The localization of stiffness variation in damaged beams through modal curvatures, i.e.,second derivative of mode shapes, is studied by exploiting a perturbative solution of theEuler-Bernoulli equation. It is shown that for low order modes the difference betweenundamaged and damaged modal curvatures has only one distinct peak if the damage islocalized in a narrow region. This phenomenon is independent of the presence ofexperimental noise and of the technique used to reconstruct the curvature mode shapesfrom the displacement mode shapes. Broader damages cause the modal curvaturedifference to have several peaks outside the damage region that could result in a falsedamage localization. The same effect is present at higher modes for both narrow andbroad damages. As a result, modal curvatures can be effectively used to localize structuraldamages only once they have been properly filtered. Here the perturbative solution isused to introduce an effective damage measure able to localize correctly narrow and broaddamages and also single and multiple damages cases.