*By Doug Stelling*

Pipe that is internally lined with refractory is used in many applications, such as for transfer lines in Fluidized Catalytic Cracking Units (**FCCU**). While the elastic modulus of a typical refractory is about 1/10 that of steel, the lining thickness can be up to about 10 times the pipe wall thickness. Therefore some stiffening of the composite pipe can be expected, and may cause excessive pipe stresses and equipment nozzle loads when the pipe expands due to temperature. There are various ways to account for this stiffening effect in piping flexibility analysis programs. The best way is to modify the elastic modulus of the pipe to account for the increased stiffness. This is because most piping Codes base their calculation of flexibility factors and stress intensification factors for elbows and tees on the pipe wall thickness, and the pipe stresses are calculated based on pipe wall thickness.

The first step in determining the modified elastic modulus of the composite pipe is to determine an effective elastic modulus for the refractory lining. In some cases the refractory manufacturers can provide data. In lieu of this, an effective elastic modulus for the refractory lining can be based on using the empirical American Concrete Institute equation for the elastic modulus of concrete (E_{r} = 33*w^{1.5}*f_{c}^{0.5}).

The equivalent stiffness (E_{c}I_{c}) of the composite pipe is equal to the sum of the stiffnesses of the steel and the refractory (E_{c}I_{c} = E_{s}I_{s} + E_{r}I_{r}). Assuming that the refractory is equally good in compression as it is in tension, the moment of inertia of the refractory can be easily calculated. While the modulus of rupture of some metal fiber reinforced refractories may approach their compressive strength, the modulus of rupture of most un-reinforced refractories is only about 1/5 to 1/10 of the compressive strength. Therefore, assuming that the refractory is equally good in tension as it is in compression may over estimate the stiffening effect if the refractory is not reinforced.

On the other hand, assuming that the refractory has no tensile strength means that any refractory on the tension side of the neutral axis of the composite section is not effective. The moment of inertia of the refractory in this case must be computed based on the assumption that the neutral axis is shifted toward the compression side of the pipe. This calculation of the moment of inertia of the refractory is then not explicit and requires an iterative solution. However for most practical cases, the shift in the neutral axis of the composite section is usually not that large and the moment of inertia of the refractory can be approximated by assuming that the refractory lining on only one half of the pipe is effective. In this case the moment of inertia of the refractory and the composite section can be explicitly calculated.

The modified modulus of elasticity can then easily be determined from the equation E_{m} = E_{c}I_{c}/I_{s}. This effective modulus varies from 1.5 to about 2.5 times that of the pipe alone, depending upon refractory lining thickness and type, and can usually be input into most piping flexibility analysis programs. The pipe stresses and equipment loads can then be calculated considering the effect of the refractory lining on pipe stiffness.