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 thrust at airy-point of the arch is measured by the projection onto the tangent to the arch at that point, of the corresponding ray of the force diagram. Since the rays of the force diagram which are parallel to the segments of the equilibrium polygon are approximately tangent to the arch rib, it is approximately true to measure the thrust at any point by measuring the corresponding rays of the force diagram; but a more precise value may be found by drawing a line from one end of a ray parallel to the corresponding tangent, and projecting the ray on it. This method is particularly useful, since it measures at the same time the amount of the shear at that point, as will be explained in the next article. Since the increase in the thickness of the arch is comparatively slight from the crown to the abutment, in this particular problem, and since the amount of the thrust evidently increases very rapidly toward the abutment, the critical point, so far as the thrust is concerned, is evidently at the abutment. Therefore we may draw from the lower end of load 20, a line parallel to the tangent to the curve at the abutment, and obtain the line wx, which scales 40,200 pounds, and which therefore measures the thrust at the abutment. Since the abutment is 21.25 inches thick, the area of a section one foot wide is 255 square inches. Dividing this into 40,200, we have a quotient of 158 as the unit-compression per square inch due to thrust. Adding the value of the compression at the intrados which is due to moment. (151), to the compression just found for thrust, we have a total of 309 pounds per square inch at the abutment. This compression does not allow for temperature stresses, which will be computed later, and which may exist simultaneously with the stresses due to moment and to thrust.