I'm not the best at answering this, and usual depend on our colleague statistician. There are couple of courses that could assist understand and teach how to do. RC help-desk might be able to help you!
If the SD's are independent and based on equal number of measurements, consider them as orthogonal vectors. Find their joint effect using the n-dimensional Pythagorean Theorem: Square root of the sum of each SD squared. If number of measurements are unequal, try doing this with standard errors instead.