Elasticity, resilient modulus

Figure 13.8 Chart for estimating structural layer coefficient of dense-graded asphalt concrete (o,) based on the elastic (resilient) modulus. (From AASHTO, AASHTO Guide for Design of Pavement Structures, Washington, DC American Association of State Highway and Transportation Officials, 1993. With permission.)...

For the determination of the asphalt concrete structural coefficient, the methodology recommends the elastic (resilient) modulus ( ac) 20°C to be less than 450,000 psi... 

It can be easily shown that equivalent expressions for the strain energy per unit volume are U=o e/2 and U = a2/2 E. The modulus of elastic resilience, Ur, of a material is defined as the strain energy absorbed per unit volume when it is stressed to its proportional limit. Thus,... 

Sulfui>-Aggregate Interaction. Substantial increases in stiffness of SA binder-based mixes, as measured by the Marshall test, tensile strength, and resilient modulus of elasticity, have been observed with increasing sulfur-asphalt ratio of the binder used (11, 15, 16). Such increases can, of course, be attributed in part to the increase in viscosity of the SA... 

Resilient Modulus of Elasticity. The addition of sulfur produced an increase in stiffness in terms of resilient modulus of elasticity, Figure 9. Generally this increase required the addition of 50% sulfur, although in some cases 20% sulfur produced a substantial increase. 

It should be re-emphasized that this analysis was only preliminary and based on assumed elastic properties of the sulfur-asphalt material. A more representative analysis using dynamic properties obtained from fatigue and resilient modulus tests is now in progress. 

The deviator stress Oa (=Oi - 02) is repeated, at a fixed magnitude and frequency. The loading of the soil specimen, under the influence of deviator stress, results in a deformation, part of which is recoverable during the stage of unloading. This recoverable strain along with the deviator stress determines the resilient modulus (Mr), or the modulus of elasticity ( ), of the material tested, using the equation... 

Elastic modulus, resilient modulus and flexural strength for design purpose... 

In most pavement design methodologies for roads and highways, the traffic load is expressed in terms of equivalent standard axle load (ESAL). The bearing capacity or strength of the subgrade material is expressed in terms of CBR or resilient modulus, Mr, whereas that of the unbound or hydraulically bound layers is expressed in terms of modulus of elasticity and that of the asphalt layers is expressed in terms of stiffness modulus. 

The subgrade material is characterised by the elastic or resilient modulus, Mr, determined by AASHTO T 307 (2007) (also see Section 1.9.1). This property changes with seasonal variation of moisture content. The seasonal resilient moduli must be determined and from that an effective subgrade resilient modulus must be established. 

The materials with which the sub-base and base course layers constructed are characterised also by elastic or resilient modulus (AASHTO T 307 2007), using different designations Eje and Egs, for sub-base and base course, respectively. 

As for the asphalt concrete, the elastic modulus, , also known nowadays as (instantaneous or total resilient modulus) is determined according to ASTM D 7369 (2011) (see also Section 7.4.8). 

As it can be seen, the structural layer coefficients for the granular base or sub-base layers may be derived from different laboratory tests including resilient modulus (Egg or sb)-Similarly, the structural layer coefficients for the cement-treated bases or bituminous-treated bases may be derived from unconfined compressive strength or Marshall stability, respectively, including elastic modulus. 

The paving materials characterisation concerns resilient modulus determination of all unbound layers, dynamic modulus for all asphalt layers and elastic modulus for Portland cement or chemically stabilised layers. 

The design data required for the determination of the slab thickness for an assumed subbase thickness (>150 mm) are as follows resilient modulus of subgrade (M ), elastic modulus of sub-base (E ), modulus of rupture of concrete (S ) (or flexural strength of concrete), elastic modulus of concrete ( (.), cumulative ESAT over the design period (W ), overall standard deviation (S ) and design serviceability (APSI) as in flexible pavement design. 

Despite the collected information on the existing pavement, coring and materials testing are strongly recommended to determine the resilient modulus of the subgrade, M, (or CBR), the elastic modulus of the asphalt, and the concrete modulus of rupture, S, in most cases. 

See compressive modulus, flexural modulus, shear modulus, modulus of elasticity and modulus of resilience. 

Modulus of Elasticity and Modulus of Resilience. (2) The absolute value of a complex number or quantity, equal to the square root of the sum of the squares of the real and imaginary parts. (3) Modulus at 300% n The tensile stress required to elongate a specimen to three times its original length (200% elongation)... 

The allowable dimensional variation (the tolerance) of a polymer part can be larger than one made of metal - and specifying moulds with needlessly high tolerance raises costs greatly. This latitude is possible because of the low modulus the resilience of the components allows elastic deflections to accommodate misfitting parts. And the thermal expansion of polymers is almost ten times greater than metals there is no point in specifying dimensions to a tolerance which exceeds the thermal strains. 

Resilin and elastin have relatively high extensibility and resilience, but as compared to the collagen and the silks, the proteins sacrifice stiffness (elastic modulus) and strength (see Table 2). Collagen and dragUne sflk are much stiffer materials, but lack the extensibility that is characteristic of the rubber-like proteins. On the other hand, the mussel byssus fibers and the viscid silk have the extensibility of resilin and elastin, but lack the resilience [208]. 

The important elastic properties of a material undergoing deformation under static tension are stiffness, elastic strength and resilience. For a material obeying Hooke s law, the modulus of elasticity, E (= o/e), can be taken to be a measure of its stiffness. The elastic... 

The current method of determining the energy properties of polyurethane is the Dynamic Thermal Mechanical Analyzer (DTMA). This instrument applies a cyclic stress/strain to a sample of polyurethane in a tension, compression, or twisting mode. The frequency of application can be adjusted. The sample is maintained in a temperature-controlled environment. The temperature is ramped up over the desired temperature range. The storage modulus of the polyurethane can be determined over the whole range of temperatures. Another important property closely related to the resilience, namely tan delta (8), can also be obtained. Tan (8) is defined in the simplest terms as the viscous modulus divided by the elastic modulus. 

It is necessary that the adhesive retain some resiliency if the thermal expansion coefficients of the adhesive and adherend cannot be closely matched. At room temperature, a standard low-modulus adhesive may readily relieve stress concentration by deformation. At cryogenic temperatures, however, the modulus of elasticity may increase to a point where the adhesive can no longer effectively release the concentrated stresses. At low service temperatures, the difference in thermal expansion is very important, especially since the elastic modulus of the adhesive generally decreases with falling temperature. 

In the second case, in which the Tg of the chain segment is above the test temperature, the uncross-linked polymer is a brittle solid. Cross linking does not appreciably increase the modulus of elasticity or resiliency, but has a very strong influence (discussed later) on the temperature dependence of these properties. 

The outstanding property of rubber in general is resilience, or low modulus of elasticity. The flexibility and physical properties of rubber account for its application in general engineering and automobile industries whereas its chemical, wear and abrasion resistance as a sacrificial material, plus its insulating properties are utilised in many corrosion and erosion applications in process industries. Rubber lined mild steel, pipes and tankages have been standard materials of construction for hydrochloric acid service for many years. 

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