Presented in the paper is the formulation of a governing second-order differential equation for the moment distribution along the length of a beam having two interfaces with partial shear interaction where two flange and two web components join to form the box shaped section. For practical applications such a closed-section beam of Fiber Reinforced Polymer (FRP) can be assembled from individual pultruded profiles using mechanical fasteners. This assembly approach can be used to construct deeper section sizes than can be achieved with a single pultrusion, and which can be transported in flat-pack units. In developing the governing equation for flexural response account is made of the finite connection stiffness at the web/flange interfaces by applying conventional elastic beam theory. The differential equation for the partial interaction problem is solved to formulate closed form equations for the flange force and the maximum deflection of a simply supported beam under four-point bending. A numerical parametric study is presented to show changes in beam performance indicators with the degree of shear interaction between the upper and lower bounds of full- and non-interaction. Results from a series of load tests using a three-layered prototype FRP beam are shown to be in good agreement. The theoretical predictions for maximum deflection are however found to be directly linked to the appropriateness of the measured connection stiffness entered into the closed-form equation.