Deflection-limited design

Figure 2.32 Young s modulus as a function of density. The guidelines of constant Elp, Elpr and Elp allow selection of materials for minimum weight for a deflection-limited design. (Adapted from Ashby, 1992. Reproduced courtesy of Heineman Publishers, Oxford, UK.)...

Resistance-Deflection Function. The resistance-deflection function establishes the dynamic resistance of the trial cross-section. Figure 4a shows a typical design resistance-deflection function with elastic stiffness, Kg (psi/in), elastic deflection limit, Xg (in) and ultimate resistance, r.. (psi). The stiffness is determined from a static elastic analysis using the average moment of inertia of a cracked and uncracked cross-section. (For design... 

In designs that are strain-limited, the maximum strain for the purposes of specifying creep modulus is simpfy the maximum allowable strain for the material in question. In designs that are deflection-limited, the maximum strain is not known in advance. In these cases, a short iteration is used an initial estimate is made, and the stress anafysis is repeated a few times until consistent results are obtained. 

The upper machine capacity limitation is essentially structural though the operator may also run out of spindle, gearbox, or drive motor capability. Because an infinitesimal length variation in the strip can produce significant waviness or out-of-flat conditions, proper leveler design must be based on control of machine deflection—not structural failure of the equipment. Thus, the upper capacity limit is a machine deflection limit. Under extreme deflection conditions, due to overloading, the strip condition can be made worse rather than belter by the leveler. 

A rotation of 13 mrad was not obtained, without adhesive failure, with the MMFG recommended connection Wmj bt+bd. However, bond failure was restricted to the top of the web cleats by the restraining effect of the top bolt row and thus this connection has adequate performance to meet the serviceability limit state. Both bolted connections Wmj bt and Wmj bt.2 achieved the required of 13 mrad, but, along with connection WmJ bt+bd, all provided insufficient rotation capacity (32.5 mrad) for the design to be considered safe if the MMFG maximum deflection limit of 1/lOOth of the beam span is used (reference 1]). 

The criteria applied in the design of the Reactor Coolant System supports are that the specific function of the supported equipment be achieved during all normal, earthquake, safety valve actuation and Branch Line Pipe Break (BLPB) conditions. (BLPB includes feedwater line breaks and all loss-of-coolant-accident conditions resulting from breaks not eliminated by leak-before-break analysis in piping to branch nozzles of the reactor coolant system.) Specifically, the supports are designed to support and restrain the Reactor Coolant System components under the combined Safe Shutdown Earthquake and Branch Line Pipe Break loadings in accordance with the stress and deflection limits of Section III, ASME Code. 

Specifically, the design of the reactor vessel supports shall address irradiation effects (including low temperature and low neutron flux) and the attendant material embrittlement, and be designed to restrain the reactor vessel under the combined Safe Shutdown Earthguake (SSE) and branch line pipe break loadings in accordance with the stress and deflection limits established in Section III of the ASME B PV Code (Reference 4). 

No assignment can require a pin to tilt beyond the predetermined deflection limit (determined by the fixture and pin design). 

Fig. 7. Schematic interpretation of the broad deflection observed in the analysis of a continuum of lipoproteins (see text). The observed pattern is interpreted as arising from the summation of overlapping deflections due to many individually migrating lipoprotein boundaries. Concentrations in such patterns are measured between chosen flotation rate limits (designated here as limit A and limit B).

As long as the volume flow is kept near design point, both the deflection angle and pressure drop can be corrected. Temperature differential increase is limited by metallurgy, so it is neglected in analytical calculations. This evaluation is based on inlet pressure changes. The new volume at a different pressure is calculated by the ideal gas equation ... 

Example 2.1 A ball-point pen made from polypropylene has the clip design shown in Fig. 2.11. When the pen is inserted into a pocket, the clip is subjected to a deflection of 2 mm at point A. If the limiting strain in the material is to be 0.5% calculate (i) a suitable thickness, d, for the clip (ii) the initial stress in the clip when it is first inserted into the pocket and (iii) the stress in the clip when it has been in the pocket for 1 week. The creep curves in Fig. 2.5 may be used and the short-term modulus of polypropylene is 1.6 GN/m. ... 

Using several materials such as PP, glass-filled PS, and PS molded structural foam that is a natural sandwich panel material, the design procedure follows to determine the deflection and stress limitations of the material in each of the several designs. 

Although one can design flexures with quite extreme ratios of stiffness, often the design is also hmited by various space constraints, limits to allowed deflections, required load carrying capacity, and the need to avoid buckling. 

---