{"id":24712,"date":"2026-02-01T21:56:37","date_gmt":"2026-02-01T21:56:37","guid":{"rendered":"http:\/\/141.23.68.248\/wp\/?page_id=24712"},"modified":"2026-02-09T19:23:04","modified_gmt":"2026-02-09T19:23:04","slug":"parametric-modeling","status":"publish","type":"page","link":"http:\/\/141.23.68.248\/wp\/?page_id=24712","title":{"rendered":"Parametric Modeling"},"content":{"rendered":"\n

Parametric Definition of a Truss:<\/h2>\n\n\n\n

For roof trusses in e.g. halls, external boundary conditions such as span, roof pitch \/ chord slope and construction depth are usually dictated by the building layout. The actual design freedom for structural engineers therefore lies inside the truss: in the web system (web pattern), cross-sections and material choice.<\/p>\n\n\n\n

Outer geometry \/ fixed parameters <\/strong>– Span of the truss L <\/em>– Minimum truss height at the supports HMin – <\/em>First height at midspan HFirst<\/em>, defining the slope of the top chord<\/p>\n\n\n\n

Web system \/ truss scheme <\/strong>– Number of panels: panel count <\/em>– Presence of end posts: hasEndPosts <\/em>and intermediate posts: hasVerticals <\/em>– Orientation pattern of diagonals (diag_dir<\/em>: towards support, towards center, alternating)<\/p>\n\n\n\n

Material configuration <\/strong>– Separate for chords and web members: tensile <\/em>and compressive <\/em>strength, density \u03c1 <\/em>– Cross-section dimensions: b, h – only full cross sections <\/em><\/p>\n\n\n\n

Loads – <\/strong>Roof line load q <\/em>and the equivalent self-weight line load resulting from the truss<\/p>\n\n\n\n

Role of the Parameters:<\/h2>\n\n\n\n

The span L <\/em>determines the bending moment level and thus the axial forces in the chords (derivations are provided in the appendix). In practice, the building layout \u2013 and therefore L <\/em>\u2013 as well as clear hall height, maximum building height and roof pitch are usually fixed; from these, HMin <\/em>and HFirst <\/em>follow. In the model, these quantities are treated as fixed boundary conditions.<\/p>\n\n\n\n

In addition to HMin <\/em>, the panel count <\/em>controls the panel lengths and the diagonal angles. The web parameters hasEndPosts<\/em>, hasVerticals <\/em>and diag_dir <\/em>govern the internal force flow: Pratt systems favour tension diagonals and compression posts, Howe systems favour compression diagonals and Warren systems alternate tension and compression in the diagonals.<\/p>\n\n\n\n

The cross-section dimensions b, h <\/em>determine the area A<\/em>, which together with the roof line load q <\/em>and the self-weight g <\/em>yields the design stress \u03c3d<\/em>; the strength classes define the design strengths fd,t <\/em>and fd,c , <\/em>so geometry and material jointly link the parametric model to structural capacity.<\/p>\n\n\n\n

Defining Input Parameters:<\/h2>\n\n\n\n

For a hall scenario with fixed roof pitch, clear height, hall width and a given roof load, the following parameters are fixed:<\/p>\n\n\n\n

Input Parameter<\/strong><\/td>Value<\/strong><\/td><\/tr>
Force q<\/em><\/td>7 kN\/m<\/td><\/tr>
Span length L<\/em><\/td>7 m<\/td><\/tr>
MinHeight HMin<\/em><\/td>1 m<\/td><\/tr>
FirstHeight HFirst<\/em><\/td>2 m<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

The following parameters are available for optimization (applied uniformly to all chords and all web members\/posts, respectively):<\/p>\n\n\n\n

\"\"<\/a><\/figure>\n\n\n\n

Logic of the Parametric Model (Dynamo):<\/h2>\n\n\n\n

The Dynamo script can be roughly divided into three blocks:<\/p>\n\n\n\n

First Block: Inputs <\/strong>On the left, all inputs are defined. Helper blocks process these inputs: for example, from the material choice (C16, C24, \u2026) a set of material properties is derived and passed to the subsequent blocks.<\/p>\n\n\n\n

Second Block: Geometry – nodes, members and solids <\/strong>A) First: all nodes <\/em>of the truss are calculated: The Python node TrussPoints <\/em>generates all truss nodes from L<\/em>, HMin<\/em>, HFirst <\/em>and panel count<\/em>: – bottom nodes equally spaced along the span, – top nodes forming a pitched top chord (interpolation between HMin <\/em>and HFirst<\/em>).<\/p>\n\n\n\n

B) Second, all lines <\/em>and solids <\/em>for chords and web are built: From these points, chord members are created as lines; hasEndPosts controls whether the outer top nodes are connected. A second Python node generates the web system with: – verticals (posts) depending on hasVerticals<\/em>, – diagonals according to DiagonalDirection <\/em>(Pratt-, Howe- or Warren-like pattern).<\/p>\n\n\n\n

These lines are then extruded in the BuildSolids <\/em>block using the cross-section dimensions b <\/em>and h <\/em>to form simple 3D solids (rectangular sweeps). This makes the structure visible and allows member lengths to be read directly from the geometry. <\/p>\n\n\n\n

Third Block: Calculations – loads, axial forces and stresses <\/strong>From the given roof line load q <\/em>and the self-weight line load g <\/em>(computed from geometry, cross-section area and density), a design line load Ed is formed. Using a deliberately simplified structural model, the following are derived: – the governing axial force in the bottom chord, and – the critical tension and compression forces in the diagonals. A Python node converts these axial forces together with the cross-sectional areas A <\/em>into design stresses \u03c3d [N\/mm\u00b2], distinguishing between tension and compression in chords and diagonals. In parallel, using kMod, \u03b3M and the material strengths, the design strengths in tension fd,t and compression fd,c are calculated.<\/p>\n\n\n\n

Performance indicators<\/strong>:<\/h2>\n\n\n\n

From stresses and strengths, the utilization ratios \u03b7 are computed for bottom chord and diagonals. In addition, the truss self-weight G is output as total mass [kg].<\/p>\n\n\n\n

Design alternatives:<\/h2>\n\n\n\n

For the variant study, a common framework is defined: Span length L = 7 m, HMin <\/em>= 1 m, HFirst <\/em>= 2 m and roof line load q <\/em>= 7 kN\/m To reduce degrees of freedom, the web pattern is fixed as: hasEndPosts <\/em>= true, hasVerticals <\/em>= true, diag_dir <\/em>= support (Howe-like). Chord parameters are kept constant (h <\/em>= 160 mm, b <\/em>= 240 mm, material = C16); only the diagonal parameters <\/em>are varied.<\/p>\n\n\n\n

The study investigates whether a higher panel count<\/em>, larger cross-sections b, h <\/em>or a higher strength class fd (at the cost of higher density \u03c1<\/em>) leads to better material efficiency. Three representative variants are considered:<\/p>\n\n\n\n

    \n
  1. few panels, relatively large profiles, C16 (standard material)<\/li>\n\n\n\n
  2. B) more panels, slender profiles, C16 (standard material)<\/li>\n\n\n\n
  3. C) more panels, slender profiles, GL28h (higher-strength, higher-density glued-laminated timber)<\/li>\n<\/ol>\n\n\n\n
    \"\"<\/a><\/figure>\n\n\n\n

    Figure 01:<\/strong> Dynamo Model<\/p>\n\n\n\n

    Truss System ><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

    Parametric Definition of a Truss: For roof trusses in e.g. halls, external boundary conditions such as span, roof pitch \/ chord slope and construction depth are usually dictated by the building layout. The actual designContinue reading<\/a><\/p>\n","protected":false},"author":300,"featured_media":0,"parent":24626,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-24712","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/24712","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/users\/300"}],"replies":[{"embeddable":true,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=24712"}],"version-history":[{"count":8,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/24712\/revisions"}],"predecessor-version":[{"id":28803,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/24712\/revisions\/28803"}],"up":[{"embeddable":true,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/24626"}],"wp:attachment":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24712"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}