The paper deals with using a visual language and graph-based structures to support the conceptual phase of designing. The design ontology-based visual language is composed of design diagrams. A symbolic representation of design structures in terms of ontological objects and relations between them is defined, and then mapped into diagrams by a given realization. Diagrams are automatically transformed into the corresponding graph-based data structures. The knowledge stored in the graph representation of diagrams is transformed into first-order logic formulas and allows the design supporting system to reason about created designs. The approach is illustrated by examples of designing transmission towers.