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172 + KN Mike Cahill Vanessa Pynn Daniel Bruce Andrew Clarke Dennis Cluett

172 + KN Mike Cahill Vanessa Pynn Daniel Bruce Andrew Clarke Dennis Cluett. Chapter 8 - Combined Loadings & Thin-Walled vessels

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172 + KN Mike Cahill Vanessa Pynn Daniel Bruce Andrew Clarke Dennis Cluett

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  1. 172 + KN Mike Cahill Vanessa Pynn Daniel Bruce Andrew Clarke Dennis Cluett

  2. Chapter 8 - Combined Loadings & Thin-Walled vessels This chapter serves as a review of the stress-analysis that has been developed in the previous chapters regarding axial load, torsion, bending and shear. The solution to problems where several of these loads occur simultaneously will be studied. Prior to this, the stresses in thin-walled vessels will be analyzed. What is a thin walled pressure vessel? Cylindrical or spherical vessel that has a radius to wall thickness ratio of 10 or more. It may be assumed for the sake of simplifying the analysis of stresses in the wall of these vessels that the stress distribution throughout its thickness remains uniform or constant. Combined Loadings & Thin Walled Vessels Also assumed is that the pressure referred to is the gauge pressure (above atmospheric pressure) and not the absolute pressure. Hibbeler Chapter 8

  3. Thin-Walled Vessels Cylindrical Normal Stress in the hoop direction Longitudinal or axial direction Both exert tension on the material To compute the values of each use equilibrium of a section of the tank Combined Loadings & Thin Walled Vessels Hibbeler Chapter 8

  4. Thin-Walled Vessels Spherical Likewise using equilibrium we can analyse spherical vessels using equilibrium as shown: The result is the same as longitudinal stress of cylinders (the lesser of the two). This is true no matter what orientation you are considering (when the weight of the contents is neglected as is usually the case). Combined Loadings & Thin Walled Vessels Hibbeler Chapter 8 Radial Stress Another stress component in thin walled vessels is radial stress . Radial stress acts along a radial line (outwards) and varies in magnitude from pressure ‘p’ at the interior surface to zero on the outer surface of the vessel wall – it is neglected due to its relatively small value compared to

  5. Thin-Walled vessels- Problem Solving Space shuttle fuel tank in the woods after crash 200 psi 0.5 in Combined Loadings & Thin Walled Vessels Hibbeler Chapter 8

  6. Thin-Walled vessels- Problem Solving (Open Ends) Combined Loadings & Thin Walled Vessels Hibbeler Chapter 8

  7. Thin-Walled vessels- Problem Solving 36 in F F Combined Loadings & Thin Walled Vessels FR 12 in Hibbeler Chapter 8 Stress in the bolts: Stress in the metal hoop:

  8. Combined Loadings We have learned to determine the stress distribution in a structural element or member subjected to either: Axial Force Bending Force Shear Moment Torsional Moments. Uniform Normal stress due to axial load Stress due to flexure Combined Loadings & Thin Walled Vessels Shear stress due to Bending Hibbeler Chapter 8 Shear stress due to torque

  9. Combined Loadings Unfortunately for the students of 4312, it is rare that a structural member is subject to only one of these loading conditions, usually a member is subject to several loadings simultaneously. The method of Superposition can be used most often to determine the resultant stress distribution caused by the loads; ie. determine the stress distribution due to each loading then superimpose them to get the resultant. Loads and stresses must be linearly related and members cannot undergo significant geometric change due to loading in order for superposition to apply. Combined Loadings & Thin Walled Vessels Hibbeler Chapter 8

  10. Combined Loadings Procedure for Analysis Step 1 Combined Loadings & Thin Walled Vessels Step 2 Hibbeler Chapter 8

  11. Combined Loadings Procedure for Analysis Step 3 Step 4 Combined Loadings & Thin Walled Vessels Step 5 Hibbeler Chapter 8

  12. Combined Loadings Procedure for Analysis Step 6 Step 7 Combined Loadings & Thin Walled Vessels Hibbeler Chapter 8

  13. Combined Loadings Procedure for Analysis Step 8 Combined Loadings & Thin Walled Vessels Hibbeler Chapter 8

  14. Combined Loadings Example Combined Loadings & Thin Walled Vessels Hibbeler Chapter 8

  15. Combined Loadings Example Combined Loadings & Thin Walled Vessels Hibbeler Chapter 8

  16. Combined Loadings Example Combined Loadings & Thin Walled Vessels Hibbeler Chapter 8

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