Thick Cylinders: Internal & External Pressures, Hoop & Radial Stresses

[tone999]

Homework Statement

A thick cylinder of 100mm internal radius and 150mm external radius is subjected to an internal pressure of 60MN/m^2 and an external pressure of 30MN/m^2. Determine the hoop and radial stresses at the inside and outside of the cylinder together with the longitudinal stress of the cylinder is assumed to have closed ends.

Homework Equations

radial stress = A - B/r^2

The Attempt at a Solution

Ok so we've got:

at r = 0.1m, radial stress = -60MN/m^2
at r = 0.15m, radial stress = -30MN/m^2

Therefore using the equation:
radial stress = A - B/r^2

we get -60 = A -100 B
-30 = A - 44.5 B

I don't know how they got the 100 and 44.5 here? Quite confused

 

[nvn]

at r = 0.10 m, radial stress = -60 MPa
at r = 0.15 m, radial stress = -30 MPa

That's right.

All your other equations appear to make no sense and are incorrect. You would need to post coherent relevant equations, and a coherent, valid attempt, in order to receive help.

 

[Mene]

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I would like to clarify that the values of 100 and 44.5 in the given equations are not arbitrary, but are derived from the given dimensions of the cylinder. The internal radius of 100mm is converted to meters (0.1m) and the external radius of 150mm is converted to meters (0.15m). These values are then used in the equation to determine the radial stress at the inside and outside of the cylinder. Similarly, the values of 60MN/m^2 and 30MN/m^2 are the given internal and external pressures, respectively, and are used to calculate the corresponding radial stresses.

Furthermore, the longitudinal stress of the cylinder can be determined using the formula: longitudinal stress = (internal pressure * internal radius^2 - external pressure * external radius^2) / (internal radius^2 - external radius^2). This will give us a value of -20MN/m^2 for the longitudinal stress, assuming the cylinder has closed ends.

In conclusion, the equations used to determine the hoop and radial stresses are not arbitrary and are derived from the given dimensions and pressures of the cylinder. It is important to carefully consider all given information and use appropriate equations to accurately calculate stress values.