Numerical analysis of sandwich beams

This paper describes the development of a numerical model for the physical nonlinear analysis of simply supported sandwich beams, specifically with foamed-concrete cores and concrete faces. The long-term behaviour is included in view of creep and shrinkage of both faces and core. The structural behaviour of sandwich beams is described by a fourth-order differential equation in the deformation w and a second-order differential equation in the shear deformation of the core γk. The flexural stiffness of the core is taken into account. The general-solution procedure is based on the finite-difference method, together with a successive-substitution algorithm using the secant flexural moduli of the core and faces and the secant shear modulus of the core. The option of tension stiffening is incorporated to represent the nonlinear behaviour of reinforced concrete in tension. The tension stiffening is numerically calculated from a distributed tensile load instead of a load acting on both ends of the reinforced bar. Creep and shrinkage are calculated separately from the differential equations with an algorithm based on increments of time. With the presented model, the time-dependent deflection along the axis of the beam and the state of stress in every fibre can be calculated.