  We describe the Gerstenhaber algebra structure on the Hochschild cohomology
HH*$(A)$ when $A$ is a quadratic string algebra. First we compute the
Hochschild cohomology groups using Barzdell's resolution and we describe
generators of these groups. Then we construct comparison morphisms between the
bar resolution and Bardzell's resolution in order to get formulae for the cup
product and the Lie bracket. We find conditions on the bound quiver associated
to string algebras in order to get non-trivial structures.
