Safety Factors

they contain iron sulphide "stringers" or microstructural

31. Distortion-Energy Theory. a. The distortion-

sulphide inclusions, oriented in the direction of working,

energy theory of failure (von Mises-Hencky) is the

and normal to the most critical stress, and thus are

accepted criterion for the design of ductile materials

inadequate in devices with high internal pressures.

under combined loads.

This theory defines an

28. Safety Factors. a. Safety factors used in the

equivalent stress that exists for a combined loading.

The distortion-energy equation for triaxial stresses given

design of propellant actuated devices may appear low,

in equation (7),

but they are adequate because they are subjected only

to controlled loads.

b. Safety factor of a part is established as a ratio

of the limiting stress to the design stress. All conditions

having an effect on the stress is included in the

determination.

c. Limiting stresses of pressure containing

structures is based on the minimum yield strength of the

is shown in more useful forms in equations (8) and (9).

material, and the design stress is based on the

The conversion of equation (7) to the forms of (8) and

Distortion Energy Theory in accordance with the von

(9) is shown in appendix I.

Mises-Hencky Concept.

Utilizing this theory, the

minimum factor of safety of the cylindrical section or

wall of the pressure chamber is 1.15.

d. The limiting stress of all other components also

Where:

corresponds to the minimum yield strength, but a

P=maximum pressure

minimum factor of safety of 1.5 is applied. In the cases

Y=yield strength of material

where shock or impact loads are applied, the minimum

W=wall ratio

factor of safety is 2.0.

29. Temperature Effects. Temperature has a marked

effect on the mechanical properties of metals at high

temperatures. The burning of propellant in the device is

When a device is designed to withstand only biaxial

for so short a time that the metal parts are unable to

stresses, equation (10) may be used.

absorb much heat; consequently, a negligible

temperature increase is experienced.

In addition,

propellant actuated devices are not exposed to ambient

temperatures exceeding 200° F., and the change in

b. The convenience of these forms of the

strength at 200°F. is small and may be neglected.

distortion-energy equation is apparent when it is realized

30. Stresses. When calculating the sizes of metal

that the internal pressure, P, can be estimated and the

parts to withstand the internal pressures of propellant

strength of the material, Y, may be found in most

actuated devices, it is necessary to consider the

engineering handbooks. The wall ratio (ratio of OD to

stresses at the weakest part of the tubes, commonly at

ID) and a tube size can then be calculated. Appendix II

the undercut at the end of the threads. The gas

contains a table of wall ratios for values of P/Y from

pressure inside the device produces a direct radial

0.010 to 0.200. This table was calculated from the

compressive stress which is greatest on the inside wall,

formulas presented in this section. Figure 23 presents

and induces a tangential stress (hoop stress) which is

curves of P/Y as a function of W for biaxial and triaxial

greatest also at the inside wall. In undamped stroking

stresses, based on the tables of appendix II.

devices, the stresses are biaxial (radial and tangential),

c. The wall ratio, W, may be used to determine the

but occasionally a longitudinal stress is introduced in the

tube size. Tubing is supplied in standard sizes and it

tube due to axial loading and the stresses become

may be necessary to use a tube which is stronger than

triaxial. Biaxial stresses put greater strains on materials

required (higher W) to avoid the expense of using

than triaxial stresses when the directions of strain are

special size tubing. Tubing sizes are presented in

directed as they are in cylindrical pressure vessels.

military standards.