M.Ing. (Mechanical Engineering) / This report describes an investigation into structural damping in simple steel structures. More specifictly, an attempt is made to obtain and compare the logarithmic decrement for different types of steel structures. The effect that welded and rivetted connections have on the logarithmic decrement is also examined. Four different types of steel are used, namely: mild steel and three types of chromium based steel. Vibration tests are performed on both cantiliver and simple bridge structures. An estimate of the inherent damping that is present in the vibrating structures are obtained from the approximate displacement-time response plots (as obtained from vibration tests). All the step input tests are modelled with a finite element. computer package to test the accuracy of the approximated response functions. Shaker tests are also performed on bridge structures. On the theoretical side the term damping is fully defined and discussed.