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 Τzy and Tzx 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 Tzy, 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 Tzx 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 Tzx in particular in the case of vertical planks, arranged side by side, connected solidly by horizontally arranged mechanical connectors, since the shear stresses Tzx developed across the width of the cross-section may considerably exceed the vertical shear stresses Tzy 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 Tzx was limited to beams with a width/depth ratio between 0.25 and 10.0.