An exact solution to the stability of weakened beams on elastic foundation subjected to uniform lateral load

Beams on elastic foundations (BEFs) play a crucial role in modeling many mechanical and civil structures. These beams are often subjected to repetitive loads, like those in railway tracks, or extreme environmental conditions, making them prone to damage such as cracks and corrosion. Additionally, beams may be connected by weakened joints, which can lead to premature failure under reduced buckling loads. Currently, the weakened BEFs (W-BEFs) are modeled as two separate BEFs linked by a spring at the weakened joint. The existing Beam-Spring Model (BSM) requires solving two coupled differential equations through iterative methods, limiting computational efficiency. This work presents a novel Equivalent Moment System (EMS) that replaces weakened joints with concentrated moments, reducing the problem to a single governing equation and enabling closed-form solutions, addressing a critical gap in existing analytical approaches. Beyond W-BEFs, the EMS framework offers a generalizable approach for modeling discontinuities in other mechanical and structural systems. Focusing on pin-ended beams subjected to uniform lateral loading, this study investigates the effects of key parameters, including beam bending stiffness, beam length, weakening location and intensity, and elastic foundation stiffness, on stability and deflection behavior. Results show that as beam length or foundation stiffness increases, the elastic foundation carries more load, causing mid-span deflections to stabilize. When the weakened section of the beam is located within this stabilized deflection region, its effect on overall beam deflection becomes minimal. Furthermore, it was observed that the buckling capacity is most sensitive to weakening in high-moment regions, though foundation stiffness partially mitigates this reduction. The results from the derived solution are compared with those from benchmark problems and finite element models, demonstrating its high accuracy.