Name the two aspects that pipe systems are analyzed for, to ensure they are not overstressed.
Added by Scott B.
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Step 1: Identify the mechanical stresses acting on the pipe system, such as axial, bending, and torsional stresses, to ensure the pipe material and joints can withstand these forces without failure. Show more…
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Pipes used in a support structure shown in the figure have an outer diameter of 245 mm and an inner diameter of 232 mm. During a particular loading situation, the pipe structure is subjected to 4 point loads with magnitudes, directions, and points of application as shown. For the pipe material, the yield strength in tension is 275 MN/m^2, the maximum allowable shear stress is 150 MN/m^2, and Young's Modulus of Elasticity is 201 GN/m^2. 1. Calculate the component stresses set up in the pipe material at point 'D' (bottom of pipe structure indicated in the figure) due to the loading conditions. 2. Evaluate the 2D complex stress system at point 'D'. 3. Determine the magnitude of the principal stresses and their nature, and the maximum shear stress analytically and graphically, and the angle of the planes on which the major principal stresses act at point 'D'. 4. By applying the Tresca and Von Mises yield criteria, evaluate the minimum factor of safety for the pipe structure and compare with a required minimum factor of safety of 2.5. 5. Produce a neat sketch of the failure envelopes for the pipe structure at point 'D'. 6. The pipe column indicated in the figure has a length of 4.25 m and can be considered to be fixed at the bottom and free at the top. Considering the Euler, BS5950, and Rankine-Gordon Formula buckling approaches, determine whether buckling is an issue. Take the Rankine-Gordon Formula constant 'a' to be 1/22500.
Adi S.
Section of double-extra-strong pipe made of steel with yield strength 50 ksi is subjected to bending moment M = (35+0.8R) kip·in and torque T = (175+0.8R) kip·in, as shown in the figure below. The outer diameter of the pipe is d = 3 in, and the inner diameter is d' = 2.3 in. Analyze using the concepts of stresses under combined loadings and theories of yielding/failure: (a) Determine the stresses under the applied moment and torque, and also the principal stresses at the stress element shown on the pipe in the figure. (b) What factor of safety is predicted by the failure criterion of the maximum shear stress theory of failure? (c) What is the value of the Mises equivalent stress for the given state of plane stress, and what is the factor of safety predicted by the failure criterion of the maximum distortion energy theory of failure?
Problem 3 (35 Marks) : A cast iron pipe (E: 100 GPa and v = 0.3) has the dimensions as shown in Figure (a). If an internal pressure 5 MPa is applied then the pipe expands such that the external diameter increases by 0.01 mm, whereas the expansion in the internal diameter is negligible; as shown in Figure (b). The brass pipe is now inserted in a steel pipe (E = 200 GPa and v= 0.3 ) without any interference and before applying the internal pressure as shown in Figure (c). Note that the assembly in Figure (c) is stresses free due to no interference and no pressure. (a) Cast iron pipe (b) Cast iron pipe with internal pressure (c) Cast iron and Steel pipe assembly (d) Cast iron and steel pipe assembly with internal pressure i. If the cast iron pipe is then loaded with the same internal pressure of 5 MPa, as shown in Figure (d), then estimate the radial and tangential stresses at point P for cast iron pipe and represent them on a stress element. ii. For a conservative design, is ASTM grade 25 suitable for the Cast iron pipe?
Sri K.
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