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The Paper describes an investigation made for the Anglo-Iranian Oil Company in connexion with large diameter pipe-lines. Formulae are developed for the stresses in a fully restrained line arising from the pressure of the liquid in it, from general variations of temperature, and from differential heating. The loading on anchor-blocks and buttress-blocks ia considered. Formulae are given for the spacing of ring-supports necessary to keep the combined stresses due to bending, eccentricities in alignment, temperature changes, and fluid pressure, within safe limits when judged by the Mises-Hencky criterion. Lack of data on possible errors of alignment and straightness of pipes make these formulæ tentative in character, but the general analysis is independent of particular assumptions in these respects. Tables of formulæ are given both in general terms and in a simplified form for a particular pipe.

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