Disclosed is a fiber-reinforced polymer (FRP) cord system and method that is useful for concrete repair and strengthening applications, including the strengthening of concrete slab edges to increase their resistance to lateral loads from extension elements, such as railings, attached to balconies or façades attached to portions of a building. In certain configurations, fiber-reinforced polymer cords are affixed to a concrete structure along an end surface that includes an extension element, with the fiber-reinforced polymer cords positioned on opposite sides of the extension element. In further configurations, fiber-reinforced polymer cords are affixed to adjacent faces of concrete structures. In particularly preferred configurations, the fiber-reinforced polymer cords are situated within grooves that extend into the faces of the concrete structures that are being reinforced.