The gas tank is made from A-36 steel and has an inner diameter of 1.50 m. If the tank is designe

step 1 In this question, they want us to find the minimum thickness of a tank that can handle the press

The gas tank is made from A-36 steel and has an inner...

The gas tank is made from $A-36$ steel and has an inner diameter of $1.50 \mathrm{m}$. If the tank is designed to withstand a pressure of $5 \mathrm{MPa}$, determine the required minimum wall thickness to the nearest millimeter using (a) the maximum-shear-stress theory, and (b) maximum-distortion-energy theory. Apply a factor of safety of 1.5 against yielding.

Key Concepts

Pressure Vessel Analysis

This concept concerns the design and structural analysis of containers that hold pressurized fluids. It involves calculating the stresses produced by internal pressure, particularly the hoop (circumferential) and longitudinal stresses, and ensuring that the vessel’s material can withstand these stresses under operating conditions. In such analyses, assumptions about the vessel's geometry (such as being thin-walled) are often made to simplify calculations.

Thin-Walled Pressure Vessels

The thin-walled assumption is used when the wall thickness of a pressure vessel is small compared to its radius, leading to nearly uniform stress distributions across the thickness. This assumption allows engineers to use simplified expressions for the hoop and longitudinal stresses, which are critical for preliminary design and analysis of the vessel’s integrity under internal pressure.

Yielding in Materials

Yielding is the point at which a material begins to deform plastically and no longer returns to its original shape once the applied load is removed. In engineering design, preventing yielding is crucial for ensuring structural integrity. This involves comparing the calculated stresses against the material’s yield strength and applying safety factors to introduce a margin of safety in the design.

Maximum Shear Stress Theory (Tresca Criterion)

The maximum shear stress theory, or Tresca criterion, is a yield criterion used to predict the onset of yielding in ductile materials. It states that yielding starts when the maximum shear stress in a material reaches a critical value, which is related to the yield strength in simple tension. This criterion is particularly useful in design because it provides a conservative estimate of the required material strength under complex stress states.

Maximum Distortion Energy Theory (von Mises Criterion)

The maximum distortion energy theory, also known as the von Mises criterion, is another yield criterion that predicts yielding based on the distortional (shape-changing) energy in the material. According to this theory, yielding occurs when the energy associated with the distortion reaches a critical level. This method is widely used due to its ability to more accurately represent the yielding behavior of ductile materials under multi-axial loading conditions.

Factor of Safety

A factor of safety is a design parameter that provides a margin for error in engineering calculations. By applying a factor of safety to the yield strength, engineers ensure that the actual operating stresses are kept safely below the threshold that could cause failure. This accounts for uncertainties in material properties, variations in manufacturing, and potential unforeseen loading conditions, thereby enhancing the reliability and safety of the design.

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