Calculating Boiler Shell Thickness and Rivet Diameter for a Boiler Seam

This problem requires us to determine the appropriate thickness of the boiler shell plate and the diameter of the rivets used in a double riveted butt joint for a longitudinal seam, given the boiler's diameter, internal steam pressure, joint efficiency, and the allowable tensile strength of the plate material.

Given Parameters:

• Boiler shell diameter, \(D = 1.5 \, \text{m} = 1500 \, \text{mm}\)
• Internal steam pressure, \(P = 0.95 \, \text{N/mm}^2\)
• Joint efficiency, \(\eta = 75\% = 0.75\)
• Allowable tensile strength of the plate, \(\sigma_t = 90 \, \text{MPa} = 90 \, \text{N/mm}^2\)
• Joint type: Double rivetted butt joint with two cover plates for a longitudinal seam.

Calculating the Required Boiler Shell Thickness

For a thin cylindrical shell subjected to internal pressure, the hoop stress (circumferential stress) is the critical stress for failure along the longitudinal seam. The formula for hoop stress in a thin cylinder is generally given by:

Where \(t\) is the thickness of the shell. However, the presence of a riveted joint with a specific efficiency \(\eta\) means that the allowable stress in the plate at the joint section is effectively reduced, or we can consider that to withstand the pressure with a joint, a greater thickness is required compared to a seamless shell for the same allowable stress. The relationship considering joint efficiency is:

Here, \(\sigma_t\) is the allowable tensile strength of the plate material. We need to find the minimum required thickness \(t\) of the boiler shell plate. We can rearrange the formula to solve for \(t\):

Performing the Calculation for Thickness

Now, substitute the given values into the formula for thickness:

Determining Plate Thickness and Rivet Diameter from Options

The calculated required thickness for the boiler shell plate is approximately 10.56 mm. We now compare this calculated thickness with the thickness values provided in the options:

• Option 1: Plate thickness = 10 mm, Rivet diameter = 20 mm
• Option 2: Plate thickness = 18 mm, Rivet diameter = 27 mm
• Option 3: Plate thickness = 12 mm, Rivet diameter = 20 mm
• Option 4: Plate thickness = 15 mm, Rivet diameter = 25 mm

Comparing the calculated thickness (10.56 mm) with the options, the value 10 mm from Option 1 is the closest and most practical thickness likely to be chosen from standard available plate sizes or as per design requirements.

For the rivet diameter, empirical formulas are often used to relate the rivet diameter (\(d\)) to the plate thickness (\(t\)), such as \(d = 6\sqrt{t}\) for a plate thickness greater than 9 mm. Using \(t = 10 \, \text{mm}\), the empirical diameter would be \(d = 6\sqrt{10} \approx 6 \times 3.162 \approx 18.97 \, \text{mm}\). The corresponding rivet diameter given in Option 1 is 20 mm. This is a standard rivet size that is close to the empirically calculated value and is provided alongside the thickness value that matches our calculation.

Therefore, based on the required thickness calculation and comparison with the given options, the thickness of the boiler shell plate is approximately 10 mm, and the corresponding rivet diameter is 20 mm.