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The Static Analysis option allows the user to select from 5 types of static analysis to be carried out on a model.
The static analysis employs matrix methods to manipulate the stiffness matrix associated with the MasterFrame model and then solve the equations, using the specified restraint conditions are the required boundary conditions. From the solution of the equations, the nodal displacements are obtained. The next stage is to use the nodal displacements in conjunction with the stiffness matrices for each individual member to obtain the member end forces and rotations. From the end forces and rotations, the member loading is then used to calculate the bending moment and shear force distribution in the members.
On selecting the Static Analysis, the following window presented, from which the analysis is selected.
The analysis type can be selected by clicking on the appropriate icon at the bottom of the window.
Depending on the type of structure and also the active MasterFrame licenses, some icons may be shown ‘greyed out’. This indicates that a particular analysis type is not available.
Below the analysis type icons, any licensed based limitation on the number of elements in the type of static analysis is indicated.
The type of static analyses are as follows: -
Space Frame
The space frame analysis is the most general type of analysis. This is a 3-dimensional analysis, allowing for model geometry in the x-, y- and z-axes. Similarly, the allowable load directions are also in the x-, y- and z-axes directions. The model may incorporate pinned, fully fixed or partial fixity connections. Models may also include non-linear elements, such as tension or compression only members and spring supports. The space frame analysis also incorporate model with Finite Element surfaces in the analysis.
Space Truss
The space truss analysis allows for the analysis of a 3-dimensional structure, with the model arranged in the x-, y- and z-axes and similarly loaded in the x-, y- and z-axes. However, all joints in a space truss are assumed to be pinned, regardless of the end restraint condition defined in the model.
In addition to the above conditions on the model, no member loading is considered in the space truss analysis. All member loads are resolved to give the equivalent end reactions in the members, and these end reactions are then taken to be nodal loads. Therefore, the space truss is taken analytically to behave as a pin jointed truss. As a consequence, all members in a space truss will only be subjected to axial loading, either compressive or tensile. No bending will occur in the members.
Plane Frame
The plane frame analysis is applicable for structures which are 2-dimensional structures in the xz plane only. Only loading in the x and y directions can be considered – loads in the z direction cannot be accommodated in the plane frame analysis so even for 2-dimensional models, if the loads are out-of-plane, the Space Frame analysis will be required.
Furthermore, the loads, even if acting in the x- or y- directions, must act in the plane of the frame itself. This means that eccentric loads, where the eccentricity would shift the loads out of the plane of the frame, cannot be analysed in a plane frame analysis. Again, in this case, the analysis would require the use of the Space Frame option.
The plane frame analysis method allows the use of pinned, fixed or partial fixity connections, where the rotations are about the global z axis.
The plane frame analysis uses 3 degrees of freedom for each node in the model. All members will therefore remain in the plane. It is not necessary to add restraints in the z-direction, nor in the theta-x or theta-y directions.
Plane Truss
The Plane Truss analysis is used for analysing pin jointed truss structures. Similar to the plane frame, the structure must be planar, being located in the xy plane only, and only be loaded in the xy plane. Unlike the plane frame, however, all members are assumed to be pinned, so they have no rotational restraint in the theta-z direction.
The loading of a pin-jointed truss is taken to act on the nodes of a frame. In this case, similar to the space truss, any member loading is resolved into the nodal reactions and then analysed as a nodal load. While this is satisfactory for small loads, in cases where the local member stresses are considered to be significant, the plane truss analysis is not satisfactory and either the plane frame or space frame analysis needs to be used.
Since all members are taken to be pinned for the purposes of the analysis, any end releases or partial fixities are ignored in the analysis and are not effective.
Similar to the plane frame analysis, loads must act in the same plane as the structure, and so eccentric loads cannot be analysed in the plane truss analysis.
Grillage
The grillage analysis is used for the analysis of 2-dimensional structures which lie in the zx plane. The degrees of freedom considered in the grillage are the x- and z-axis, along with the theta-x and theta-z axes. Only loading considered in the y-axis. Thus, the only loading considered in the grillage analysis is out-of-plane, vertical loading.
End releases and partial fixities can be applied to any member in the model, but these only relate to the rotations about the theta-z and theta-x directions. Any releases or partial fixities relating to the theta-y direction will be ignored for the purposes of the analysis.
The grillage analysis will consider eccentrically applied loads where the eccentricity is an offset in the global x or z directions. The y-axis offset for eccentric loads will not have an effect since it is not possible to apply loading in the xz plane.
Of the analysis types available, the most generally applicable is the Space Frame analysis, which covers the full range of degrees of freedom. The Space Frame can be used for any of the other types of structure, but the model needs to be analytically stable in all the degrees of freedom. Therefore, where a model analyses without issue in another analysis type, it may require the use of additional restraint conditions when analysed by means of the Space Frame analysis type. Further, since the Space Frame considers all forms of loadings, if member loads are intended to be applied only to act at the ends of members, it would be necessary to define them as nodal loads in the Space Frame analysis.
In the Analysis Type and License window, it is possible to tick the checkbox under the suspend column. This enables specific load cases to be excluded from an analysis. The list of load cases can be scrolled using the mouse wheel, or by clicking on and dragging the side scroll bar. You can also multi-select loading cases and suspend/unsuspend in one operation.
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Analysis Results
The results of the analysis can be reviewed in the Results section of the software. The analysis results can be viewed graphically or tabular form. When viewing the results graphically the results can be viewed for the frame or part of the frame, or for individual members.
For details of the results menu, refer to the Results chapter of the manual.
Possible Analysis errors
The MasterFrame analysis uses methods from linear algebra to solve the system of static equations represented by the stiffness matrix of the modelled structure. The set of equations represented by the structure, loads and restraints is given in matrix notation as f = Kd, where f is the external forces matrix, d is the displacement matrix and K is the structural stiffness matrix. Both f and d are column vectors.
To solve the system of equations, the stiffness matrix must be singular. If the matrix is not singular, then the system of equations represented by the stiffness in the matrix is not stable. When this occurs, the software is unable to complete the solution of the system of equations and will return an analysis error.
Analysis errors can occur for a number of reasons and may be related to the type of analysis being run on a model. The most common errors relate to the degrees of freedom in the model, representing the end releases in a model. Errors of this type are generally reported as relating to the θx, θy or θz directions. Other errors can relate to the displacement of nodes and are noted as dx, dy or dz degrees of freedoms. When these types of error occur, the software will also report the node at which the analysis error relates. It is possible to get a number of degree of freedom errors at any one node, and analysis errors can occur at multiple nodes.
When an analysis error occurs at a node or nodes, the nodes will be highlighted in red on the model. It is also possible to search for nodes using the Zoom to Member/Node function.
A typical cause of errors relates to rotational degrees of freedom on members meeting at a node. When a member is released rotationally from a node by the introduction of an end release, the end of the beam is free to rotate relative to the node. However, it also means the node can rotate relative to the beam. In the case that all the members concurrent to the node are release rotationally in at least one direction, then the node will be free to rotate relative to all the members. The consequence of this is that the stiffness term for that rotational direction of the node will be zero, since there is nothing to resist any rotation. This means that the system of equations will not be able to be solved and so the software will report an analysis instability at the node. In general, a node needs to be connected laterally and rotationally to at least one member joining the node.
Under certain circumstances, the software will report an analysis error but will allow the analysis to proceed based on a 1% fixity to all connections. The 1% fixity will prevent the type of error discussed above, since all pinned end members and end releases will be replaced by a partial fixity. The aim of this option is to allow the analysis to complete such that the deflected diagram of the structure can be viewed by going to Results>Graphic Analysis Results. The deflection results will help to identify the part or parts of the model which are giving rise the analysis warning. The aim of the 1% fixity is purely to work as a diagnostic tool, by allowing the deflected shape of the model to be viewed. If the option to proceed based on a 1% fixity to all released joints is used, the software will not allow the user to proceed to the Design tools.
Some analysis errors relate specifically to the use of the non-linear analysis, either due to non-linear elements in the model, or due to the use of the P-delta analysis. In either case, in order to run a non-linear analysis, the software utilises an iterative analysis method and calculates a convergence factor at the end of each iteration. If the iteration factor is increasing, this indicates that rather than converging to an equilibrium position, the structure is continuing to deflect after each iteration, and is not going to converge to a solution. When running the analysis, the iteration factor will display at the bottom of the screen. When a non-convergence error occurs on a P-delta analysis, it is often necessary to remove the P-delta analysis, rerun the analysis and then review the deflections of the frame to identify potential areas of large deflections which could be contributing to the problems with the convergence of the analysis. In cases where the non-convergence is not due to a P-delta analysis, the issue will be related to the non-linear elements in the frame. The non-convergence may be related to the deflection of the model under particular load cases, and it may be necessary to review the section sizes of elements such as bracing elements.
For more information on detecting where the non-convergence may have occured see User Defined Non-Linear Convergence Settings.
Additional note:-
When an eccentric load is applied to a beam or beams, the frame analysis takes account of the torsional stiffness of the beams, but doesn’t take account of the warping stiffness, which is essentially a second order analysis. When you go into the steel design the warping stiffness is now taken account of – see SCI P385 for further details on the design of steel members with torsion.
Therefore, the values in the steel design are more accurate where torsional rotation is concerned than those derived directly from the initial frame analysis.