Methods determining stresses and deflections

The determination of stresses developed in a pavement constitutes a fundamental prerequisite and is achieved by implementation of various methods depending on the number of distinct pavement layers. 

By definition, the subgrade is considered as one layer. Thus, in the typical flexible pavement that consists of unbound layer (base/sub-base) and bitumen-bound layers all consisting of asphalts with the same mechanical properties, the number of distinct layers is three. 

Generally, each of the constructed layers consisting of materials having different mechanical properties is considered as a distinct structural layer. 

This chapter presents methods for determination of stresses, strains and deflections developed in a one-layer, two-layer, three-layer and multi-layer system. 

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Skirt construction permits radial growth of pressure vessel due to pressure and temperature through the bending of skirt acting like a beam on an elastic foundation. The choice of proper height of the skirt support ensures that bending takes place safely. Finite-element methods can be effectively used to determine the stresses and deflections due to imposed pressure and temperature distribution. 

Finite element analysis (FEA) is a computer-based technique for determining the stresses and deflections in a structure. Essentially, this method divides a structure into small elements with defined stress and deflection characteristics. The method is based on manipulating arrays of large matrix equations that can be realistically solved only by computer. Most often, FEA is performed with commercial programs. In many cases these programs require that the user know only how to properly prepare the program input. 

The equations and methods for determining viscosity vary greatly with the type of instmment, but in many cases calculations may be greatly simplified by calibration of the viscometer with a standard fluid, the viscosity of which is known for the conditions involved. General procedures for calibration measurement are given in ASTM D2196. The constant thus obtained is used with stress and shear rate terms to determine viscosity by equation 25, where the stress term may be torque, load, or deflection, and the shear rate may be in rpm, revolutions per second (rps), or s F... 

Quantitative evaluation of a force-distance curve in the non-contact range represents a serious experimental problem, since most of the SFM systems give deflection of the cantilever versus the displacement of the sample, while the experimentalists wants to obtain the surface stress (force per unit contact area) versus tip-sample separation. A few prerequisites have to be met in order to convert deflection into stress and displacement into tip-sample separation. First, the point of primary tip-sample contact has to be determined to derive the separation from the measured deflection of the cantilever tip and the displacement of the cantilever base [382]. Second, the deflection can be converted into the force under assumption that the cantilever is a harmonic oscillator with a certain spring constant. Several methods have been developed for calibration of the spring constant [383,384]. Third, the shape of the probe apex as well as its chemical structure has to be characterised. Spherical colloidal particles of known radius (ca. 10 pm) and composition can be used as force probes because they provide more reliable and reproducible data compared to poorly defined SFM tips [385]. 

This test is only a guide. It represents a method that could be correlated to product designs (see Chapters 4—5), but, as with most other tests conducted on test specimens and not on a finished product, it is just a guide. In this test, if the specimen contains internal stresses the value will be lower than a specimen with no stresses. In fact, the test can be used to determine the degree of stress. Since a stress and the deflection for a certain depth of test bar are specified, this test may be thought of as establishing the temperature at which the flexural modulus decreases to particular values 35,000 psi (240 MPa) at 66 psi load stress, and 140,800 psi (971 MPa) at 264 psi. 

ISO 75 An International Organization for Standardization (ISO) standard test method for determination of heat deflection temperature (HDT) and deflection temperature under load (DTUL). HDT is a relative measure of a materials ability to perform for a short time at elevated temperatures while supporting a load. The test measures the effect of temperature on stiffiiess a standard test specimen is given a defined surface stress and the temperature is raised at a uniform rate. Alternate test methods for HDT and DTUL are DIN 53461 and ASTM D648. 

ASTM D 648 describes a method for determining the heat deflection temperature (HDT) or deflection temperature under load (DTUL). With the trend toward globalization, this method is reflected in and refined by ISO 75. Both tests seek to define the temperature at which a given degree of bending is achieved in a sample placed under a fixed flexural stress. The apparatus used to conduct the test is shown (Figure 1). The working portion of the instrument is immersed in an oil-based fluid, which is used as the heat transfer medium. A specimen is placed in a 3-point bend fixture and the desired stress... 

In the method of Martens a test rod is mounted upright in a support and the upper free end is put under a bending stress via a small weighted lever. The rod is slowly heated in an oven until a specified deflection is attained. The softening point determined in this way is called the Martens temperature. 

Several experimental procedures can be used to measure the residual stresses. The three preferred methods involve diffraction (X-ray or neutron), beam deflection, and permanent strain determination. X-ray diffraction measurements have the limitation that the penetration depth is small, such that only near-surface information is obtained. Moreover, in composites, residual stresses are redistributed near surfaces.47 Consequently, a full stress analysis is needed to relate the measured strains to either q or a. ... 

The most commonly used direct method for determination of surface stress is the bending beam method in which a lever bends when subjected to a change in surface stress in one of its faces in order to minimize its stored strain energy. The relationship between the deflection of a cantilever and the different stresses in its smfaces was first determined by Stoney [25] and in surface science it has been used to measure the stress changes associated with the reconstructions of semiconductor surfaces [26 - 27]. 

The low-speed mechanical properties of polymer blends have been frequently used to discriminate between different formulations or methods of preparation. These tests have been often described in the literature. Examples of the results can be found in the references listed in Table 12.9. Measurements of tensile stress-strain behavior of polymer blends is essential [Borders et al., 1946 Satake, 1970 Holden et al., 1969 Charrier and Ranchouse, 1971]. The mbber-modified polymer absorbs considerably more energy, thus higher extension to break can be achieved. By contrast, an addition of rigid resin to ductile polymer enhances the modulus and the heat deflection temperature. These effects are best determined measuring the stress-strain dependence. 

BS 2782, Methods 121A and 121B, Determination of Temperature of Deflection under a Specified Bending Stress of Plastics and Ebonite, London (1976). 

The importance, feasibility, and value of in situ investigations of thin-film deposition from the gas phase by PVD and CVD methods have been demonstrated using two selected techniques. In both cases, the measurement conditions ensure a direct relationship between the obtained data and thin-film deposition. Special efforts are made to avoid any interference of the processes from the measurements and vice versa. TOF-MS with laser ionization is applied to detect intermediate gas-phase species involved in thin-film formation. Deflection of two probe laser beams induced by reflection from a curved substrate is used to determine the direction and amount of mechanical stress in the growing layer. 

The consideration of general missile effects on the barrier should include the possible deformation of the structure by local missile effects. If there is no major local deformation of the structure by penetration, then methods of energy balance and momentum balance can be used to predict the deflections or stresses in principal members for the purpose of determining whether the barrier can contain the missile and continue to perform its design function. If, however, local missile effects are severe, as they often are, an appUed force-response time history should be developed and the structural response should be analysed as for an impulse load. The dynamic loads induced by missile impacts should be considered with due attention to the frequency response of the target structure. This is particularly important when the response of the barrier may interfere with the operability of equipment either mounted directly on the barrier or installed in the vicinity of the barrier. 

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