Design elastic modulus determinations

A different design approach is used in this case. Instead of assuming an apparent modulus of elasticity using a constant creep situation covering the life of the chair, it is better to determine the actual creep deflection over a typical stress cycle, the creep recovery over a non-use cycle, and so on until the creep is determined after a series of what might be considered typical hard usage cycles for the chair. The accumulated creep after a period of two weeks can be assumed to represent the base line for an apparent modulus of elasticity to determine the design life of the chair. 

The Weissenbeig Rheogoniometer (49) is a complex dynamic viscometer that can measure elastic behavior as well as viscosity. It was the first rheometer designed to measure both shear and normal stresses and can be used for complete characterization of viscoelastic materials. Its capabilities include measurement of steady-state rotational shear within a viscosity range of 10-1 —13 mPa-s at shear rates of 10-4 — 104 s-1, of normal forces (elastic effect) exhibited by the material being sheared, and of an oscillatory shear range of 5 x 10-6 to 50 Hz, from which the elastic modulus and dynamic viscosity can be determined. A unique feature is its ability to superimpose oscillation on steady shear to provide dynamic measurements under flow conditions all measurements can be made over a wide range of temperatures (—50 to 400°C). 

In a pavement design methodology such as the AASHTO methodology (AASHTO 1993), the elastic modulus, E (ASTM C 469 2010), or alternatively, the unconfined compressive strength (7 days) (ASTM D 1633 2007) of the CTA base, needs to be determined. With either value, the structural coefficient (<72) is derived and the thickness of the corresponding layer as well as of all layers of a flexible pavement is determined (see Section 13.4.4.3). For a rigid pavement design, the elastic modulus of the sub-base is used (see Section 14.11.1). 

In the Mechanistic-Empirical Pavement Design Guide (MEPDG) (AASHTO 2008), for a new pavement design, when CTA or LC material is used, the elastic modulus is required to be determined (ASTM C 469 2010). In the case of a flexible pavement only, its flexural strength is also required to be determined, according to AASHTO T 97 (2010). 

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. 

Other input data for the determination of the concrete slab are as follows elastic modulus of concrete, E, mean concrete modulus of rupture, (three-point bending test), load transfer coefficient, J (from Table 2.6 of AASHTO 1993), drainage coefficient, Cj (coefficient similar to the one used in flexible pavements), design serviceability loss (APSI), estimated future traffic, Wjg (as determined in flexible pavements but using equivalency coefficients for rigid pavements), the overall standard deviation, (usually 0.35), and the reliability, R (as determined in flexible pavements). 

In order to study the feasibility of the proposed designs shown in Figure 11.4, a finite element simulation was performed by Mazzoldi and eoUeagues [13], To simulate the strueture s meehanieal behaviour, parameters whieh quantify the expansion or eontraetion of the CP due to eleetroehemieal exeitation need to be determined. These parameters inelude Young s modulus of the passive catheter sheaths, the conjugated polymer and of the SPE, and the CP electrochemical strain. In the simulation reported [13], a commercial biocompatible polyethylene tube with an elastic modulus of 140 MPa was assumed to form the internal and external sheaths and to act as the electrochemical insulator. The two active configurations shown in Figure 11.4 were modelled. 

It is appropriate to note that industry specification sheets often give the elastic modulus, yield strength, strain to yield, ultimate stress and strain to failure as determined by these elementary techniques. One objective of this text is to emphasize the need for approaches to obtain more appropriate specifications for the engineering design of polymers. 

This chapter covers some of the methods and instruments used to determine the mechanical properties of polymers. Examples of instrument designs and typical data generated in these measurements will be introduced. In particular, automated axial tensiometers (to find elastic modulus, yield stress, and ultimate stress), dynamic mechanical analyzers (to determine storage and loss moduli), and rheometers (to measure flow viscosity) will be introduced. This chapter considers the principles behind the devices used to establish and measure the properties of viscometric flows. One of the common techniques used to determine viscous flow properties, PoisueiUe (laminar) flow in cylindrical tubes, is also important in technical applications, as polymer melts and solutions are often transported and processed in this manner. The time-temperature superposition principle is also covered as a way to predict polymer behavior over long timescales by testing materials across a range of temperatures. 

The use of solid polymers for long-term structural applications that are stiffiiess limited in design requires the determination of the modulus of elasticity or the compliance for loading in tension (or compression). For metals, this is a simple matter since the value determined from a tension test, a compression test or a flexural test will be the same. However, for solid polymers, the tensile and compressive compliance are not the same, and thus, the flexural compliance will be different from both[l], combining as it does tensile and compression in a single test. To furdier complicate matters, all three compliance values are time-dependent, for polymeric solids[2]. The creep compliance is the time-dependent creep str divided by the constant applied stress that caused the creep, but the inverse is not the same as the relaxation... 

Plastic having apparent modulus of elasticity in the range of 10,000-100,000 psi at 23°C, as determined by the Standard Method of Test for Stiffness in Flexure Plastics (ASTM Designation D747). 

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