Steel Tube Truss Calculator
About Steel Tube Truss Calculation
The Steel Tube Truss Calculator performs geometric calculations for single-slope and double-slope steel trusses made from structural tubing. It determines the top chord slope angle, dimensions of individual outer-frame members, vertical posts and diagonal braces, and the total length of steel tubing.
The calculation is useful when preparing drawings and cut dimensions for trusses used in canopies, awnings, roofs and other steel structures. All geometric dimensions are calculated in millimetres.
Guidelines and recommendations
Truss geometry and slope angle
Outer frame. The calculation starts with the horizontal truss length A, height H1 and height H2. The bottom chord is horizontal, while the top chord consists of sloping segments. The height difference is the absolute difference between the two heights.
Single-slope truss. The top chord has one sloping segment over the full length. Its angle relative to the horizontal is calculated as follows:
α = arctan(|H1 - H2| / A)
Double-slope truss. The top chord comprises two symmetrical sloping segments meeting at the centre. Height H1 refers to the centre, while H2 refers to the ends. Since each slope spans half the horizontal length, the angle is calculated as follows:
α = arctan(|H1 - H2| / (A / 2))
The angle is displayed in degrees to 0.1°. With the same length and height difference, a double-slope truss has a steeper angle because the same rise occurs over half the horizontal distance.
Determining outer-frame member dimensions
Sloping chords. The geometric length of a sloping segment depends on its horizontal projection and the height difference. The distance between its endpoints is calculated using the Pythagorean theorem:
L = √(a2 + ΔH2)
Here a is the horizontal projection in mm and ΔH is the height difference in mm. For a single-slope truss the horizontal projection is the full length A. For each half of a double-slope truss it is half that length.
Cut dimensions. When individual members are drawn, the depth of the tube section in the truss plane is taken into account. Member outlines are formed at intersections of sloping and horizontal lines, so cut dimensions follow the actual member geometry rather than only the distance between centre lines. For inclined members, the length is measured after rotating the outline to a horizontal position.
End members. Their dimensions follow the geometry of the junction between top and bottom chords. In a single-slope truss, the two end members differ in height. In a symmetrical double-slope truss, they are identical.
Positioning and calculating internal posts
Post positions. The interior of the truss is divided into equal panels, taking the post width into account. In a single-slope layout, posts are distributed along the length. In a double-slope layout, one post is placed at the centre and the others form symmetrical pairs about the midpoint.
Post lengths. For each post, the distance between the inner edges of the top and bottom chords is determined at its position. The top chord slope and post width are taken into account. Posts in different panels can therefore have different lengths.
Placement limit. The calculated spacing between posts must exceed their width. If there is insufficient room, the corresponding members are not generated. The actual number of members therefore depends on the available truss geometry as well as the selected number of posts.
Constructing diagonal braces
Brace geometry. Diagonal braces are positioned between the chords according to the post layout. The direction of each brace follows the geometry of its panel, and its ends are shaped by the lines where it meets adjacent members.
The calculation accounts for the transverse dimension of the tube. Brace endpoints are found from intersections of geometric lines, then the length of the resulting member is determined. If the geometry does not allow the brace to be drawn at an admissible angle of less than 90°, that member is omitted.
Symmetry. In a double-slope truss, braces on opposite slopes form mirror-image pairs. One set of dimensions is calculated for each pair, while the total count includes two pieces.
Dimension limits and assumptions
Minimum dimensions. The calculator applies the following limits when constructing its geometric model:
- The truss length is at least three times the section depth of the outer-frame tube.
- Height H1 is at least three times the section depth and cannot be less than H2.
- If H2 does not exceed the outer-frame section depth, it is set to that depth. If it exceeds the depth but is no more than twice the depth, twice the section depth is used.
- If the specified outer-frame section depth or the transverse dimension of posts and braces is 10 mm or less, the corresponding value is replaced with 80 mm.
- The transverse dimension of posts and braces is limited by the available internal space between outer-frame members.
These limits are used to generate the geometric model and do not represent code-prescribed dimensions for steel trusses.
Tube sections. The same section depth is used for the top and bottom chords. A separate transverse dimension is specified for posts and braces. The second dimension of a rectangular tube does not affect the two-dimensional geometric model.
Calculating member quantities and total tube length
Member quantities. Every geometrically distinct member receives its own number. In a symmetrical double-slope truss, identical mirrored members are grouped in pairs of 2 pieces. Individual members count as 1 piece.
Total length. The total tube length is calculated separately for the outer frame, posts and braces. Each member length is rounded to the nearest whole millimetre and multiplied by the number of identical pieces. The resulting values are added together:
Ltot = Σ(ni × Li)
Here ni is the quantity of identical members and Li is the rounded length of one member in mm. The total is converted to metres by dividing by 1000 and displayed to 0.001 m, without unnecessary trailing zeros.
A factor of 1.00 is used when summing lengths. No additional allowances for cutting, fabrication gaps or material waste are added.
European standards
For the design of steel trusses in Europe, relevant standards include EN 1993-1-1 "Eurocode 3: Design of steel structures. General rules and rules for buildings" and EN 1993-1-8 "Eurocode 3: Design of steel structures. Design of joints". Fabrication requirements, including dimensional tolerances and workmanship, are covered by EN 1090-2 "Execution of steel structures and aluminium structures. Part 2: Technical requirements for steel structures".
The dimensions produced by the calculator can be used when preparing truss detailing. Applicable editions of European standards and national annexes are taken into account when producing working drawings.
FAQs
Why is a sloping chord longer than the horizontal truss length?
A sloping chord forms the hypotenuse of a right triangle, so its geometric length increases with the height difference. The steeper the slope, the larger the difference between the horizontal projection and the actual length. The geometry of the end cuts is also taken into account when determining the cut length.
How does the number of posts affect truss geometry?
Increasing the number of internal posts reduces the spacing between them and changes the dimensions of individual truss panels. This changes post and brace lengths and the total number of members. When preparing the fabrication layout, sufficient room should remain between adjacent members for their connections.
Why are some members listed as two pieces in a double-slope truss?
A double-slope steel truss is symmetrical about its central vertical axis. The top chords, end members, and some posts and braces form identical mirrored pairs. The calculator shows the dimensions of one member from each pair, but includes both pieces in the total tube length.
Why do brace lengths differ even when post spacing is equal?
A brace length depends not only on the horizontal distance between adjacent members but also on the height of its truss panel. The sloping top chord changes that height along the structure. Tube width and end-joint geometry also affect the cut dimensions.
How should the total tube length be used when planning materials?
The total length shows the combined tube requirement for each group of members, including the quantity of identical pieces. For example, 12.5 m means a combined cut length of 12500 mm, not the length of one tube. This figure can be compared with available stock lengths and the planned cutting layout.