Effect of horizontal reaction force on the deflection of short simply supported beams under transverse loadings

• An accurate analysis of simply supported Timoshenko beams is made.
• Effect of the horizontal reaction force on the deflection is analyzed.
• Consideration of horizontal force makes a simply supported beam more compliant.
• Load–deflection exhibits a nonlinear relation and agrees with experimental data.
• Shear deformation increases the bending deflections of a beam.

In the classical analysis of bending of a beam resting on simple supports, the effect of the horizontal component of reaction force is often neglected for small deflection analysis. This paper presents an adequate analysis of a simply supported beam with emphasis on the effect of the horizontal reaction force. Based on Timoshenko׳s kinematic relation, a governing equation is derived. Three typical cases including uniformly distributed loading, three-point bending and four-point bending are analyzed. Expressions for the bending deflection and the cross-section rotation are obtained and a non-linear load–deflection relation is derived. When neglecting the horizontal force, the results available for Euler–Bernoulli and Timoshenko beams are recovered from the present. The influences of shear deformation and loading position on the transverse deflection are discussed. The deflection and load–maximum displacement curve are graphically presented. A comparison of the deflections with and without the horizontal reaction force and with experimental data is made. Obtained results are useful in safety design of linear and non-linear beams under complicated loading.