In-plane behaviour of web-tapered beams

• Conventional analysis incorrectly predicts shear stresses.
• Normal stresses are radial, not parallel.
• External shear is reduced by vertical components of flange forces.
• Shear stress magnitudes are controlled by gradient of flange stresses.
• Calculated shear stresses are close to more accurate predictions.

Shear stress distributions in tapered web I-beams are incorrectly predicted by the conventional beam analysis method used for uniform beams. More accurate predictions are obtained by adopting the finding for wedges that the normal stress trajectories are radial instead of parallel.The shear stress distributions in web-tapered I-beams are influenced by the vertical components of the inclined flange forces (which are zero in uniform beams), as well as by the normal stress gradients in the flanges. The net web shear equal to the difference between the external shear and the vertical components of the inclined flange forces is resisted by the resultant of the vertical components of the normal stresses and the circumferential shear stresses.The circumferential shear stresses τrθ have linear components due to axial force and parabolic components due to moment and shear. The magnitudes of these stresses are controlled by the normal stress gradients at the flange-web junctions and by the requirement that the web shear resistance must equal the net web shear force.