  We introduce $\delta$ type vertex conditions for beam operators, the fourth
derivative operator, on metric graphs and study the effect of certain
geometrical alterations (graph surgery) of the graph on the spectra of beam
operators on compact metric graphs. Results are obtained for a class of vertex
conditions which can be seen as an analogue of {\delta} vertex conditions for
quantum graphs. There are a number of possible candidates of {\delta} type
conditions for beam operators. We develop surgery principles and record the
monotonicity properties of the spectrum, keeping in view the possibility that
vertex conditions may change within the same class after certain graph
alterations. We also demonstrate the applications of surgery principles by
obtaining several lower and upper estimates on the eigenvalues.
