and creep strains. At low mean axial stresses (< 0.94σy), it was found that the ratchet strains increased with load and dwell period. It was also found that the ratchet strains in the fillet region were significantly larger than those in the shank and are induced at lower mechanical loads than those in the shank. For higher stresses, the ratchet strains were found to be relatively insensitive to both load and dwell period. Also, the ratchet strains in the fillet and shank were found to be of the same magnitude.

Measurement of surface strains in GRP products

Current work on fibre composite materials required the measurement of surface strains on glass reinforced plastics (GRP) products subjected to static loading. A study undertaken to account for anomalous results obtained with electrical resistance strain gauges showed that strains measured at a given load, increased with decreasing gauge length and foil gauge resistance. Measurement of localised strains using gauges of length up to 25 mm are subject to considerable discrepancy when compared with gauge lengths of less than 13 mm.

Simplified Laser-Speckle Strain Gauge

An automatic method of measuring surface strain by electro-optical techniques is described. It is a real-time and point-by-point method in which a specimen surface is illuminated by a thin laser beam and the displacements of the speckle pattern resulting from the surface deformation are detected by linear image sensors followed by a microcomputer. The displacements are calculated as the peak positions of the cross-correlation functions of image sensor signals before and after the deformation. By adopting a differential system consisting of two image sensors positioned symmetrically about the surface normal we can eliminate the effect of rigid body motion. The sensitivity depends on the surface to sensor distance, while the gauge length is given by the diameter of the laser spot. These relations derived from physical optics are verified by experiments using a metal plate specimen subject to tensile strain that is monitored by an electrical resistance strain gauge. The minimum strain value measured was a few ten microstrains with a gauge length of 1 mm. We could also measure thermal strain by this method.

The behaviour of post yield strain gauges

The calibration of post yield electrical resistance strain gauges in tension shows that their behaviour is strongly dependent upon gauge construction, bond strength, the presence of instability and the mechanism of plastic deformation. For medium tensile strains in the range 0‐5% the calibrations reveal that the gauge sensitivity factor consists of separate elastic and plastic components which are respectively identified with recoverable and irrecoverable strain components.

A rig for creep and thermal ratchet testing of lead alloy models

The development and calibration of a rig and an axisymmetric lead alloy component for isothermal creep, non-isothermal creep, and thermal ratchetting testing is described. Steady and variable, axial mechanical loads are applied by a dead weight and lever system. Thermal loads are applied by controlled variations of the temperature of water flowing through the bore and along the outside of the component. Strains and temperature are measured with electrical resistance strain gauges and thermocouples, respectively.

Contact pressure distribution in circular tube expansion using a conical plug

The technique of evaluating contact pressure distributions along a plug metal interface by measuring the deformations in terms of plug surface strains using electrical resistance strain gauges has been explored. To relate the unknown pressure distributions to the strain gauge readings, a finite element model of a plug was used assuming that the normal and shear pressures can be represented as a linear combination of generalized distributions, which have the form of polynomials up to the fourth order. This technique has been suitably applied to a thin brass tube expanding process for a single expansion ratio, and a single conical hollow plug with and without lubricant. To ensure good accuracy in the results, particular care was given to technological plug design and the choice of a number of appropriate strain gauged points on the inside surface of the plug. The more adequate polynomial representations of the normal and shear contact pressures were found by analyzing the degree of randomness in the distribution of the residuals. A comparison was made between experimental pressure distributions and those predicted by the slab method. Results obtained were compared with those derived from the use of a polynomial curve fitting method, besides assuming an average coefficient of friction at the interface.

Tests on a simply supported rhombic plate

This paper deals with tests done on a simply supported isotropic rhombic plate subjected to certain conditions of lateral loading. The loading conditions used were (i) uniformly distributed load covering the whole plate, (ii) patch load at the centre of the plate, (Hi) uniformly distributed load over a quarter of the plate. Bending moments were obtained at certain important locations on the plate, using electrical resistance strain gauges. The central deflections were also recorded. The results obtained were compared with the available theoretical results. The correlation for the case of uniformly distributed load covering the whole plate was found to be good.

A Study of Hyperbolic-Paraboloidal Concrete Shell Structures

This paper presents a report on the theoretical, experimental and constructional problems related to a Hyperbolic-Paraboloid (H-P) shell of an inverted umbrella type, supported on a single column. The geometry of an H-P shell model of 1 metre by 1 metre and 3cm thick was chosen for study in this work. The shell was designed and analyzed by the finite element method. Electrical resistance strain gauges were mounted both inside and outside at several locations on the surface of the shell. The structure was loaded within the elastic limit. The experimental values of membrane stresses are calculated and compared with theoretical values. These results are in close agreement at most locations, and the discrepancies between the experimental and theoretical results is less at points located at some distance away from the support and the edges of the shell. Following the non-destructive test, the model was loaded to failure. Based on the information gained by this study, a larger shell structure was successfully c...