A cylindrical pressure vessel, with a diameter of 40cm and a wall thickness of 10mm is made of steel (isotropic, with Young’s modulus = 200GPa; Poisson’s ratio = 0.28) and is pressurized to 20MPa. The longitudinal and hoop stresses in the wall, σl and σh, respectively, are given by:
σl=pr2t
and σh=prt
What is the strain in the radial direction, through the thickness of the pressure vessel?
-8.4 *10^-4
-8.4 *10^-5
-8.4 *10^-5 wrong!
it's almost good
-8.4 *10^X*
*find correct X :)
epsilon_r=-ni*epsilon_h-ni*epsilon_l/E
epsilon_h=sigma_h/E
epsilon_l=sigma_l/E
thx
I can't understand the epsilon r, could you write it again? because it seems
- nu ?(epsilon h - Epsilon L/E) and this is not unitless
To determine the strain in the radial direction through the thickness of the pressure vessel, we can use Hooke's Law. Hooke's Law states that strain is directly proportional to stress, and the proportionality constant is the material's elastic modulus.
In this case, the strain in the radial direction can be calculated using the formula:
εr = σr / E
Where:
εr is the strain in the radial direction
σr is the stress in the radial direction
E is the elastic modulus of the material
Since we have the formula for the stress in the hoop direction (σh), which is in the radial direction, we can substitute it into the equation.
σr = σh = prt
Now, let's calculate the strain. We already know the values for the pressure (p), the radius (r), and the thickness (t) of the pressure vessel. However, we still need to find the elastic modulus (E) for steel in order to complete the calculation.
Given that the Young's modulus of steel (E) is 200 GPa (gigapascals), we need to convert it to pascals (Pa) before substituting it into the equation.
1 GPa = 10^9 Pa
E = 200 GPa = 200 × 10^9 Pa
Now, we can substitute the values into the strain equation:
εr = (prt) / (200 × 10^9 Pa)
Please make sure to use consistent units for pressure (Pa) and dimensions (meters) to obtain accurate results.
By calculating this equation, you will find the strain in the radial direction through the thickness of the pressure vessel, expressed as a decimal or a percentage.