The transport road network design problem examines the expansion or addition of link capacity in a network. While this topic has a rich history in the literature, it becomes particularly challenging when complexities such as dynamics or inherent network uncertainties are considered. This work introduces a dynamic, system optimal flows approach which includes demand uncertainty and for which a globally optimal solution can be found due to the linear programming model at its foundation. In the proposed model, stochastic demand scenarios are accounted for using a strategic approach, in which optimal flow proportions are identified to minimize total system travel time in all demand scenarios. This approach results in non-optimal flows for any particular demand realization. The network design linear program model proposed here does not add significant computational complexity to the base model. Results are demonstrated on a sample cell network.