#Calculator degrees of freedom free

all nodes remain at the same points in space), then this top structure shown in Figure 9.1 is considered to be a non-sway frame. Since there are only rotational DOFs in this structure, and no translational DOFs (i.e.

The same rotation is applied to the ends of both members that frame into node E (BE and DE). It can rotate, and will have a rotation of $ heta_E$ as shown in the figure. Node E cannot translate vertically due to the restraint provided by member BE which is restrained vertically by the fixed end at node B.

#Calculator degrees of freedom free

(Total free DOFs = 1) Node E cannot translate horizontally due to the restraint provided by member DE which is restrained horizontally by member CD which is restrained horizontally by the pin at point C. The same rotation is applied to the ends of all three members that frame into node D (AD, CD, and DE). It can rotate, and will have a rotation of $ heta_D$ as shown in the figure. Node D cannot translate vertically due to the restraint provided by member AD which is restrained vertically by the fixed end at node A. (Total free DOFs = 1) Node D cannot translate horizontally due to the restraint provided by member CD which is restrained horizontally by the pin at point C (recall that we are considering the frame members to be rigid axially). It can rotate, and will have a rotation of $ heta_C$ as shown in the figure. (Total free DOFs = 0) Node C cannot translate (displace) either horizontally or vertically because of the pin at that location. In this frame structure, we can look at each node individually to evaluate the total number of degrees of freedom in our system: Nodes A and B cannot translate (displace) horizontally or vertically and cannot rotate because of the fixed end supports at those locations. By making this assumption, we reduce the number of effective DOFs in the slope-deflection analysis and, therefore, reduce the number of equations in the system of equations that we have to solve.Ī simple example is shown at the top of Figure 9.1 (labelled 'Non-Sway Frame'). This is usually a good assumption for beam and frame analysis since the structural deformations are mostly caused by bending of frame elements, not axial elongation. we assume that the beams cannot elongate or compress). In a slope-deflection method analysis, we will typically make the assumption that all frame members are axially rigid for the purpose of determining the number of degrees of freedom in the system (i.e. Although three DOFs are possible for each node, individual directions may be considered to be restrained, either by a support reaction or by one of the members connected to the node. Usually, we consider the horizontal and vertical axes as the two perpendicular translational degrees-of-freedom. In a 2D system, each node has three possible degrees-of-freedom: translation (movement) in one direction, translation in another direction perpendicular to the first one, and rotation. This concept was previously briefly introduced in Section 1.5.

Although the elements have deformations between the nodes, we can, using structural analysis methods, characterize the behaviour and deformation of the structure based on the deformations at the nodes alone.Ī degree-of-freedom (or DOF) represents a single direction that a node is permitted to move or rotate. When doing structural analysis, we often conceptualize a real structure as a simplified stick model with elements connected to each other at specific locations called nodes. >When you're done reading this section, check your understanding with the interactive quiz at the bottom of the page.