Expressions are presented in this paper for the deflection, angle of slope, and angle of twist of the free end of a circular cantilever beam with a bending moment applied at the free end. Like expressions are also given for the same beam with a twisting moment acting at the free end. The values of the reaction and the angles of slope and twist at the simple support are given for a circular beam built in at one end, simply supported at the other, and loaded as in each of the foregoing cases. Also, equations are included for the three internal reactions, i.e., bending moment, twisting moment, and shear existing at the plane of symmetry of a cantilever arc beam, built in at both ends, with an arbitrarily placed concentrated load acting perpendicular to the plane of the beam, and at its center line. Corresponding expressions for the same element with a uniformly distributed load covering the half of the beam to one side of the axis of symmetry, and an expression for the bending moment at the plane of symmetry of the same beam when its entire length is uniformly loaded, are also stated.

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