Equation for the simplified calculation of the horizontal shear stress in composite beams of rectangular cross-section with considerable width

Abstract

The theory of elasticity allows describing the law of variation of shear stresses Τ_zy and T_zx for a beam of rectangular cross-section, however, the expressions are extensive and complex. For beams with a width/depth ratio equal to 0.25, it is allowed to calculate approximately the maximum shear stress T_zy, with the Collignon-Zhuravski equation. Depending on the width/depth ratio of the beam, it will depend on the percentage of error made. Unfortunately, for the shear stress T_zx there is no approximate formula available to determine the value of the shear stress. Using a simplified procedure, a differential beam element was analyzed in the elastic field for different width/depth ratios and a very simple expression was obtained. The results of the approximate formula were compared with the values obtained from the application of the exact formula and the results of a linear numerical analysis using the finite element method. For cross-sections of homogeneous beams and composite beams of considerable width, it is essential to determine the horizontal shear stresses T_zx in particular in the case of vertical planks, arranged side by side, connected solidly by horizontally arranged mechanical connectors, since the shear stresses T_zx developed across the width of the cross-section may considerably exceed the vertical shear stresses T_zy and furthermore govern the pattern, spacing and cross-section of the mechanical connectors.  The validity of the approximate expression for calculating the maximum value of the shear stress T_zx was limited to beams with a width/depth ratio between 0.25 and 10.0.