This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
The compression in a rib results in shortening the arch rib very slightly; and this produces precisely the same effect in altering the moment as an equivalent fall in temperature. For example, in the above case, we have at the abutment a thrust of 296 pounds per square inch; dividing this by E, the modulus of elasticity, 2,400,000, we have .0001233, the proportional shortening; dividing this by .0000065, the coefficient of expansion, we find that the thrust due to this rib shortening is the equivalent of a reduction of temperature of 19 degrees. Since we have found that a reduction of temperature of 30 degrees produced a unit-stress of 113 pounds per square inch, a virtual reduction of 19 degrees would produce a unit-stress of 72 pounds per square inch. Since such a stress is always the same as that due to a reduction of temperature, and since this always has the effect of increasing the stresses for usual loading, such unit-stress must be added to the value found above; therefore,-adding this 72 pounds per square inch to the total previously found (422), we have a unit-compression at the intrados at the abutment, of 494 pounds per square inch.