Trusses

This mode enables to perform all the necessary strength and stability checks of truss members, and it also checks their slenderness. The work begins with calculating the design values of the forces caused by the given external loads in structural designs most frequently used in practice. There is an option of finding a section from a pre-composed assortment of cross-sections.

The mode performs the following checks in compliance with the selected design code for each member of the truss:

Check	SNiP II-23-81*	SNiP RK5.04-23-2002	SP 53-102-2004	SP 16.13330	DBN B.2.6-163:2010	DBN B.2.6-198:2014	ShNK 2.03.05-13
Strength	Sec. 5.1	Sec. 5.1	Sec. 8.1.1	Sec. 7.1.1	Sec. 1.4.1.1	Sec. 8.1.1	Sec. 7.1
Stability in the truss plane	Sec. 5.3	Sec. 5.3	Sec. 8.1.3	Sec. 7.1.3	Sec. 1.4.1.3	Sec. 8.1.3	Sec. 7.3
Stability in the truss plane (post-buckling behavior)	Sec. 5.3, 7.20*	Sec. 5.3, 7.30	Sec. 8.1.3, 8.3.5	Sec. 7.1.3, 7.3.6	Sec. 1.4.1.3, 1.4.3.5	Sec. 8.1.3, 8.3.5	Sec. 7.3, 9.20
Stability out of the truss plane	Sec. 5.3	Sec. 5.3	Sec. 8.1.3	Sec. 7.1.3	Sec. 1.4.1.3	Sec. 8.1.3	Sec. 7.3
Stability out of the truss plane (post-buckling behavior)	Sec. 5.3, 7.20*	Sec. 5.3, 7.30	Sec. 8.1.3, 8.3.5	Sec. 7.1.3, 7.3.6	Sec. 1.4.1.3, 1.4.3.5	Sec. 8.1.3, 8.3.5	Sec. 7.3, 9.20
Web slenderness based on local stability constraint	Sec. 7.1, 7.2, 7.14, Table 27	Sec. 7.1, 7.2, 7.23	Sec. 8.3.1, 8.3.2, Table 8, Sec. 8.3.10	Sec. 7.3.1, 7.3.2, Table 9, Sec. 7.3.11	Sec. 1.4.3.1, 1.4.3.2, Table 1.4.3	Sec. 8.3.1, 8.3.2, Table 8.3	Sec. 9.1, 9.2, 9.3, Sec. 9.15
Flange overhang (flange plate) slenderness based on local stability constraint	Sec. 7.22, 7.23, Table 29, Sec. 7.26, 7.27*	Sec. 7.32, 7.33, 7.37	Sec. 8.3.7, Table 9, Sec. 8.3.10	Sec. 7.3.8, Table 10, Sec. 7.3.11	Sec. 1.4.3.7, Table 1.4.4	Sec. 8.3.7, Table 8.4	Sec. 9.22, 9.23, Sec. 9.27
Pipe radius to thickness ratio based on local stability constraint	Sec. 8.6	Sec. 8.6	Sec. 12.2.2	Sec. 11.2.2	Sec. 1.10.2.2	Sec. 14.2.2	Sec. 10.6
Local stability of the pipe wall based on closed circular cylindric shell calculation	Sec. 8.5-8.13	Sec. 8.5-8.13	Sec. 12.2.1-12.2.8	Sec. 11.2.1-11.2.9	Sec. 1.10.2.1-1.10.2.9	Sec. 14.2.1-14.2.9	Sec. 10.5-10.13
Stability of the curved member
Slenderness	Sec. 6.1-6.4,6.16	Sec. 6.1-6.4, 6.15	Sec. 11.1.1-11.1.4, 11.4.1	Sec. 10.1.1-10.1.4, 10.4.1	Sec. 1.9.1.1-1.9.1.4, 1.9.4.1	Sec. 13.1.1-13.1.4, 13.4.1	Sec. 8.1-8.4, 8.18
Rigidity of the truss

Limitations

The following values of the service factor, γ_c, are used for finding and checking the truss members:

0,95 for chords, support diagonals, lattice members in tension, lattice members in compression with cross-shaped sections;
0,8 for lattice members in compression of tee section, the slenderness being greater than 60.

Since the standard requirement to the limitation of the slenderness of a tension member is related to the limitation of its self-weight sag, the slenderness check of tension members is performed only in the vertical plane(for example, according to Note 1 to Table 33 of SP 16.13330).

The truss plane is assumed to be the vertical one in the Trusses mode. Slenderness of the tension truss members out of the truss plane is not checked. Thus, the out-of-plane bracing of the bottom (tension) chord does not affect the result of its slenderness check.

If the user has to check the slenderness of the tension members out of the truss plane (for horizontal and inclined trusses), the Resistance of Sections mode can be used. When the calculation of a tension member is performed in the Resistance of Sections mode, both slenderness values are checked, because the very concept of a vertical plane is absent in this mode.

The dialog box for this mode contains four tabs: General, Section, Properties and Loads.

The General tab contains a drop-down list for selecting the truss type by its chord shape and a group of buttons for selecting the truss configuration. The following types of trusses can be analyzed: parallel chord, triangular, trapezoid, with a polygonal top chord, one slope roof trusses and double slope roof trusses. All trusses are statically determinate and are assumed to be fixed in the end nodes of their bottom chord in a statically determinate way according to a beam scheme.

Specify the span of the truss and its height on the support for the selected configuration. Additional geometric parameters have to be specified in case of a trapezoid truss.

The respective radio buttons and checkboxes are used to specify the method of out-of-plane bracing of the top and bottom chord nodes (the bracing in the truss plane is assumed to be statically determinate: a hinge support for the left support node and a roller support for the right one). When the User-defined checkbox is checked, the Node numbers button becomes accessible. Clicking this button invokes the Out-of-plane bracing dialog box. The dialog provides a design model of the truss with numbered nodes and a table where each truss node is assigned a checkbox. A checked checkbox means that there is a bracing in the given node. The braced nodes are highlighted in blue in the model. Nodes in grey are braced by default and their condition cannot be modified.

The Section tab is used to assign cross-sections to truss members. It is assumed that neither the sections of the chords nor those of the lattice members vary along the truss. The sections are made from double equal or unequal angles arranged as a tee (the latter come in two variations) or a cross of equal angles; and from round and rectangular pipes.

The sections are selected from a database of rolled profiles. The gap between the angles is specified in a table above the truss model when selecting a profile for each section type. Members of the same type selected with the respective checkboxes are highlighted in red in the model, and the selection field displays their section.

It should be noted that the standard checks of the load-bearing capacity of bar elements of steel structures depend on the internal forces and geometric properties with respect to the principal axes of inertia of the section. Thus, the stability checks of the truss members under central compression are performed in the Trusses mode depending on the geometric properties of the section (in particular, depending on the moments of inertia and the radii of inertia) with respect to the principal axes of inertia.

One of the principal axes of inertia of most types of cross-sections implemented in the Trusses mode lies in the plane of the truss, and the other one lies in the plane perpendicular to the truss plane. Thus, the buckling of a truss member that has lost its stability under central compression can occur either in the truss plane or out of the truss plane. Therefore, the stability checks of the truss member under central compression are related to the truss plane, i.e. the Stability in the truss plane and Stability out of the truss plane factors are calculated. The only exception is a compound section made of two equal angles arranged as a cross with its principal axes of inertia lying neither in the truss plane, nor in a plane perpendicular to the truss plane. The buckling of a truss member made of two equal angles arranged as a cross at the loss of its stability is not related to the truss plane. Nevertheless, in order to unify the names of the factors, the Stability in the truss plane and Stability out of the truss plane factors are used for this type of section as well.

The Properties tab enables you to specify a deflection limit (for characteristic and/or characterisric long-term loads) of the truss in fractions of its span length (it will be compared with the relative deflection under the loads with design values which correspond to the serviceability limit state). You can specify the deflection for the truss in fractions of the span expressed as 1/А where А is one of the most frequently used values (500, 750, etc.).

The Web instability is forbidden checkbox is used to perform the check of the section taking into account its post-buckling behavior (after the local buckling of the web). The checked checkbox enables to reject the post-buckling behavior of the section if the check indicates local buckling of the web.

This mode enables to perform the check analysis taking the corrosion into account. Moreover, you can specify not only the information on corrosion but also the values of initial imperfection for each truss member made from double angles. To do it, check the Allow for corrosion and initial imperfections checkbox and click the button $image\table_question.png$ which invokes a dialog box. This dialog is used to enter information on the damages of the structure (once you have entered the information, the button changes into: $image\table.png$ ).

The table is used to specify the data on the thickness of the corrosion layer for each member of the truss (numbers of the members are shown in the model) and the value of the initial imperfection both in the truss plane and out of the truss plane. Moreover, every row of the table has the button $image\calc.png$ which invokes the calculation of the corrosion layer thickness. Note that the inclination angle of a member to the horizon does not need to be specified because it is calculated automatically for all the truss members.

If you check the Apply for all elements of the bottom (top, ...) chord checkbox in the Corrosion layer thickness dialog box, the result of the analysis will be inserted not only into the current row of the table but also into all the rows that correspond to the members of the whole group. The analysis is based on an assumption that the corrosion layer thickness is uniform over the whole perimeter of the member section.

The behavior analysis of the damaged structure will be performed according to the recommendations of Guide to design of reinforcing for steel structures (to SNiP II-23-81*). The analysis takes into account the possibility for the member with an initial imperfection to experience spatial buckling, therefore the set of factors generated in the result of the analysis may not include the results of in-plane or out-of-plane stability checks, or the results of both of these checks.

The Loads tab is much similar to that described in the Envelopes mode. However, there are some differences. The user can specify either a uniformly distributed load or a concentrated load upon nodes. The distributed load is applied to either the whole chord (upper or lower) or to the half of it. The load application area is defined using the respective radio buttons in the Group of elements group. Number of the load application node is selected from the Node number drop-down list.

The graphical control of the input data can be performed in the special window located in the Loads tab on the right and displaying a truss model. Once you click the button to select the chord the unifromly distributed load is applied to, the respective chord will be highlighted in red in this window, and when you select the number of the node the concentrated load is applied to, the respective node will be highlighted in red.

After clicking the Add button, a schematic of the respective load case with all the specified loads will appear in the window.

To edit the values of particular loads, you can use a table invoked by the button $image\table.png$ .

Clicking the Forces in the truss members for the current load case button invokes an information window displaying a design model of the truss with a diagram of forces.

Kristall (unlike SCAD) assumes that a truss is subjected to a nodal load. Thus the specified distributed load is not transferred onto the truss members; instead, it is assumed to be applied to some enclosing roof structure which performs the function of transferring the load onto the truss nodes.

As a rule, the top truss chord is subjected to a distributed load, and this fact is taken into account in the truss analysis performed by SCAD. The longitudinal force changes over the length in inclined members. SCAD calculates and displays the maximum value of the force in the member. When converting the distributed load into the nodal loads, Kristall will display a value corresponding to the force in the middle of a SCAD finite element. Therefore the results generated by the two applications may differ.

It is possible to indicate the presence or absence of the dynamic loads on the truss. If all loads are static, the slenderness check of tension members is performed only in the vertical plane.

Clicking the Calculate button will display the value of K_max and indicate the type of check (strength, stability, slenderness) in which the maximum takes place. You can also browse all the other utilization factors of restrictions by clicking the Factors button.

The Find button enables you to switch to a mode that performs the purposeful search of cross-sections for the truss members and replaces the numbers of profiles selected by the user (the cross-section type and bracing conditions are not modified). The application switches to the next number of profile greater in area in the catalogue the cross-sections were initially selected from if during the checks of the considered member (e.g., a top chord) the value of the utilization factor of restrictions K > 1 has been detected, or it switches to the next number of profile smaller in area if K < 1. Such switches are performed until all checks give K < 1 and the replacement of the profile with its adjacent smaller one gives K > 1, i.e. until the smallest profile that satisfies the requirements of the design codes is found.

The searches through different groups of members (the top and bottom chords, diagonals, verticals) are mutually independent.

When the search is completed, a dialog with the recommendations on the selection of cross-sections appears on the screen.

The user can reject these recommendations (using the Exit button) or accept them. In the latter case the Apply button is clicked, and all the recommended sections are transferred to perform the check analysis of the new structure.

If the maximum profile of the assortment was used in the search process and the value was still K > 1, the dialog will display the respective message and the Apply button will become inactive.

Note that the limitation of the deflection does not affect the results of the search.

Moreover, the report document will contain a table with support reactions, total weight of the truss, and paint area.