4. Eccentric axial loading, cross section core z（4所示。）.pdfVIP

Adam Pawe艂 Zaborski 4. Eccentric axial loading, cross-section core Introduction We are starting to consider a more general case when the axial force and biaxial bending act simultaneously in the cross-section of the bar. By virtue of Saint-Venant鈥檚 principle we can replace the original loading by the statically equivalent eccentric longitudinal loading, Fig. 4.1, and vice versa. z z M y y Mz zN N yN y Fig. 4.1 Eccentric axial loading Due to superposition principle, we can add the solutions of the simple cases, tension and biaxial bending, and obtain the normal stress equation for the eccentric axial loading: N M y M z 飦硏 飥 z 飥 y . A J J y z The relation obtained shows that the distribution of stresses across the section is linear. As before, we need to know the neutral axis position. The most distant fibers from the neutral axis are the most exerted section part, where the normal stress is maximal. The neutral axis equation can be written in the form: J y 飪 z N 飪 飦硏 0 飩 z 飪 y 飥 飪? M 飪 J A 飪 y 飪 z 飪 The neutral axis is the straight line, but this time it doesn鈥檛 pass through the section centroid. From the ultimate limit state we get the design condition: max 飦 飩 x , where the maxim