Rotational spring

The physical origin of the internal displacements is more easily seen in a two-dimensional analogue of the three-dimensional lattice illustrated in F ig. 8-8 and treated in Problem 8-3. If wc imagine the bonds as freely rotating springs (setting the constant C, equal to zero), we see that the elastic distortion tends to pull the shaded atoms upward with respect to the others. These are conventionally thought of as positive internal displacements. Note that if in contrast there were... 

Wang [8] 2004 Stretching and rotating springs, equivalent continuum plate 0.2-0.8 for zigzags 0.57-0.54 for armchairs Effective in-plane stiffness and bending rigidity of SWCNTs... 

FEM using beam element to model the stretching component of potential and also nonlinear rotational spring to take account the anglebending component... 

K-.6x6 Stiffness matrix Kq. Rotational spring stiffness M Lumped masses... 

The TdealGear element introduces these equations to the spur gear model. The Disconnect and Jam elements are rotational spring-dampers described by ... 

Plastic Hinge and Plastic Zone Seismic Analysis of Frames, Fig. 1 Lumped plasticity model of a portal frame three beam-column FE and four rotational springs... 

In the case of surface foundations, a simple system of three translational (two horizontal, x and y, one vertical, z) and two (less often three) rotational springs can be used at the base of the footing the spring constants for the x, y, and z springs can be estimated from relationships (ASCE 2007) derived from the solution of the problem of a rigid plate resting on the surface of a homogeneous half-space ... 

Figure 6a shows a concentrated plasticity model for a multistory three-bay steel moment-resisting frame, whose plan configuration is shown in Fig. 6b. At both ends of each beam and column, a nonlinear rotational spring is arranged with an offset from the node to account for the member s cross section. In contrast, generic frame models used for research purposes are often centerline models, i.e., the lumped plasticity elements are located at the nodes without any offset from the nodal point.

Beam-column joint modeling is still at an early and less mature stage with respect to member modeling (i.e., beam and columns), and practical available solutions are to consider rotational springs capable to describe the beam-column joint behavior that is governed by shear and... 

The model is based on the theory of bending in combination with a process zone model. The tensile specimen with its boundary conditions is replaced by a small zone (in the following denoted as fracture zone) of the specimen, that encompasses the process zone (see Fig. 2). The surroundings of this zone is replaced by translational and rotational springs, that are connected to this zone through a rigid interface. For the stiffness of the specimen against rotation the beam theory is used, M = (EI/Jl)( >. The model does not account for the influence of horizontal displacements. For the sake of clarity, there is no direct relation between the depth of the fracture zone, which will... 

T is the torque reaction of the rotational spring and damper at point O and it is calculated as... 

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