Load-Dependent Non-Uniform Bending Stiffness and Curvature-Based Deflection Calculation in Timber–Concrete Composite Beams

The effective bending stiffness formula for cross-sections of timber–concrete composite (TCC) beams was derived under semi-sinusoidal loading condition in Eurocode 5; however, this formula does not account for the non-uniform distribution of bending stiffness along the span. This limitation prevents it from characterizing the mechanical behavior under real loading conditions, which could potentially compromise the safety and serviceability of the structural design. To investigate the distribution pattern of bending stiffness, differential segment analysis was conducted, incorporating interfacial slip effects. A governing differential equation for curvature was established, and the resulting curvature distribution was used to compute deflections by means of the conjugate beam method. The results demonstrate that the bending stiffness distribution depends critically on shear connector arrangement and loading conditions. Under third-point loading, the bending stiffness monotonically decreases from the mid-span to the load application points and increases toward the supports. Under uniform loads, bending stiffness peaks at the mid-span and declines gradually toward the supports. Reducing shear connector spacing enhances composite action while amplifying bending stiffness non-uniformity. Experimental validation confirms that both the conjugate beam method (using analytical curvature solutions) and the simplified approach in Eurocode 5 achieve 99% average accuracy in predicting the mid-span deflection of TCC beams. In addition, careful attention must be paid to the deflection values at loading points, particularly when the loading position is close to the supports.