The present paper gives analytical solutions for shear deformable two-layer beams with weak shear connections. Timoshenko's kinematic assumptions are applied to both layers with different cross-sectional rotations. A linear constitutive equation is used between the horizontal shear force and the interlayer slip. The applied loads act in the plane of symmetry of a two-layered beam and the material-geometrical properties do not depend on the axial coordinate. For simply supported beam closed form solutions are derived for the deflection, slip and cross-sectional rotations. The eigenfrequencies of a simply supported beam are determined and compared with the solutions obtained by the applications of Euler-Bernoulli and Euler-Bernoulli-Rayleigh beam models.Mathematical Subject Classification: 74G05, 34B05

Compound circular bar consists of two bars with same cross sections and different homogeneous isotropic elastic materials. The bond between the bar components is perfect. The free end cross sections of the bar components are subjected to torsional shear stresses. Closed-form solutions are presented for circumferential displacement, longitudinal and radial shearing stresses.

Exact second-order analysis of two-layer composite beam-columns with weak shear connection which are subjected to transverse axial loads is presented. Closed-form solutions for the deflection, interlayer slip, bending moment and shear force are derived for simply supported beamcolumns. Results of the present paper are compared with the solutions obtained by a different method as which is used in this paper.