Downloaded from https://www.everyspec.com Chapter 3 H STRESS ANALYSIS * 3-1. GENERAL CONSIDERATIONS pressure, and compressive when the opposite In the fifty-odd years since the first suc- is true. cessful flight of a heavier-than-air machine, 3-2.2. Conical Shell. In a conical shell under the analysis of the stresses in aircraft struc- a uniform internal pressure the tangential tures has been developed toa highly perfected stress, (,, and the axial stress acting in the art. Good textbooks on airplane stress analy- direction of the generator, a,, are sis are readily available.
The purpose of this a, = pR/h cos y (3 3) chapter is to present those principles and at = pRt2h cos -y (3 4) formulas which are peculiar to missile struc- where R "s the local mean radius of the shell tural analysis and are not to be found, as a measured in a plane prpendicular to the rule, in books on airplane structures. axis of the cone, y is the angle subtended by In this category belong shell analysis, the any generator with the axis of the cone (the study of thermal stresses, and the investiga- half apex angle of the cone), and the remain- tion of the effects of creep. Shell analysis is ing symbols -. re defined as before.
peculiar to ballistic missile design because 3 most of the structural elements of these 3.2.3. Spherical Shell. The normal stress missiles are thin shells, often unreinforced acting in any direction in the plane tangen- The customary methods of reinforced thin tial to the sphere at the considered point ;hell analysis, amply di.icussed in textbooks known as the membrane .Atres.,%, aM,. may be on aircraft structures, are not applicable to expressed as - these missiles. Thermal stresses and creep =pR (3 5) arise as a consequence of aerodynamic heat- 2h ing; for this reason they are o. great impor- 3-2.4. Thin Shell.
All of the stresses given tance to very-high-speed missiles but of little heretofore are membrane stresses. These are account in conventional airplanes. stresses distributed uniformly through the thickness of the wad. Under their action the 3-2. STRESSES AND DEFORMATIONS IN THIN shell change. its size slightly. When the ma- SHELLS UNDER UNIFORM INTERNA. terial is perfectly slastic and when it follows PRESSURE Hooke's uniaxial law 3-2.1. Circular Cylindrical Shell. The tan- = E (3 6) gential or hoop stress, n.
and the stress i whpre t is the strain (elongation per unit the longitudinal or axial direction, ,, within length) and E Young's Modulus of elasticity, circular cylindrical shells under a uniform the mean radius of tie cylinder inicreases by internal pressure are the amount pR p" _= h- (3 1) R, (3 7) pR where x is Poisson's ratio who,,e value is .' , ax = 2 h (3 2) for steel and aluminum alloys. For the cone where p is the excess of the internal pressure the corresponding quantity is in the closed cylindrical shell over the exter- AR . - P pR 2 nal pressure, R is the mean radius of the A 2 Ehcosy (3 8) cylindrical shell, and h is the wall thickness.
and for the sphere The stresses , and 7, are tensixc if the in- ternal pressure is larger than the external AR,),, = (1 - ) (3 9) 41 itt