Chapter 9
Dynamic Stresses Due to Bending


Dynamic stresses during bending vary due to system geometry. Multiplying the pressure surge magnitude times the pipe cross-sectional area approximates the forces on both elbows and blind flanges. For step pressure surges during water hammer, the DMF < 2 for forces on an elbow in a pipe system. For the step pressure surges on a closed end pipe, an axial force DMF < 4 may exist due to wave reflections at the pipe end, depending on the pipe length and pressure duration. For pipes with U-bends or Z-bends, the forces are also related to the geometry. Although the DMF < 2 at each elbow, the opposing forces may either counter or multiply the DMF, depending on the phase shift in vibrations at opposing elbows. The forces at each elbow act at different times, and accordingly, a phase shift will exist between the opposing forces at the elbows. If the distance between elbows is small, the opposing forces will cancel, and in some cases, the forces will add. In general, few problems can be reasonably approached without the aid of a computer. To provide some insight into dynamic stresses, simple hand calculations are presented here along with an example of a more complicated computer simulation. Also, some graphic techniques to estimate loads due to water hammer are available in ESDU-86015 B [238]. Before examples are presented, equations for frequencies, deflections, and stresses are presented to be used along with single degree of freedom (SDOF) responses.

  • 9.1 Deformations, Stresses, and Frequencies for Elastic Frames
  • 9.2 Elastic Stresses Due to Bending
  • 9.3 FEA Model of Bending Stresses
  • 9.4 Plastic Deformation and Stresses Due to Bending
  • 9.5 Summary of Stresses During Water Hammer

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