Machinery's Handbook, 31st Edition
580 STRUCTURAL ANALYSIS OF PLASTICS Safety Factors: In setting safety factors for plastics parts, there are no hard and fast rules. The most important consideration is the consequence of failure. For example, a little extra deflection in an outside wall or a crack in one of six internal screw bosses may not cause much concern, but the failure of a pressure vessel or water valve might have serious safety or product liability implications. Tests should be run on actual parts at the most extreme operating conditions that could possibly be encountered during product life. For example, maximum working load should be applied at the maximum tempera- ture and in the presence of any chemicals that might be encountered in service. Loads, temperatures, and chemicals to which a product may be exposed prior to its end use also should be investigated. Impact loading tests should be performed at the lowest tempera - ture expected, including during assembly and shipping. Effects of variations in resin lots and molding conditions must also be considered. Failures in testing of preproduction lots often can be corrected by increasing the wall thickness, using ribs or gussets, and eliminating stress concentrations. Changing the mate rial to another grade of the same resin or to a different plastics with more suitable mechan ical properties is another possible solution. Reviews of product data and discussions with experienced engineers suggest the design stresses shown in Table 5 are suitable for use with the structural analysis information indicated above and the equations presented here, for preliminary design analysis and for evaluating general product dimensions. Products designed under these guidelines must be thoroughly tested before being marketed.
Table 5. Design Stresses for Preliminary Part Designs Expressed as a Percentage of Manufacturers’ Data Sheet Strength Values Failure Not Critical
Failure Critical
Intermittent (nonfatigue) loading Continuous loading (creep or fatigue)
25–50% 10–25%
10–25%
5–10% Failure Criteria: Specification of failure criteria is beyond the scope of this section, which is intended to give only basic general information on plastics. Designers who wish to rationalize complex stress states and analyses might consider the calculated Von Mises stresses relative to the stress limits expressed in Table 5 or investigate the maximum shear theory of failure (otherwise known as Coulomb or Tresca theory). It is further suggested that the shear strength be taken as the manufacturer’s published shear strength, or half the tensile strength, whichever is lower. Pressure Vessels: The most common plastic pressure vessel is a cylindrical tube with internal pressure. In selecting a wall thickness for the tube it is convenient to use the thin- wall hoop stress equation: (18) where P = uniform internal pressure in the tube, d i = inside diameter of the tube, and t = tube-wall thickness. This equation is reasonably accurate for tubes where the wall thickness is less than 0.1 3 d . Also, it is easy to solve for the wall thickness t required to support an internal pressure P with an allowable hoop stress s . For wall thicknesses greater than 0.1 d , the maximum hoop stress on the wall surface inside the tube can be calculated from (19) where d i and d o are the inside and outside diameters of the tube, and R = ( d i / d o ) 2 . By substituting d o = d i + t into the left equation one can solve it for the required wall thickness t to provide a working equation for design. The result is (20) In the above equations, all units must be consistent. t Pd 2 hoop stress i σ= P d d d d − + hoop stress or o i o i 2 2 2 2 σ σ = P R R 1 1 = − + t d = P P − + − 2 1 i σ σ a k
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