Question
Download Solution PDFA boiler of 1.6 m diameter is made of a 20-mm thick plate. What will be the permissible steam pressure in the boiler in the maximum tensile stress in the plates must NOT exceed 80 MPa?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
For thin cylinder:
|
Hoop stress \({σ _h} = \frac{{Pd}}{{2t}} = {σ _1}\) |
Hoop strain \({\epsilon_h} = \frac{{Pd}}{{4tE}}\left( {2 - \mu } \right)\) |
|
Longitudinal stress \({σ _L} = \frac{{Pd}}{{4t}} = {σ _2} = \frac{{{σ _1}}}{2}\) |
Longitudinal strain \({\epsilon_L} = \frac{{Pd}}{{4tE}}\left( {1 - 2\mu } \right) = \frac{{{σ _2}}}{E}\left( {1 - 2\mu } \right)\) |
Calculation:
Given:
d = 1.6 m, t = 20 mm, σmax = 80 MPa = σl (Longitudinal stress in case of thin cylinder)
Maximum working stress
\({σ _1} = {σ _h} = \frac{{Pd}}{{2t}} \Rightarrow {\rm{P}} = \frac{{{\rm{2t \sigma_h }}}}{{{{\rm{d }}_{\rm{}}}}} = \frac{{2 \times 20 \times 80}}{{ 1.6 \times 1000}} = 2\ MPa\)
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