Stress isometrics

The stress engineer uses the stress isometrics to serve as the basis for a formal calculatioa The piping layout designer draws the preliminary isometrics as shown in exhibit 16.4. 

Strain and constant time can give respectively isometric stress-log time curves and isochronous stress-strain curves Figure 9.10). Whilst not providing any new information, such alternative presentations of the data may be preferred for certain purposes. 

Figure 9.10. Presentation of creep data sections through the creep curves at constant time and constant strain give curves of isochronous stress-strain, isometric stress-log (time) and creep modulus-log (time). (From ICI Technical Service Note PES 101, reproduced by permission of ICI...

Long-term deformation such as shown by creep curves and/or the derived isochronous stress-strain and isometric stress-time curves, and also by studies of recovery for deformation. 

As indicated above, the stress-strain presentation of the data in isochronous curves is a format which is very familiar to engineers. Hence in design situations it is quite common to use these curves and obtain a secant modulus (see Section 1.4.1, Fig. 1.6) at an appropriate strain. Strictly speaking this will be different to the creep modulus or the relaxation modulus referred to above since the secant modulus relates to a situation where both stress and strain are changing. In practice the values are quite similar and as will be shown in the following sections, the values will coincide at equivalent values of strain and time. That is, a 2% secant modulus taken from a 1 year isochronous curve will be the same as a 1 year relaxation modulus taken from a 2% isometric curve. 

This is a stress relaxation problem and strictly speaking stress relaxation data should be used. However, for most purposes isometric curves obtained from the creep curves are sufficiently accurate. By considering the 1.5% isometric curve shown in Fig. 2.8 it may be seen that the initial stress is 16 MN/m2 and the stress after 1 week is 7 MN/m2. 

Accurately performed relaxation tests in which the strain in the material was maintained constant and the decaying stress monitored, would give slightly lower values than those values obtained from the isometric data. 

This is a stress relaxation problem but the isometric curves may be used. 

From the 0.417% isometric curve, the stress after 1 year is 1.45 MN/m ... 

Then from a 1.6% isometric taken from the creep curves it may be determined that the stress after 10 seconds is 15.1 MN/m and after 1 year it is 5.4 MN/m. ... 

ISOMETRIC STRESS ISOCHRONOUS STRESS VS LOG TIME VS STRAIN... 

The resulting data can then be presented as a series of curves much like the isometric stress curves in Fig. 2-27. A relaxation modulus similar to the creep modulus can also be derived from the relaxation data. It has been shown that using the creep modulus calculated from creep curves can approximate the decrease in load from stress relaxation. 

For fluid handling plants. Based on average of actual cases. For solid handling plants - best estimate. Piping work hours breakdown P ID drafting 0.07 Layouts 0.05 Model 0.10 Orthographies 0.33 Material take-offs 0.10 Stress analysis 0.05 Isometrics 0.30 ... 

As muscle hypertrophy is an adaptive response by the body to stress, you should always strive to go as far as you can go on that "impossible" rep. Every centimeter matters. Your "impossible" rep should last between 10-15 seconds. One could even call this an "isometric rep". 

Isometric failure by accelerated deformation with elevated stress and strain. This method involves using durability data (creep, tensile strength and lifetime) to plot the tensile stress versus the logarithm of time to failure over a wide range of stresses at the use temperature. 

The assumption that the contraction process is ideally adiabatic, while perhaps not entirely permissible practically, seems indicated by modern theory of the behavior of molecular chains, which pictures these as undergoing, when freed of restraints, a sort of segmental diffusion, much like the adiabatic expansion of an ideal gas into a vacuum (155). In the case of the molecular chain, it diffuses to the most probable, randomly coiled configuration, which is much less asymmetric, hence shorter, than an initially extended chain. Because rubber most nearly presents this ideal behavior, those fibers which develop increased tension (a measure of the tendency toward assumption of the contracted form) when held isometrically under conditions of increasing temperature (favoring the diffusion ) are said to be rubber-like. Most normal elastic solids upon stress are strained from some stable structure and relax as the temperature is raised. 

Isometric curves are obtained by plotting stress vs. time for a constant strain isochronous curves are obtained by plotting stress vs. strain for a constant time of loading. These curves may be obtained from the creep curves by taking a constant-strain section and a constant-time section, respectively, through the creep curves and replotting the data, as shown in Eigure 3.17. 

An isometric curve provides an indication of the relaxation of stress in the material when the strain is kept constant. Since stress relaxation is a less common experimental procedure than creep testing, an isometric curve, derived like the preceding curves from creep curves, is often used as a good approximation of this property. 

The idea for this distributed muscle fiber model arose in 1990 [44]. At that time, muscle fibers were assumed to be functionally similar to muscle strips. Recently, experiments on isolated muscle libers show this to be the case. Predictions from the model have recently been borne out, for example, the magnitude of computed peak isometric force compared to that measured on isolated guinea pig myocytes [34]. Peak isometric stress measured on isolated rabbit myocytes (5.4 mN/mm ) is very close to peak stress from rabbit papillary muscle strips (6.4 mN/mm ) [45]. The distributed model generates peak isometric stress of 2.5 mN/mm. Other muscle phenomena measured on the isolated fiber include a quadratic force-length relation [45], inotropic changes in contractile state [37], quick release and stretch [37,39], and isotonic contractions [46], all in agreement with model predictions. 

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