Thin Cylinders · Strength of Materials · GATE ME

Marks 1

A thin cylindrical pressure vessel with closed-ends is subjected to internal pressure. The ratio of circumferential (hoop) stress to the longitudinal stress is

GATE ME 2016 Set 2

A cylindrical tank with closed ends is filled with compressed air at a pressure of $$500 kP$$a. The inner radius of the tank is $$2 m,$$ and it has wall thickness of $$10 mm.$$ The magnitude of maximum in-plane shear stress (in $$MP$$a) is ________

GATE ME 2015 Set 3

A gas is stored in a cylindrical tank of inner radius $$7$$ m and wall thickness $$50$$ mm. The gage pressure of the gas is $$2$$ MPa. The maximum shear stress (in MPa) in the wall is

GATE ME 2015 Set 2

A long thin walled cylindrical shell, closed at both the ends, is subjected to an internal pressure. The ratio of the hoop stress (circumferential stress) to longitudinal stress developed in the shell is

GATE ME 2013

A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is

GATE ME 2012

Marks 2

A cylindrical pressure vessel made of steel has diameter of 3 m and wall thickness of 15 mm . For steel, Young's modulus and Poisson's ratio are 210 GPa and 0.3 , respectively. The cylinder is designed such that the allowable normal strain at the outer cylindrical surface is equal to 0.00034 . The permissible pressure in the tank is $\_\_\_\_$ kPa (rounded off to 1 decimal place).

GATE ME 2026

The figure shows a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an angle $\alpha = 60^\circ$ with the horizontal. The closed vessel has a wall thickness of 10 mm and diameter of 2 m. When subjected to an internal pressure of 200 kPa, the magnitude of the normal stress acting on the weld is _________ MPa (rounded off to 1 decimal place).

GATE ME 2024

The figure shows a thin-walled open-top cylindrical vessel of radius 𝑟 and wall thickness 𝑡. The vessel is held along the brim and contains a constant-density liquid to height ℎ from the base. Neglect atmospheric pressure, the weight of the vessel and bending stresses in the vessel walls.

Which one of the plots depicts qualitatively CORRECT dependence of the magnitudes of axial wall stress (σ₁) and circumferential wall stress (σ₂) on 𝑦?

GATE ME 2023

A thin-walled cylindrical pressure vessel has mean wall thickness of t and nominal radius of r. The Poisson’s ratio of the wall material is 1/3. When it was subjected to some internal pressure, its nominal perimeter in the cylindrical portion increased by 0.1% and the corresponding wall thickness became t̅. The corresponding change in the wall thickness of the cylindrical portion, i.e. 100 × (t̅ − t)/t, is ________% (round off to 3 decimal places).

GATE ME 2022 Set 1

A thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa. The maximum permissible working stress is restricted to 100 MPa. The minimum cylinder wall thickness (in mm) for safe design must be ____________.

GATE ME 2014 Set 4

A cylindrical container of radius $$R=1$$m, wall thickness $$1$$mm is filled with water upto a depth of $$2$$m and suspended along with its upper rim. The density of water is $$1000$$kg/m³ and acceleration due to gravity is $$10$$ m/s². The self weight of the cylinder is negligible. The formula for hoop stress in a thin walled cylinder can be used at all points along the height of the cylindrical container.

The axial and circumferential stress $$\left( {{\sigma _{a,}}\,{\sigma _c}} \right)$$ experienced by the cylinder wall a mid-depth ($$1$$ m as shown) are

GATE ME 2008

If the Young's modulus and Poisson's ratio of the container material are $$100$$GPa and $$0.3$$, respectively. The axial strain in the cylinder wall at mid height is

GATE ME 2008

A thin cylinder of $$100$$mm internal diameter and $$5$$mm thickness is subjected to an internal pressure of $$10$$ MPa and a torque of $$2000$$ Nm. Calculate the magnitudes of the principal stresses.

GATE ME 1996