Abstract
The primary aim of the paper is to present the fundamental theory on the thrusts and stresses of two-dimensional pipe expansion bends incorporating the Karman flexibility factor. The application of this theory to a series of typical expansion bends is demonstrated for three well-established methods of fixing the ends: fixed at one end and free at the other, fixed at one end and guided at the other, and fixed at both ends. A series of tables summarizes the formulae and data on the expansions, thrusts, and bending stresses for 90 deg. bends, 180 deg. U-bends, and 45 deg. lyre expansion-bends for the three methods of fixing the ends indicated above.
The importance of the methods of fixing the ends of expansion bends on the thrusts and bending stresses for four typical cases is indicated in a table that gives the ratio of the resultant thrusts and maximum bending stresses due to expansion for bends fixed at one end and guided at the other end, and for those fixed at both ends, in relation to the corresponding amounts for bends fixed at one end and free at the other.
The detailed analysis for typical cases shows distinctly that the thrusts and bending stresses are greatly increased for a pipe bend fixed at both ends or fixed at one end and guided at the other, as compared with those fixed at one end and free at the other.
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