SD = sqrt(S*S) = sum (x - mean)^2/ N, where x = value, mean = average value, N is the number of values.

If x = mean for all x, then difference = 0 and sum = 0, so variance = S*S = 0 and SD = 0.

More [link|http://davidmlane.com/hyperstat/A16252.html|here].

Or in a more hand-waving way, the Standard Deviation is a measure of the spread of a distribution. Small SD -> small spread. Since all of the values are identical, there is no spread so the SD should be zero.

Cheers,
Scott.