**Task 1**

A member of your engineering team asked if a vertical stretch of an in-service pipe transporting hot pressurized water would be subject to torsion. The pipeline is installed on a platform, a few hundred of meters above the sea. Provide an answer to the query, elaborating on what mechanical loads this vertical pipe may be subject to. Explain how these mechanical loads are developed.

Using a fictional tubular cross-section whose internal radius is half the outside radius, prove that the tubular cross-section is the best geometry to resist torsion.

Choose a commercially available pipe diameter. Analyse, via Finite Elements, a stretch of a pipe whose length is eight times the chosen diameter under an externally applied torque of 1500 kN.m. Use SolidWorks software to create the 2D drawing with the correct dimensions and the 3D for the simulation. Compare the results of the simulation with the analytical calculation.

**Task 2**

You have to design a pressure vessel. Preliminary measurements of the cylindrical vessel indicate that the normal stresses due to pressure are as shown. The state of plane stress at a point is represented by the element shown in Figure 1. Determine the state of stress at the point on another element oriented 30° clockwise.

Determine the maximum in-plane shear stresses in the pressure vessel

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Determine the principal stresses acting on the pressure vessel. Compare the result using the online calculator or simulator for stress transformation and the analytical solution. Are the answers the same? if not, explain with reasons.

**Task 3**

in the previous project task, you estimated the weight of the bypass pipeline. The next step is devoted to the project of the support itself. The engineering team has decided to deploy variable spring support on each anchorage point from task 3. A spring, having a free length of 407 mm and a solid length (this latter identifies the length of a spring when it is fully compressed) of 186 mm, is to be used. The initially selected spring has a constant k = 20 N/mm, but it can be replaced if needed.

For one support, calculate the length of the spring with the pipeline installed on it.

Given that the by-pass line will also transport hot water, and knowing that the heated-up pipeline displaces 2 cm vertically, determine the new load on the spring, after it has been relieved by this displacement.

Knowing that the relieved load is transmitted to the neighboring supports and that the American Petroleum Institute API 570 Standard recommends a maximum of 12% of the load to be transferred, determine if pre-compression (a.k.a. pre-load) should be applied on the spring, for compliance with the standard.

The by-pass pipeline is connected to a pump operating at 2960 rpm. Check if the spring of the pipe support is adequate for this condition. if not, recommend a value.

Using the APPLET or online calculator/simulator, demonstrate the effect of introducing damping into the system (play with the applet varying the value of the damping constant “C) and include an explanation, in your report, of the effect of damping on the frequency of the system and on its amplitude.

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