A thin cylindrical shell made of mild steel plate is $1000 m m$ in diameter. It is to be subjected to an internal pressure of $2 N / m m^{2}$ . If the material yields at $200 N / m m^{2}$ , the thickness of the plate in mm on the basis of Rankine's theory of failure with assuming a factor of safety of $3$ would be

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Solution

The correct option is C $15$
$Factor of safety = \frac{Yield stress}{Max. normal stress}$
Here, maximum normal stress is Hoop stress
$σ_{h} = \frac{p d}{2 t}$
$t = \frac{p d}{2 σ_{h}} = \frac{2 \times 100}{2 \times 200} = 5 m m$
$F O S = 3$
Thickness required
$= 3 \times t = 15 m m$

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A thin cylindrical shell made of mild steel plate is 1000 mm in diameter. It is to be subjected to an internal pressure of 2 N/mm2. If the material yields at 200 N/mm2, the thickness of the plate in mm on the basis of Rankine's theory of failure with assuming a factor of safety of 3 would be

The correct option is C 15Factor of safety=Yield stressMax. normal stress Here, maximum normal stress is Hoop stress σh=pd2t t=pd2σh=2×1002×200=5 mm FOS=3 Thickness required =3×t=15 mm

The correct option is C $15$
$Factor of safety = \frac{Yield stress}{Max. normal stress}$
Here, maximum normal stress is Hoop stress
$σ_{h} = \frac{p d}{2 t}$
$t = \frac{p d}{2 σ_{h}} = \frac{2 \times 100}{2 \times 200} = 5 m m$
$F O S = 3$
Thickness required
$= 3 \times t = 15 m m$