Tham khảo tài liệu 'introduction to elasticity part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | compelling advantages for engineered materials that can be made stronger in one direction than another the property of anisotropy . If a pressure vessel constructed of conventional isotropic material is made thick enough to keep the hoop stresses below yield it will be twice as strong as it needs to be in the axial direction. In applications placing a premium on weight this may well be something to avoid. Example 1 Figure 6 Filament-wound cylindrical pressure vessel. Consider a cylindrical pressure vessel to be constructed by filament winding in which fibers are laid down at a prescribed helical angle a see Fig. 6 . Taking a free body of unit axial dimension along which n fibers transmitting tension T are present the circumferential distance cut by these same n fibers is then tan a. To balance the hoop and axial stresses the fiber tensions must satisfy the relations . pr hoop nT sin a 1 b axial nT cos a pb tan a b Dividing the first of these expressions by the second and rearranging we have tan2 a 2 a This is the magic angle for filament wound vessels at which the fibers are inclined just enough toward the circumferential direction to make the vessel twice as strong circumferentially as it is axially. Firefighting hoses are also braided at this same angle since otherwise the nozzle would jump forward or backward when the valve is opened and the fibers try to align themselves along the correct direction. Deformation the Poisson effect When a pressure vessel has open ends such as with a pipe connecting one chamber with another there will be no axial stress since there are no end caps for the fluid to push against. Then only the hoop stress ơỹ pr b exists and the corresponding hoop strain is given by Hooke s Law as _ Ơ0 _ pr ee E bE Since this strain is the change in circumference ỎC divided by the original circumference C 2nr we can write pr ỖC C g 2nrf- bE 4 The change in circumference and the corresponding change in radius ỗr are related by ỗr ỗc 2n so the .
