Enable Interpolation

Multiple records with varying temperatures and stress values may exist for a given combination of Material Specification, Material Grade, and Design Code values. So, after a match is found on Material Specification, Material Grade, and Design Code, Thickness Monitoring (TM) evaluates Design Temperature.

If the Design Temperature in the TML is an exact match to a temperature value in a Piping Stress or PV Stress record, TM will simply use the corresponding Allowable Stress value. For example, consider a TML that contains the following values:

Material Specification = SA-216
Material Grade = B
Design Code = ASME B31.3
Design Temperature = 100

Now, consider a Piping Stress record that contains the following values:

Material Specification = SA-216
Material Grade = B
Design Code = ASME B31.3
Design Temperature = 100
Allowable Stress = 20000

In this case, the values in the TML are an exact match to the values in the Piping Stress record. Therefore, TM will use the Allowable Stress value of 20000 to calculate Maximum Allowable Working Pressure and T-Min.

Thickness Monitoring uses reference tables to look up the Allowable Stress values for performing T-Min calculations and for calculating Maximum Allowable Working Pressure. You have two choices regarding how the stress reference tables will be used to determine Allowable Stress when an exact match cannot be found:

You can specify that the lowest temperature in the established range should be used.
You can specify that Thickness Monitoring should use linear interpolation to determine the Allowable Stress.

By default, interpolation is disabled.

Interpolation is Enabled

If TM cannot find an exact match in the Piping Stress or PV Stress reference table, and the Application Settings specify that interpolation should be used, TM will calculate the interpolated Allowable Stress value using the temperature and stress values that make up a range that includes the TML Design Temperature.

For example, consider a Piping Stress reference table that contains the following two records.

	Record #1	Record #2
Material Specification	SA-403	SA-403
Material Grade	WP316	WP316
Design Code	ASME B31.3	ASME B31.3
Design Temperature	100	200
Allowable Stress	20000	18000

Now, consider a TML that contains the following values:

Material Specification = SA-403
Material Grade = WP316
Design Code = ASME B31.3
Design Temperature = 150

The TML Design Temperature falls within the range established by the two Piping Stress records in the table. Linear interpolation assumes that stress varies linearly as a function of temperature within the defined range. Using this assumption, the Allowable Stress at 150 degrees can be calculated using the following formula:

Sx = S1 - (T1 - Tx) / (T1 - T2) * (S1 - S2)

Where:

Sx = Allowable Stress for the TML
S1 = Allowable Stress at Lower Boundary
S2 = Allowable Stress at Upper Boundary
T1 = Temperature at Lower Boundary
Tx = Temperature defined for TML
T2 = Temperature at Upper Boundary

Given the values from our example, we calculate Sx as:

Sx = 20000 - ((100 - 150) / (100 - 200) * (20000 - 18000))

So:

Sx = 19000

This interpolated Allowable Stress value will then be used to populate the Allowable Stress field in the TML.

Note: For TM to determine Allowable Stress in this way, the Piping Stress and PV Stress reference tables must contain records that establish the range that includes the TML Design Temperature.

Interpolation is Disabled

If TM cannot find an exact match in the Piping Stress or PV Stress reference table, and the Application Settings specify that interpolation should not be used, TM will use an Allowable Stress value that corresponds to the lowest temperature value in the temperature range that includes the TML Design Temperature.

For example, consider a Piping Stress reference table that contains the following two records.

	Record #1	Record #2
Material Specification	SA-403	SA-403
Material Grade	WP316	WP316
Design Code	ASME B31.3	ASME B31.3
Design Temperature	100	200
Allowable Stress	20000	18000

Now, consider a TML that contains the following values:

Material Specification = SA-403
Material Grade = WP316
Design Code = ASME B31.3
Design Temperature = 150

In this case, the Design Temperature in the TML is not an exact match to a Piping Stress record. The TML Design Temperature, however, does fall within the temperature range established by the two Piping Stress records in the table. So, in this case, TM will use the record that contains the most conservative (i.e., lowest) Allowable Stress value. Therefore, in this case, an Allowable Stress value of 18,000 will be used in the TML.

Note: For TM to determine Allowable Stress in this way, the Piping Stress and PV Stress reference tables must contain records that establish the range that includes the TML Design Temperature.