Take The Case Of A Pressure Vessel That Is Being Tested In The Laboratory To Check Its Ability To Withstand Pressure Fo 1 (68.78 KiB) Viewed 38 times
Take The Case Of A Pressure Vessel That Is Being Tested In The Laboratory To Check Its Ability To Withstand Pressure Fo 2 (9.95 KiB) Viewed 38 times
Take the case of a pressure vessel that is being tested in the laboratory to check its ability to withstand pressure. For a thick pressure vessel of inner radius a and outer radius b, the differential equation for the radial displacement u of a point along the thickness is given by du 1 du 0 (E2.3) dr? r dr r? The inner radius a = 5" and the outer radius b = 8', and the material of the pressure vessel is ASTM A36 steel. The yield strength of this type of steel is 36 ksi. Two strain gages that are bonded tangentially at the inner and the outer radius measure normal tangential strain as Exime = 0.00077462 Ertraj = 0.00038462 (E2.4a,b) at the maximum needed pressure. Since the radial displacement and tangential strain are related simply by (E2.5) then me= 0.00077462 x 5 = 0.0038731" = 0.00038462x8 = 0.0030769 The maximum normal stress in the pressure vessel is at the inner radius r=a and is given by E (4) (E2.7) where E = Young's modulus of steel (E= 30 Msi) v = Poisson's ratio (v =0.3) The factor of safety, FS is given by FS Yield strength of steel (E2.8) a) Divide the radial thickness of the pressure vessel into 6 equidistant nodes, and find the radial displacement profile b) Find the maximum normal stress and factor of safety as given by equation (E2.8) c) Find the exact value of the maximum normal stress as given by equation (E2.8) if it is given that the exact expression for radial displacement is of the form +12 dr. max u=Cr+ Calculate the relative true error.
Bisection Method 6 secant Methel & Euber Method
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!