For more information on the approximate value of beam mass that contributes to the effective end mass, see Problem 3.30 on page 89 of An Introduction to Mechanical Vibrations (2nd ed.) by Robert F. Steidel, Jr. Effectively the fraction of a beam's mass that contributes to the effective end mass of a beam that is clamped at both ends is 13/35.
Source: Steidel, Jr., Robert F., An Introduction to Mechanical Vibrations (2nd ed.), New York: John Wiley and Sons, Inc., 1989.Problem3.30 page 89.