A flexible strengthening joint for a pressurized vessel includes an outer skin having a localized abrupt change in shape. The outer skin includes a first skin section and a second skin section, the localized abrupt change in shape being located at a junction between the first skin section and the second skin section. A reinforcing bulkhead is located in the interior of the pressurized vessel. The reinforcing bulkhead includes a first bulkhead section that is directly attached to the first section of the outer skin and a second bulkhead section that unattached directly to the first section. A kick frame is located in the interior, the kick frame spanning at least the second bulkhead section. At least one intercostal is secured to the second bulkhead section. The at least one intercostal is also secured to the kick frame.