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Bending Strength Ratio (BSR) Calculator

A Bending Strength Ratio (BSR) Calculator is a tool used to compute the BSR for connections, such as those found in drill collars or other components of a Bottom Hole Assembly (BHA) in drilling operations. The calculator typically requires inputs for the section modulus of the box and pin connections to determine their ratio, which indicates the relative bending strength and stiffness between these two components.

what is Bending Strength Ratio (BSR)

The Bending Strength Ratio (BSR) is a ratio used to evaluate the relative stiffness and bending strength of two components in a connection, typically in the context of drill collars or other Bottom Hole Assembly (BHA) components used in drilling operations.

Purpose of BSR

The BSR indicates how well-balanced the bending strengths of the box and pin are. If the BSR is too high, the pin may be more prone to failure under bending stress. If it’s too low, the box may be the weaker component. Ideally, the BSR should fall within a certain range to ensure the longevity and reliability of the connection under operational stresses.

Acceptable BSR Ranges:

Standards like API RP 7G-2, NS-2â„¢ Standard, and Standard DS-1Â® Volume 3 provide guidelines on what constitutes an acceptable BSR for various sizes of BHA components. These guidelines are based on historical experience and are used to help prevent premature fatigue failures in drilling operations.

• For BHA smaller than 6 inches: 1.80 to 2.50
• For BHA 6 to 8 inches: 2.25 to 2.75
• For BHA larger than 8 inches: 2.50 to 3.20

Bending Strength Ratio (BSR) Formulas

Let's consider a scenario where a drilling engineer is designing a Bottom Hole Assembly (BHA) for an oil drilling operation. The BHA includes various components such as drill collars, stabilizers, and heavy-weight drill pipe, all connected together using threaded connections. The engineer needs to ensure that these connections are strong enough to handle the stresses encountered during drilling, particularly in terms of bending.

Scenario:

The engineer is working with a specific drill collar that has the following dimensions:

• Outside Diameter (OD) of the Box: 8 inches
• Inside Diameter (ID) of the Box: 4 inches
• Outside Diameter (OD) of the Pin: 7 inches
• Inside Diameter (ID) of the Pin: 3.5 inches

Step 1: Calculate Section Modulus

The section modulus ($$Z$$) for both the box and pin connections is calculated using the formula:

$Z = \frac{\pi \times \left(OD^4 - ID^4\right)}{32 \times OD}$

For simplicity, let's assume the section modulus values are provided or pre-calculated as:

• Section Modulus of the Box ($$Z_{\text{box}}$$): 500 inÂ³
• Section Modulus of the Pin ($$Z_{\text{pin}}$$): 250 inÂ³

Step 2: Calculate Bending Strength Ratio (BSR)

The BSR is calculated using the formula:

$BSR = \frac{Z_{\text{box}}}{Z_{\text{pin}}} = \frac{500}{250} = 2.0$

Step 3: Compare with Acceptable Ranges

The engineer compares this BSR value with the recommended ranges from standards like API RP 7G-2. For a BHA with an outside diameter larger than 8 inches, the acceptable BSR range is 2.50 to 3.20.

Step 4: Analysis and Decision

BSR = 2.0: The calculated BSR is lower than the acceptable range (2.50 to 3.20).

Implication: This indicates that the box connection is not strong enough relative to the pin connection. The box is likely to fail under bending stress before the pin, which could lead to connection failure and possibly a costly breakdown in the drilling operation.

Given the low BSR, the engineer might decide to:

• Increase the box's section modulus by using a thicker wall or stronger material.
• Reduce the pin's section modulus to balance the connection.

The engineer could opt for a different design or adjust the materials and dimensions to achieve a BSR that falls within the acceptable range of 2.50 to 3.20, ensuring a more balanced connection that is less likely to fail under bending stresses.

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