Which construction project would not require a building permit?

In Virginia, building permit requirements can vary based on the size, type, and location of the construction project. The correct choice here, which pertains to a one-story detached accessory structure measuring 190 square feet, is not mandated to have a building permit because it falls under the threshold set by many local building codes.

Typically, structures that have a total area less than 200 square feet may not require a building permit, as they are often classified as minor projects. This exemption is designed to streamline the permitting process for small-scale builds that are unlikely to have significant impacts on safety or zoning regulations. In this specific case, the detached accessory structure's size keeps it within allowable limits for permit exemption.

On the other hand, the other options represent projects that exceed this critical threshold. For instance, a two-story structure comprising 400 square feet or any addition, even if it’s only 200 square feet, often requires a permit due to the increased complexity and potential impact these projects could have on existing structures and utilities. Therefore, option C accurately identifies a project that typically would not necessitate a building permit.