Trusses as plane frames

In Roof trusses the trusses of the house were placed, Lattice trusses shows the web post and diagonal patterns of a truss, and in Roof the roof was closed with battens and tiles. There the subject was geometry: where each piece is created and how it joins the others. Here it is what the engine checks in it.

To the engine, each truss is a set of bars in a vertical plane. The chords are continuous and split at the nodes. Web posts and diagonals are pinned at the ends. The battens do not enter as bars: the weight they carry reaches the top chord by area, and their position says where that chord is braced.

The example is T2, a common truss of the house: a 7.00 m span between the walls, a 30% pitch and every piece in C 89x41/39x12x0.95, ZAR-280 steel. The numbers come from the calculation of the whole house, on screen: 26 combinations and 1,113 bar segments in the Bar Verification list.

• 7.00 m: span of T2, wall to wall
• 30 %: pitch of both roof slopes
• 0.95 mm: thickness of every truss piece
• 1.00: the highest ratio of T2, in the top chord

The load travels in the plane of the truss

The tile rests on the battens, and the battens rest on the top chord. From the chord, the load goes down through the nodes: the web posts and diagonals carry it to the bottom chord and to the supports, on the walls. The wind comes in by the same path, as pressure on the roof slopes. All of this happens in the plane of the truss, and that is the plane where it is strong.

Out of the plane, it is a thin piece that needs bracing. The drawing is the right half of T2, to scale, with what braces each chord and the buckling length the engine gives each piece.

Each piece with its role and its length

The label of each bar says what it is. That is how you find it in the Bar Verification list, and that is how the engine chooses how to model the piece and where its buckling length comes from.

• 38 cm: largest gap between battens: top chord, out of the plane
• 109 cm: top chord panel: in the plane
• 30 cm: ceiling fastener spacing: bottom chord, out of the plane
• 106 cm: web post m4 and diagonal d3 of T2: the whole piece

Cold-formed steel, item by item

The truss pieces are cold-formed Ue sections, and the engine checks them by ABNT NBR 14762:2010, the Brazilian standard for cold-formed steel. NBR 16970-2:2022, the Brazilian LSF standard, brings the deflection limit of the chord. The table says which item answers for which check in the bar report.

Two checks weigh more in the truss. In the top chord, flexo-compression: it is compressed by the truss and, at the same time, bent between the nodes by the weight of the battens and tiles. In the web members, slenderness: they are straight pieces, with a small axial force and the whole length as buckling length.

1. Read the top chord by the panel

With the web laid across, the gap between battens falls on the strong axis of the section. In T2, 38 cm give a slenderness of 10.7 out of the plane. In the plane, the 109 cm panel with the weak axis gives 72.4. What limits the top chord is the panel, and what shortens the panel is one more web post or one more diagonal.

2. Screw the ceiling to the truss

Without a ceiling, the bottom chord is braced only at the braced nodes: the wall it rests on, the diaphragm and the bracing line. With the ceiling screwed underneath, the bracing drops to the fastener spacing, 30 cm in the house.

3. Look at the web members by slenderness

Web posts and diagonals carry little force and buckle over the whole piece. In T2, the compressed web post stays at 0.35 by slenderness, and that is also the worst web post and the worst diagonal of the house. A long piece in the middle of the truss is the first one to check.

4. Thickness does not fix slenderness

Slenderness is the length divided by the radius of gyration, and thickness barely changes the radius. To lower slenderness, shorten the piece or change the section.

5. Read the truss by its worst segment

The chord is split into one segment per panel, and each has its own ratio. The utilization of the truss is that of the worst segment.

1. Calculate and look at the truss from the side

With the house complete, press Calculate. Then rotate the 3D until you look at the roof along the ridge: the trusses appear from the side, one behind the other, with the nearest in front.

2. Turn on the colors

On the results card, the first button, with a green ✓ and a red ×, shows the OK/FAIL colors on the bars; hovering over it, the tooltip says Verification Colors. On the first calculation of the project, they turn on by themselves. Green passes, red fails. In T2, every piece comes out green, and the figure in the overview is this same view with the colors on.

3. Click the top chord and read the report

With the colors on, click the top chord of T2, on the right side, in the last panel before the support. The Bar Diagnostic Report opens: the header gives the piece, the section, the length and the governing check; further down come the forces at the ends and the loads that reach it, one per load case.

• 1.00: flexo-compression, the governing check, in CB2
• 10.5 kN: compression, against 24.3 kN of resistance
• 17.9 kN·cm: moment about the weak axis, against 37.8
• 72.4: slenderness, out of a maximum of 200

CB2 is the weight combination: the self-weight, the roof weight and the live load, all multiplied by 1.4. In the loads of the report, every load reaching this segment is distributed and lies in the plane of the truss: the roof weight, the live load and the wind. That is why the moment is about the weak axis, the in-plane one, and the moment about the strong axis is practically zero.

4. Open the Bar Verification list

On the same results card, the Bar Verification button opens the list of every calculated segment, with the label, the section, the ratio and the combination. Click a row and it expands into one row per check.

Compression alone uses 0.43 of the resistance, and weak-axis flexure, 0.47. Added up, they would give 0.90, close to the 0.91 of section yielding, which is that sum on the section, without buckling. Flexo-compression goes beyond that because the engine amplifies the moment, as step 5 shows.

5. Read the flexo-compression card and the slenderness card

In the report, each check has a card with the resistances, the demands, the standard item and the combination. The two that explain the top chord are these.

The axial term is Pr/Pc = 10.47/24.25 = 0.43. The weak-axis term is the moment divided by the resistance and by α_ny = 1 − Pr/Ne_y = 1 − 10.47/66.18 = 0.84: 17.92/(37.79 × 0.84) = 0.56. The sum is 0.995. The card shows 1.00 rounded, and OK, because it does not reach 1. The chord passes with half a percent of margin.

The Ne_y of 66.18 kN comes from the same 109 cm panel about the weak axis. It is what makes the amplification grow: the closer the compression gets to Ne_y, the smaller α_ny and the larger the moment term. Shortening the panel or thickening the section raises Ne_y; the trial in step 7 shows how much.

6. Click the bottom chord, a web post and a diagonal

The bottom chord of T2 is in tension. In segment TL:TL1:T2:bi:15, 1.00 m long, slenderness comes with Lx = 30 cm, the ceiling fastener spacing, and Ly = 100 cm, the panel. The item is 9.6.3: tensioned bar, value reported, ratio 0.00. Flexo-tension governs, at 0.51: tension uses 0.11 and the moment from the weight it carries, 0.39.

Web post TL:TL1:T2:m4:0 and diagonal TL:TL1:T2:d3:0 have almost the same length, 106 cm, and the same section. Slenderness comes out equal in both, 70.6. The difference is the force: in CB2 the web post compresses and the diagonal pulls.

The deflection: the limit and how it is measured

The top and bottom chords of the truss have a deflection limit of L/250, the roof beam line of Table 3. L is that of the segment: the panel between two nodes. Deflection is measured in each segment, not in the whole truss.

Measuring in the segment calls for care with what counts. Under weight and wind, the whole truss moves: the supports go down with the walls, the nodes travel. That movement is not bending of the chord. That is why the engine draws the chord line between the two ends of the segment, already displaced, and measures the deflection from it.

• L/250: limit of the chord, top and bottom
• 4.4 mm: limit of segment bs2:6, 1.09 m long
• 0.26 mm: deflection of that segment, relative to the chord line
• 28 mm: L/250 of the 7.00 m span, to check by hand

Trial: the same section, at 1.15 mm

7. Change the thickness of the Tesoura comum class and calculate

The roof pieces use the class section, and the class is changed in the Classes panel, which is hidden in LSF mode. Switch to the Structure tab, open Classes and click the Tesoura comum row. In the form, open the Profile, choose Dob and the C family and search for 89x41 1.15. Choose C 89x41/39x12x1.15, press Save, go back to the LSF tab and calculate.

The resistance went up more than the demand, which grew a little with the self-weight of the thicker pieces. The margin of the chord went from half a percent to 19%. The web post did not improve: slenderness is geometry, and the radius of gyration of the thicker section is practically the same.

What tends to mislead in the truss

1. Reading 1.00 as a failure. The top chord of T2 gives 0.995. The screen shows 1.00, rounded, and OK. It passes, but with no margin: any heavier tile or wider truss spacing takes it to red.
2. Tightening the battens to save the top chord. With the web laid across, the gap between battens works on the strong axis, and gives a slenderness of 10.7. What governs is the panel, about the weak axis, at 72.4.
3. Thickening the sheet to fix slenderness. From 0.95 to 1.15 mm, web post m4 went from 0.35 to 0.36. Slenderness is fixed with a shorter piece or a larger section.
4. Assuming the tensioned diagonal never compresses. The 0.00 slenderness ratio holds for the combination where it pulls. With suction wind the force can reverse, and the engine enforces the 200 in the combination where it compresses.
5. Expecting the change to stay in one truss. The section of the roof pieces is the class section. Changing the Tesoura comum class changes every chord, web post and diagonal of the common trusses. The Tesoura de oitão (gable truss) and the Travamento do banzo (bottom chord bracing) have their own classes and do not change with it.
6. Looking for the batten in the list. The batten is not checked: it leaves the calculation model, and the weight it carries reaches the chord by area. Its position is what counts, in the buckling length of the top chord.

What each sign means

It checks the truss that is drawn

Each truss piece is a bar of the model, checked by NBR 14762 in each of the 26 combinations. The highest ratio of all governs and gives the color of the piece.

What stays with the designer

1. The truss connections: chords, web posts and diagonals to each other and the truss to the wall (see Connections panel).
2. Web crippling at the truss bearing on the wall, in the chord and in the track.
3. The deflection of the whole span: L/250 over the 7.00 m of T2, or 28 mm, against the sag of the ridge node relative to the supports (see Roof trusses).
4. The detailing of the bracing the calculation assumes: battens, purlins or rafters at the drawn spacing, line L1 and the ceiling fastening (see Roof).

Where to read each thing

The path, in one line

Calculate → look at the truss from the side in 3D → turn on the colors → click the top chord and read the report → open Bar Verification and check the segments → read the web members by slenderness → check the span by hand → change the class, if needed, and calculate again.

The numbers of T2

• 1.00: top chord, flexo-compression (0.995)
• 0.51: bottom chord, flexo-tension
• 0.35: web post, by slenderness
• 0.81: top chord at 1.15 mm, in the trial