Restrained torsion of open thin-walled beams including shear deformation effects

A first-order torsion theory based on Vlasov theory has been developed to investigate the restrained torsion of open thin-walled beams. The total rotation of the cross section is divided into a free warping rotation and a restrained shear rotation. In first-order torsion theory, St. Venant torque is only related to the free warping rotation and the expression of St. Venant torque is derived by using a semi-inverse method. The relationship between the warping torque and the restrained shear rotation is estab- lished by using an energy method. The torsion shear coefficient is then obtained. On the basis of the torsion equilibrium, the governing differential equation of the restrained torsion is derived and the corresponding initial method is given to solve the equation. The relationship between total rotation and free warping rotation is obtained. A parameter λ, which is associated with the stiffness property of a cross section and the beam length, is introduced to determine the condition, under which the St. Venant constant is negligible. Consequently a simplified theory is derived. Numerical examples are illustrated to validate the current approach and the results of the current theory are compared with those of some other available methods. The results of comparison show that the current theory provides more accurate results. In the example of a channel-shaped cantilever beam, the applicability of the simplified theory is determined by the parameter study of λ.

Crustal deformation and tectonic levels of Nujiang Gorge since the Miocene

Crustal deformation shows different patterns at different depths due to changes in the physical properties of rock.Tectonic levels can be defined based on the geometry and deformation mechanisms of crustal deformation patterns. Nujiang Gorge, with a high riverbed drop, great erosion depth, and strong deformation, has rock exposures at different tectonic levels and thus provides an ideal lab for deformation study. This paper takes the Nujiang Gorge from Chawalong to Fugong as the object to identify structural deformation patterns at different depths through field study and deformation analysis. At depth, the primary form of deformation is flow deformation, as shown on the outcrops at Maji. Ductile shear deformation can be found in many outcrops within the study region, e.g., the Gaoligong dextral shear zone and Puladi-Songta sinistral shear zone that lie to the south and north of Maji, respectively. Further to the north of Puladi, the dominated deformation pattern is similar fold and dense sub-vertical foliation. In addition, brittle faults, as evidence of shallow deformation, can be seen overprinting on the deeper deformation features all over the region. Based on those observations, this paper identifies four tectonic levels from depth to the surface: flow deformation, ductile shear deformation, similar fold, and brittle fault deformation, all of which result from the NEE-SWW compressive stress field. Further evidence from studies on the region′s thermal evolution and regional tectonics suggests that the development of different tectonic levels is closely linked to the discrepant uplift or denudation since the Miocene(~21 Ma).