Method for manufacturing a curved composite part, said curved composite part at least comprising: a curved web with an inner edge (2.1) and an outer edge (2.2) and a neutral axis (2.3) therebetween, wherein said outer edge (2.2) is longer than said inner edge (2.1), and an outer cap close to such outer edge (2.2) end of the curved web, and adapted to provide a continuous surface (3.1) to be joined to a skin; wherein the method comprises the steps of: - providing a tool adapted to support at least one preform, and to form them up to their final shape before curing; - laying up a first flat preform composed by a set of stacked plies, such preform comprising at least one folding line (5.1) substantially parallel to the neutral axis (2.3) of the curved composite part, the folding line (5.1) dividing the first flat preform into: ∘ a curved web for being part of the curved web of the curved composite part, and ∘ a flange for being part of the outer cap of the curved composite part, such flange being delimited by the folding line (5.1) and a free end (7.1); in such a way that at least one ply is provided with at least one discontinuity within the flange zone, such at least one discontinuity being substantially perpendicular to the folding line (5.1) and being initiated from the free end (7.1); - bending in a form-up step the first flat preform by the folding line (5.1); and - curing the at least one formed-up preform, the curved composite part being manufactured; characterized in that the plies provided with at least one discontinuity are only those oriented in the direction of the folding line (5.1) local tangent. a curved web with an inner edge (2.1) and an outer edge (2.2) and a neutral axis (2.3) therebetween, wherein said outer edge (2.2) is longer than said inner edge (2.1), and an outer cap close to such outer edge (2.2) end of the curved web, and adapted to provide a continuous surface (3.1) to be joined to a skin; - providing a tool adapted to support at least one preform, and to form them up to their final shape before curing; - laying up a first flat preform composed by a set of stacked plies, such preform comprising at least one folding line (5.1) substantially parallel to the neutral axis (2.3) of the curved composite part, the folding line (5.1) dividing the first flat preform into: ∘ a curved web for being part of the curved web of the curved composite part, and ∘ a flange for being part of the outer cap of the curved composite part, such flange being delimited by the folding line (5.1) and a free end (7.1); in such a way that at least one ply is provided with at least one discontinuity within the flange zone, such at least one discontinuity being substantially perpendicular to the folding line (5.1) and being initiated from the free end (7.1); ∘ a curved web for being part of the curved web of the curved composite part, and ∘ a flange for being part of the outer cap of the curved composite part, such flange being delimited by the folding line (5.1) and a free end (7.1); - bending in a form-up step the first flat preform by the folding line (5.1); and - curing the at least one formed-up preform, the curved composite part being manufactured;