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Thermal Gradient Stress Calculation

Thermal Gradient Stress Calculation

Thermal Gradient Stress Calculation

(OP)
I would like to know a simple method for estimating the strain/stress resulting from a temperature gradient across a very thick-walled pipe.  The low alloy steel part is essentially a donut shape, having 11" I.D. and wall thickness 5".  Temperatures are 1000°F internal and ~300°F external.  
I have zero expertise in and no access to computational methods and software .  Thanks in advance.   

RE: Thermal Gradient Stress Calculation

Another classic text that provides a wide range of thermal stress solutions is by Timoshenko.

Some other interesting approximations are associated with linear gradients thru the pipe wall, such as:
- As per background tehnical papers to the  TRD 301 annex 1 ( and later EN codes) , a constant increase in the rate of change of mid-wall metal temperature will yield a linear temperature gradient thru the wall of the pipe. The thermal stress generated will be proportional to the (wall thickness ) squared * rate of change mid wall metal temperature.
- a simple "boiler stress monitor " can be based on the above approximation, by installing a thermocouple at the mid wall location and moitoring the rate of cahgne of mid wall metal temperature. Within the DCS, this rate is multiplied by the know ( wal lthickness ) squared and other material properties to generate an apparent therma stress. This can be added to the current stress caused by fluid pressure to yield total stress , and either the rate of fatigue life consumpti nis calculated ( using the rainflow cycle counting algorithm) or the rate of unit startup/shutdown is restrained based on limiting this total stress. Using such fatigue monitoring  is one requirement  of the new fast startup Siemens combined cycle plants.  

RE: Thermal Gradient Stress Calculation

error-
 should read " a constant rate of increase in midwall metal temperature"

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