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EM 319 - Review 2 - Review 2 Fall 08 1 A pressurized steel...

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Review 2 Fall 08 1. A pressurized steel tank is constructed with a helical weld that makes an angle α = 60 o with the longitudinal axis (see figure). The tank has radius r and wall thickness t and is subjected to an internal pressure p . An electrical resistance strain gage placed along the weld measure the extensional strain in the weld direction 0 ε . The Young’s modulus and Poisson’s ratio for the tank material (steel) are given as E and ν , respectively. (a) Find expressions for longitudinal (axial) strain a ε , circumferential (hoop) strain h ε and shear strain ah γ in terms of E , ν , p , r and t . (b) Using the strain transformation (formula or Mohr’s circle), find an expression for the strain along weld direction, in terms of E , ν , p , r and t . (c) Equating the expression obtained in part (b) to the measured strain 0 ε , find internal pressure p in terms E , ν , r , t and 0 ε . (d) If a h ε ε 5 = , find Poisson’s ratio ν ( use expressions obtained in part a ) .
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