Hencky bar-chain model for buckling analysis and optimal design of trapezoidal arches

This chapter presents a Hencky bar-chain model (HBM) for buckling analysis and optimal design of funicular trapezoidal arches. Based on the energy approach, canonical elastic and geometric stiffness matrices are derived for the HBM trapezoidal arch. The HBM comprises a finite number of rigid segments connected by frictionless hinges and rotational springs. The chapter considers trapezoidal arches under vertical point loads at different positions from the supports, as well as various base support conditions, such as hinged-hinged, fixed-hinged and fixed-fixed. It focuses on funicular trapezoidal arches under two vertical point loads applied at the joints. The HBM furnishes accurate buckling solutions when a sufficient number of bar segments is adopted for each member. For an economical design of trapezoidal arches considering both strength and stability, the optimal arch solution against buckling should also be used in addition to the condition for the optimal fully stressed trapezoidal arches.