A container apparatus includes a sandwich structure. In another aspect, a sandwich structure of a container apparatus employs at least one core sheet including alternating peaks and valleys therein in addition to at least one adhesively bonded outer face sheet. Moreover, another aspect of a container apparatus includes a wheeled box trailer, an intermodal shipping container, a railroad car, or other box-like holding and transporting device. An inner container liner, such as a floor, or structural container frame rail is attached to a structural sandwich in another aspect. A joint or connection between adjacent sandwich structures and/or a sandwich structure and an elongated beam, for a container apparatus is also provided.