only such as space trusses, cables and diagonal members as well as for modeling contact surfaces.
For example, truss elements resisting axial tension and compression forces can be used to model a truss structure. Tension-only elements are suitable for modeling cables whose sagging effects can be neglected and for modeling diagonal members that are incapable of transmitting compression forces due to their large slenderness ratios, such as wind bracings. Compression-only elements can be used to model contact surfaces between adjacent structural members and to model ground support conditions taking into account the fact that tension forces cannot be resisted. Pretension loads can be used when members are prestressed.
Because these elements do not retain rotational degrees of freedom at nodes, Singular Errors can occur during the analysis at nodes where they are connected to the same type of elements or to elements without rotational d.o.f. MIDAS/Civil prevents such singular errors by restraining the rotational d.o.f. at the corresponding nodes.
If they are connected to beam elements that have rotational degrees of freedom, this restraining process is not necessary.
As shown in Figure 1.39, you should exercise caution not to induce unstable structures when only truss elements are connected. The structure shown in Figure 1.39 (a) lacks rotational stiffness while being subjected to an external load in its plane, resulting in an unstable condition. Figures 1.39 (b) and (c) illustrate unstable structures in the loading direction (X-Z plane), even though the structures are stable in the Y- Z plane direction.
You should use tension-only and compression-only elements with care. Element stiffness may be ignored in the analysis depending on the magnitudes of loads; e.g., when compression loads are applied to tension-only elements.
(a) When a force is applied in the X-direction on the X-Z plane
(b) When a force is applied in the X-direction perpendicular to the Y-Z plane
(c) When a force is applied in the X-direction perpendicular to the Y-Z plane
Figure 1.39 Typical examples of unstable structures that are composed of truss (tension-only & compression-only) elements
force force
Beam Element
This element is typically used for modeling prismatic and non-prismatic tapered structural members that are relatively long compared to section dimensions. The element can be also used as load-transfer elements connecting other elements having differing numbers of d.o.f.
In-span concentrated loads, distributed loads, temperature gradient loads and prestress loads can be applied to beam elements.
A beam element has 6 d.o.f. per node reflecting axial, shear, bending and torsional stiffness. When shear areas are omitted, the corresponding shear deformations of the beam element are ignored.
The beam element is formulated on the basis of the Timoshenko beam theory (a plane section initially normal to the neutral axis of the beam remains plane but not necessarily normal to the neutral axis in the deformed state) reflecting shear deformations. If the ratio of the section depth to length is greater than 1/5, a fine mesh modeling is desirable because the effect of shear deformations becomes significant.
The torsional resistance of a beam element differs from the sectional polar moment of inertia (they are the same for circular and cylindrical sections). You are cautioned when the effect of torsional deformation is large, as the torsional resistance is generally determined by experimental methods.
Beam and truss elements are idealized line elements, thus their cross-sections are assumed to be dimensionless. The cross-sectional properties of an element are concentrated at the neutral axis that connects the end nodes. As a result, the effects of panel zones between members (regions where columns and beams merge) and the effects of non-alignment of neutral axes are not considered. In order for those nodal effects to be considered, the beam end offset option or geometric constraints must be used.
The tapered section may be used when the section of a member is non-prismatic. It may be desirable to use a number of beam elements to model a curved beam. When members are connected by pins or slotted holes (Figure 1.40 (a) and (b)), the Beam End Release option is used.
Note that a singularity error can result in a case where a particular degree of freedom is released for all the elements joining at a node, resulting in zero stiffness associated with that degree of freedom. If it is inevitable, a spring element (or an elastic boundary element) having a minor stiffness must be added to the corresponding d.o.f.
Refer to Numerical Analysis Model of CIVIL>Stiffness Data of Elements. Refer to Numerical Analysis Model of CIVIL>Boundaries> Beam End Offset.
Refer to “Model> Properties>Section” of On-line Manual.
Refer to
“Model> Boundaries> Beam End Release” of On-line Manual.
(a) Pin connection
(b) Slot-hole connection
(c) When multiple beam elements are pin connected at a node
(d) When elements having different d.o.f. are connected
Figure 1.40 Examples of end-release application
When several beam elements are pin connected at a node, the degree of freedom for at least one element must be maintained while the ends of all other elements are released in order to avoid singularity.
beam
Rigid connection
Beam element Rigid beam element for connectivity All rotational degrees of freedom and vertical displacement degree of freedom released Plane stress or plate elements
Column
Slot hole Girder
Axial direction d.o.f. released Rotational d.o.f. released
Girder
Beam
Rotational d.o.f. released
The rigid beam element can be effectively used when elements having different degrees of freedom are connected. The rigid effect is achieved by assigning a large stiffness value relative to the contiguous beam elements. In general, a magnitude of 105 ~ 108 times the stiffness of the neighboring elements provides an adequate result, avoiding numerical ill conditions.
Figure 1.40 (d) illustrates the case where a beam member is joined to a wall. The wall element may be a plane stress or plate element. The nodal in-plane moment corresponding to the beam element’s rotational degree of freedom will not be transmitted to the planar element (plane stress or plate element) because the planar element has no rotational stiffness about the normal direction to the plane. The interface will behave as if the beam was pin connected. In such a case, a rigid beam element is often introduced in order to maintain compatible connectivity. All degrees of freedom of the rigid beam at the beam element are fully maintained while the rotational and axial displacement degrees of freedom are released at the opposite end.
Plane Stress Element
This element can be used for modeling membrane structures that are subjected to tension or compression forces in the plane direction only. Pressure loads can be applied normal to the perimeter edges of the plane stress element.
The plane stress element may retain a quadrilateral or triangular shape. The element has in-plane tension, compression and shear stiffness only.
Quadrilateral (4-node) elements, by nature, generally lead to accurate results for the computation of both displacements and stresses. On the contrary, triangular elements produce poor results in stresses, although they produce relatively accurate displacements. Accordingly, you are encouraged to avoid triangular elements at the regions where detailed analysis results are required, and they are recommended for the transition of elements only (Figure 1.41).
Singularity errors occur during the analysis process, where a plane stress element is joined to elements with no rotational degrees of freedom since the plane stress element does not have rotational stiffness. In MIDAS/Civil, restraining the rotational degrees of freedom at the corresponding nodes prevents the singularity errors.
When a plane stress element is connected to elements having rotational stiffness such as beam and plate elements, the connectivity between elements needs to be preserved using the rigid link (master node and slave node) option or the rigid beam element option.
Appropriate aspect ratios for elements may depend on the type of elements, the geometric configuration of elements and the shape of the structure. However, aspect ratios close to unity (1:1) and 4 corner angles close to 90° are recommended. If the use of regular element sizes cannot be achieved throughout the structure, the elements should be square shaped at least at the regions where stress intensities are expected to vary substantially and where detailed results are required.
Figure 1.41 Crack modeling using quadrilateral/triangular elements
Triangular elements are used for connecting the quadrilateral elements.