Theoretical Basis of Cold-Formed Steel Design

This article summarizes the theory on which the StatiCAD cold-formed steel module is based and the implementation of the HCBTİE (Turkish Design Principles for Cold-Formed (Light) Steel Buildings) equations in the program. For usage, see the article Cold-Formed Steel Panel and Stud Design.

1. Buckling types in cold-formed sections

In thin-walled (t ≈ 1–4 mm) cold-formed sections, the load-carrying capacity is generally governed not by yielding but by the interaction of three buckling types:

Type	Behaviour	Counterpart in the method
Local buckling	Short-wavelength wrinkling of the plate elements (web, flange, lip); the section axes do not displace.	Effective widths → effective area and effective section modulus
Distortional buckling	Deformation of the lipped flange by rotating about the web–flange junction line (intermediate wavelength).	Separate strength row based on the distortional critical stress
Global buckling	Flexural, torsional or flexural–torsional buckling of the member as a whole (long wavelength).	Global critical load and column curve

2. Section model

The section is built as a connected mid-line chain with the dimensions in the manufacturer’s catalogue (H, A, B, C1, C2, E, F, G, T for Sigma). The torsional properties are obtained from the same chain with open thin-walled section theory: J = Σ(b·t³)/3; the shear centre and warping constant Cw by the sectorial coordinate method.

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The sharp-corner mid-line model gives the area and moments of inertia a few percent higher than the real section with rounded corners. For this reason the gross A, Ix and Iy are taken from the catalogue values; the effective area and effective section moduli calculated in the model are reduced by the same ratio (the ratio is applied only in the reducing direction).

3. Effective Width Method (EWM)

For each plate element under compression, the slenderness and the effective width ratio:

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• λp = √(f / Fcr,plate), Fcr,plate = k · π²E / [12(1−ν²)] · (t/b)²
• ρ = (1 − 0.22/λp) / λp ≤ 1 → beff = ρ·b

k = 4.0 is used for elements supported along both edges (web, flange) and k = 0.43 for elements with one free edge (lip). In bending, generalized expressions depending on the stress gradient are used; the tension zone is fully effective. In axial compression, the effective widths are calculated at the level of the strength stress to obtain the effective area, and in bending the effective section moduli are found with respect to the compression face.

4. Axial compression strength

• Global: The smallest of the combinations of flexural buckling about the two axes, pure torsional buckling and flexural–torsional buckling depending on the shear centre eccentricity (HCBTİE 4.10.3.1).
• Column curve: λc = √(Fy/Fcre); λc ≤ 1.5 → Fn = 0.658^(λc²) · Fy; λc > 1.5 → Fn = (0.877/λc²) · Fy; Pne = Ae(Fn) · Fn.
• Local: Pnl with the effective area.
• Distortional: Via the distortional critical stress Fcrd; if λd ≤ 0.561, Pnd = Py, otherwise Pnd = [1 − 0.25·(Pcrd/Py)^0.6]·(Pcrd/Py)^0.6·Py.
• Nominal strength: Pn = min(Pne, Pnl, Pnd).

Method	Compression	Bending	Shear
LRFD (default)	Pd = φc·Pn, φc = 0.85	Md = φb·Mn, φb = 0.90	φv = 0.90
ASD (comparison)	Pd = Pn/Ωc, Ωc = 1.80	Md = Mn/Ωb, Ωb = 1.67	Ωv = 1.60

5. Bending, shear and combined effects

• Bending: The two cases where the top and bottom fibres are in compression are followed separately. The smallest of the global (lateral–torsional buckling, HCBTİE Eq. 4.10.21), local (effective section modulus) and distortional rows: Mn = min(Mne, Mnl, Mnd). In beams, positive and negative moments are enveloped separately and each is compared with the strength calculated with its own lateral bracing length and Cb factor (Section 9). If the member is laterally braced (if there is sheathing on the panel; for a floor joist, under positive moment if the top flange is connected to the sheathing), the lateral–torsional buckling limitation is not applied. Cb = 1 is used in columns.
• Shear: With the flat web height, Vy = 0.6·Fy·Aw and shear buckling Vcr; the yielding, inelastic or elastic shear buckling regions according to web slenderness.
• Axial + bending: |PEd|/Pd + |Mx,Ed|/Md,x + |My,Ed|/Md,y ≤ 1.0 (HCBTİE Eq. 4.8.4).
• Shear + bending: Simultaneous check with M and V at the same section and in the same combination (Eq. 4.8.5/4.8.6; Section 9).
• Axial tension (column): Td = min(φy·Fy·Ag; φt·Fu·An), An = Ag; tension + bending Eq. 4.8.1/4.8.2.

6. Distortional buckling: general method and finite strip

The simplified kd expression of HCBTİE is defined only for C and Z sections with simple lips, with six geometric conditions, and is markedly conservative. StatiCAD calculates the distortional critical stress with the general method of HCBTİE 4.10.3.3: for each lipped flange, the properties of the flange unit (flange + lip, with return lip if any) are calculated numerically from the mid-line chain, and the critical stress is found from the rotational stiffnesses (Eq. 4.10.32–4.10.37 in compression, 4.10.41–4.10.47 in bending).

• In Sigma, Sigma+ and C+ sections and in C/Z sections that do not satisfy the conditions, only the general method is used. In C/Z sections that satisfy the conditions, both methods are permitted, so the more favourable one is taken. The report footnote states which method was applied.
• The general method does not reduce the capacity in any profile compared with the simplified expression.
• The Sigma web is assumed to be a flat web in this method; compared with the finite strip solution, the result for Sigma is markedly conservative.

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Finite strip option (HCBTİE 4.10.2 (a)): The Distortional option in the “Cold-Formed Steel Member Design Method” box under Project General Settings → Code Selection takes three values: General method, Finite strip for C+ (default) and Finite strip for all sections. In the finite strip solution, the buckling signature curve of the section is calculated and the critical stress is taken from the distortional minimum; if there is no distinct distortional minimum, the value cannot exceed the general method (safe side). Since the general method overestimates the distortional stress in C+ sections, the finite strip is the default for these sections. If “All sections” is selected, the capacity of Sigma and Sigma+ increases markedly.

7. Rotational restraint of the sheathing (kφ)

OSB or plywood sheathing restrains the stud flange against rotation and thereby increases the distortional buckling strength. If sheathing data has been entered, kφ is calculated from the board bending stiffness and connection stiffness components according to AISI S240 Appendix 1 and added to the distortional equations. The smaller of the two faces is used; gypsum board is not taken into account in the strength calculation (kφ = 0). If the conditions of screw spacing ≤ 305 mm and stud spacing ≤ 625 mm are not met, kφ = 0 is taken.

The deflection is calculated with the effective moment of inertia at the service moment (HCBTİE 4.9.5).

8. Panel sheathing shear capacity and stud demands

• Panel shear capacity: Vc = 0.6 · vc · L (L ≥ 0.30 m and h/L ≤ 4); 2L/h reduction in the range 2 ≤ h/L ≤ 4. Equal sheathings on the two faces are added; for different sheathings max(2·smaller, larger) is taken.
• Intermediate stud demand: Nint = N · s/L. End stud demand: Nend = max[N·(s/2)/L + (V·h/L)/n; Cd]; Cd is calculated from the combinations in which the earthquake effect is magnified by D (TBDY 10.4.1.1(a)).
• In exterior wall studs, the out-of-plane wind moment M = γW · w · b · h²/8, with second-order magnification; w = max(0.8·q; 0.5) kN/m².
• Unsheathed panel: The panel shear capacity comes from the sheathing (TBDY 10.3.2.1); in a panel marked unsheathed on both faces, Vn = 0. In the classical shear distribution the panel stiffness is taken as zero; in the finite element solution, with the “capacity” stiffness type, the in-plane stiffness factor is 0.001 (panel not participating in shear). The panel is not included in the capacity share floor or the gypsum-board share; the studs are designed with the unsheathed buckling lengths (h/(n+1) with bridging). If the panel nevertheless receives shear in the analysis (“classical stiffness” type) and this shear exceeds one thousandth of the panel shear of the storey in the same direction, an error is given (same as the short panel rule). Since sheathing on both faces is the default for new walls, leaving both faces unticked is a user choice; the program does not change this choice.
• Storey–direction degeneration: If no panel with shear capacity remains in one direction (the dominant component of the wall axis), the division Vi = Di/ΣD·Q in the classical shear distribution becomes 0/0 and the storey shear cannot be distributed. In this case, solely for force distribution, the panels in that direction are given stiffness on the assumption of sheathing on both faces (a small value proportional to length if vc has not been entered or the panels are short); since the capacity remains zero, the panel checks turn out inadequate, and a storey–direction error is also written. In the finite element solution no capacity scaling is performed in the same situation; the panel receives shear and an error is given.

9. Floor joist: signed bending, Cb, combined bending–shear, web crippling, 7.4 and 7.5

Signed moment envelope. M3 and V2 at the beam segment ends (stations) are built from the load case results for each strength combination of the cold-formed steel combination list. Positive moment (span; top flange in compression) and negative moment (support; bottom flange in compression) are enveloped separately: M+ = max M, M− = max(−M); the name of the governing combination is stored. The effective width calculation is performed three times:

1. Positive: Ly = Lz = Lb+, Cb+; if the top flange is continuously connected to the sheathing there is no lateral–torsional buckling → Md+ (section with the top flange in compression).
2. Negative: Lb−, Cb−, unbraced → Md− (section with the bottom flange in compression).
3. Braced (Fn = Fy, HCBTİE 4.6.3) → Mdlo± = facb·Mnl; where a stiffener is declared, the smaller of this and the distortional row (4.6.4).

The bending ratio is max(M+/Md+, M−/Md−). In the axial interaction (Eq. 4.8.4) the Md value of the governing sign is used.

Cb. HCBTİE 4.10.21 contains no Cb equation; HCBTİE 1.3 and AISI S100 F2.1.1 are applied. The value is calculated from the |M| diagram of the governing combination:

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Cb = 12.5·Mmax / (2.5·Mmax + 3·MA + 4·MB + 3·MC), 1 ≤ Cb ≤ 3

MA, MB and MC are the values at the quarter points (linear interpolation between stations). Cb = 1 is used for a beam with one end unsupported (cantilever) and when Lb < L (intermediate bracing) (safe side; the diagram between intermediate bracing points is not known).

Combined bending + shear (HCBTİE 4.8.2). M and V are taken together at each station and combination; the denominator is Mdlo± according to the sign of the moment:

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• Without stiffener: √((M/Mdlo)² + (V/Vd)²) ≤ 1.0 (Eq. 4.8.5)
• With stiffener, only when M/Mdlo > 0.5 and V/Vd > 0.7: 0.6·M/Mdlo + V/Vd ≤ 1.3 (Eq. 4.8.6)

Web crippling (HCBTİE 4.8.3). 4.8.3 requires M̄ ≤ Mdlo and P̄ ≤ Pd; it gives no equation for Pd. HCBTİE 1.3 (Table 1.1) and TS EN 1993-1-3 6.1.7.2 are applied: single-web section, web angle φ = 90°; hw = H − t, k = fyb/228:

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• k1 = 1.33 − 0.33k; k2 = 1.15 − 0.15·r/t (0.50 ≤ k2 ≤ 1.0); k3 = 1.0; k4 = 1.22 − 0.22k; k5 = 1.06 − 0.06·r/t ≤ 1.0
• End support, stiffened flange (C, Z, C+): Rw,Rd = k1·k2·k3·[9.04 − hw/(60t)]·[1 + 0.01·ss/t]·t²·fyb/γM1
• End support, unstiffened flange (U): k1·k2·k3·[5.92 − hw/(132t)]·[1 + 0.01·ss/t] (ss/t ≤ 60) or ·[0.71 + 0.015·ss/t] (ss/t > 60)
• Interior support: k3·k4·k5·[14.7 − hw/(49.5t)]·[1 + 0.007·ss/t] (ss/t ≤ 60) or ·[0.75 + 0.011·ss/t] (ss/t > 60)
• Two opposite local forces: at the end k1·k2·k3·[6.66 − hw/(64t)]·[1 + 0.01·ss/t]; in between k3·k4·k5·[21.0 − hw/(16.3t)]·[1 + 0.0013·ss/t]

Validity: r/t ≤ 6 and hw/t ≤ 200. A Sigma web is a stiffened web; it is out of scope because the 6.1.7.4 conditions are not checked. In LRFD, Pd = Rw,Rd (γM1 = 1.0); in ASD, Rw,Rd/1.5 is used. The demand is the end shear in all strength combinations. If the end of a cold-formed steel beam in the same direction lies within 1 cm, the support is treated as an interior support and the shears of the two sides are added. With the automatic support type, if there is a vertical member (column) at the end, the beam is considered connected through the web (no check); if there is no column and there is a wall, bearing is assumed. The TS EN 1993-1-3 6.1.11 interaction (M/Mc,Rd + F/Rw,Rd ≤ 1.25) is reported for information because it is not required in HCBTİE.

Web stiffener (HCBTİE 7.4). An intermediate stiffener is required for a flat web with h/t = (H − 2(t + r))/t > 180 or V > 0.8Vd: thickness ≥ web, spacing s ≤ min(4h; 500 mm), width ≥ 20 mm, bolted. The bearing length of a floor joist is at least 40 mm (7.4(e)).

Live-load-only deflection (Table 7.1). Calculated with the largest absolute value of the sum of the moments of the Q load cases: 5/48·MQ·L²/(E·I) ≤ L/250; I is the service effective moment of inertia. It is not applied to the cantilever deflection type.

Vibration (HCBTİE 7.5). Condition: L/d ≤ 18 and natural frequency ≥ 8 Hz; if this is not satisfied, the joist spacing must be less than 40 cm and at least two rows of bridging must be provided. The frequency is estimated from the mid-span moment with an equivalent uniformly distributed load (w = 8M/L², M = MG + 0.3·MQ) as a single-span simple beam:

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fn = π/(2L) · √(E·Ix·g / (8·M))

In a continuous or fixed-end beam the span moment is smaller, so the estimate increases; however, this increase is less than the real frequency increase (with both ends fixed the estimate is 1.73 times, the real value 2.27 times), so the estimate is on the safe side. For the exact value the finite element model of the floor should be used.

10. Cold-formed steel floor generation: strips and pinned beams

When the slab is left as a single shell and a beam is added inside it, a regular shell mesh does not place nodes on the interior beams and the beams take no load; in an irregular mesh the load passes but its distribution is irregular and artificial axial forces occur in the beams. Therefore, as in ribbed slab generation, the slab is divided into strips between the beams: each strip is connected to the beams on its edges by the classical load transfer or in the finite element shell (strip edge nodes lie on the beam).

• Division: If the coordinates perpendicular to the axis of the edges parallel to the beams are a0 < a1, then n = ⌈(a1 − a0)/s⌉ and s′ = (a1 − a0)/n; the beams lie on the lines a0 + j·s′ (j = 1 … n−1), with their ends on the other two edges (which may be sloped). The edge members (beam or wall) take the place of the first and last beams.
• Load width: In the classical transfer, trapezoids fall on the long edges of the strip with 45° lines; for L = 4.0 m and s′ = 0.4 m, the area a beam receives from its two sides is 2·(4.0 + 3.6)/2·0.2 = 1.52 m², and the equivalent load width is 0.38 m (the triangles on the short edges go to the edge beams).
• Hinges: The beams are generated with M2 + M3 released at both ends and act as simple beams (end moment zero).
• Shell effect: If the strips participate in the system stiffness as shells, the out-of-plane stiffness of the sheathing shares load between the beams. The effect is small with rigid edge beams and large with flexible edge beams; the analysis gives a warning. For design with the load width, the classical transfer and not including the slabs in the stiffness are recommended.

11. Cold-formed steel floor diaphragm

Code. TBDY 10.5 and HCBTİE 7.4 (a)–(e) are identical: (a) floors are designed for the earthquake effect with D (2 for cold-formed steel); (b) it is shown by calculation that diaphragm forces are transferred by screws or bolts to the vertical panels, floor joists and chords; (c) a longitudinal transfer element is used for chord forces if necessary; (d) if the opening is ≤ 3 % no separate calculation is needed (if exceeded, a shell model and a load transfer mechanism); (e) bearing ≥ 40 mm. The codes contain no diaphragm shear strength table, no aspect ratio limit and no separate diaphragm force equation.

Force. According to TBDY 4.5.6.4, the force transferred from the floor to the vertical member is the difference between the member's storey top-section shear and the bottom-section shear of its continuation in the storey above. The program builds this difference on a wall-line basis (same direction ±5°, perpendicular distance to the axis ≤ 20 cm): F = Σ Vtop(panels of the lower storey)·u − Σ Vbottom(panels of the upper storey)·u (u: line direction). Thus no matching error occurs in panels split at doors and windows or when the numbers of upper and lower storey walls differ. Horizontal earthquake cases are multiplied by the D coefficient of their direction, wind is taken without D; earthquake combinations and wind-only combinations are enveloped separately.

Sheathing. The TBDY Figure 10.11 model: v = F/B. The line force is divided by the sum of the intervals where the line intersects the floors (diaphragm depth B); if the wall is shorter than B, the collector carries the force in between. Capacity φ·vn (earthquake 0.60 / Ω 2.5; wind 0.65 / 2.0; TBDY Table 10.4 panel coefficients by analogy).

Collector. Unit forces along the line: the upper storey panels give V/ℓ, the lower storey panels receive V/ℓ, and the sheathing gives F/B uniformly. N(s) = ∫(qupper − qlower + qd) ds is piecewise linear; |N|max is compared with the tensile strength of the floor joist profile (HCBTİE 4.4; An = Ag − 2·dv·t) and with its compression strength (EWM; see below). For a single short wall N = F·(1 − ℓ/B), for offset upper and lower walls it equals the upper wall shear, and for walls stacked on top of each other ≈ 0.

Connection. In platform framing, the whole top-section shear of the lower storey panel passes through the screws between the floor joist / rim profile and the top track of the panel. The demand is the envelope shear magnified by D; the capacity is n·Ps: n = max(1, round(ℓ/s)), Ps = φ·Pns (TBDY 10.3.4: Pns1 = 4.2·√(t2³·dv)·Fu2, Pns2 = 2.7·t1·dv·Fu1, Pns3 = 2.7·t2·dv·Fu2; φ = 0.5 / Ω = 3.0); t1 is the thickness of the floor joist and t2 that of the panel top track.

Chord. Each floor family receives an area share of the net force of the level: Ffamily = Fk·Afamily/Ak. In the X direction T = C = F·Ly/(8·Lx), in the Y direction F·Lx/(8·Ly) (simple beam; on the safe side for a continuous diaphragm); T = C ≤ min(Td; Pd).

Compression and splice. Since the diaphragm force changes sign with the direction of the earthquake and wind, the collector and chord forces must be carried both in tension and in compression: |N| ≤ min(Td; Pd). Pd is the EWM compression strength of the floor joist profile (the distortional buckling option is the same as in stud design). The buckling lengths are Lx = Ly = Lz = Lb = floor joist spacing (400 mm if not entered): the member is assumed to be restrained about both axes and in torsion at the points where the joists are connected, to have its top flange restrained by the sheathing, and to be continuously supported from below on top of the wall. In a collector portion spanning an opening (with no wall below it), the strong-axis buckling length is the opening width; this portion must be checked separately. Since the collector and chord consist of pieces of limited length and the position of the splice is not known, the lap screws required for |N|max are given: n = ⌈|N|max/Ps⌉, Ps = φ·Pns (TBDY 10.3.4; t1 = t2 = wall thickness of the joist, dv = diameter of the floor connection screw, Fu1 = Fu2 = Fu value of the joist material; φ = 0.5 / Ω = 3.0; limited by the manufacturer’s screw shear strength Pnvs if entered).

Reinforced concrete checks. In levels where all floors are cold-formed steel, the TBDY 7.11 reinforced concrete diaphragm stress, connection and opening reinforcement checks are not performed; in mixed levels they are.

12. Beam axis offset: removal of the composite axial force

If Take Offset1 and Offset2 values into account in the system stiffness matrix or, with a defined axis, Take eccentricities into account in the system stiffness matrix is ticked in Project General Settings, the beam axis is modelled lower than the joint axis by e2. Because the rigid diaphragm or the supports restrain the axial displacement of the joints, the profile behaves like a composite section working together with an infinitely rigid flange and receives an axial force that does not exist in reality. This force is constant in each chain between diaphragm joints:

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• Nk = ck · M̄3, ck = A·e2 / (I3 + A·e2²)
• M̄3: length-weighted average moment along the chain (average of the segment end moments); M3 is the total moment about the joint axis.

For example, for a 5 m C200x80x16x2 floor joist (A = 7.51 cm², I3 = 471.9 cm⁴, e2 = −10 cm), ck = −6.14 m⁻¹; the finite element segment axial forces agree with this equation within 0.02 %. In the cold-formed steel beam envelope this share is subtracted from the segment axial force of each load case; M3 does not change, i.e. the profile carries the total moment without the composite contribution. The subtracted share does not exceed |N| and does not reverse its sign; in a load case without a diaphragm or in partial restraint the remaining real axial force is kept. Since the segment average is taken from the end moments by the trapezoidal rule, about 0.7 % of the peak value under a distributed load (in 10 segments (2/3)/n²) remains on the safe side. The same correction is also applied to heavy (hot-rolled) steel beams (see Theoretical Basis of Steel Design); the finite element beam results continue to show the raw axial force.

13. Panel bottom and top tracks and bridging

Code. According to TBDY 10.3.1.3 and HCBTİE Chapter 6, the panel bottom and top tracks are U or C sections with a minimum wall thickness of 0.8 mm; for any other section it is shown that it safely carries the design load. TBDY 10.4.1.1(a) requires the edge studs, the bottom and top tracks and, if present, the bridging to be sized with the forces from the loading cases magnified by D. In a panel with the same sheathing on both faces, the single-face values are added and it is shown by calculation that the tracks resist the shear force (10.3.2.3(b)). If the long edge of the sheathing is used horizontally, horizontal bridging that transfers the shear into the panel is provided (10.3.1.4). HCBTİE 6 gives detail rules for bridging: (a) if stud height / depth > 50, one row of bridging at mid-height; (b) tab length ≥ 6d; (c) edge distance ≥ 1.5d, screw spacing ≥ 3d; (d) bridging wall thickness ≥ 0.8 mm; (e) width of the flange to which the bridging is connected ≥ 3d; (f) at least two No.8 or larger screws in each connection. The codes give no equation for the track and bridging force; the models below are interpretations.

Track profile. It is selected from the catalogue (U, C, C+) in the Wall Properties > Cold-Formed Steel Track tab. If it is not selected, the U profile closest to the stud web height is taken; in a tie, the one closest to the track wall thickness of the anchorage tab (the stud wall thickness if that is not entered) (and the thicker one if still tied); “otomatik” (automatic) is written in the report.

Bottom track. The sheathing shear is assumed to be uniformly distributed along the track: v = Vd/L (sum of the two faces; Vd is the governing combination of the anchorage check magnified by D; D is applied only to horizontal earthquake loading cases). The shear anchors are at spacing a, and the first anchor at the end is at distance e1 (a/2 if not entered). The track axial force has a sawtooth shape; its largest value is N = v·max(a/2; e1). If the number or spacing of anchors has been entered, a is L/n; if not, it is taken from the required number of anchors (L/nreq), and if there is none either, a = L is taken (information row). Tension strength HCBTİE 4.4: min(φt·Fy·Ag; φu·Fu·An), An = Ag − dh·t (one hole in the web; for a bolt the HCBTİE Table 8.1 standard hole: d + 1 for d < 12 mm, d + 2 for 12–22 mm, d + 3 if larger; for the screw type, the screw diameter). Compression strength by EWM (Sections 3–4): strong-axis (out of the wall plane) buckling length max(a; e1), weak-axis and torsional length the stud spacing s. Ratio = N/min(Td; Pd). The material is S350GD (Fu = 420 MPa).

Top track. Within the panel, the shear coming from the floor is transferred to the sheathing by the storey connections: Nin = vtop·max(sconn/2; e1). sconn and vtop are taken from the floor–panel top track connection of the cold-formed steel floor diaphragm (Section 11) (screw spacing and top-section shear magnified by D); if there is no connection, sconn = a and vtop = v. If the wall is a lower-storey panel on a diaphragm line, the top track is the collector of the line: N = |N|max (N(s) diagram of the line, earthquake magnified by D, or wind) + Nin (safe side; the largest value may be in another part of the line). In a double top track the tension and compression strengths are taken as double. In compression the strong-axis length is max(sconn; e1). At levels without a cold-formed steel floor diaphragm the collector check is not performed and an information row is written in the project checklist. The floor joist (rim profile) collector row in Section 11 remains separate.

Bridging. Bridging shortens the buckling length of the stud. In a stud without sheathing, with n rows of bridging the weak-axis and torsional buckling length is taken as Ly = Lz = h/(n+1); in a sheathed stud (Ly = Lz = stud spacing) there is no change. For the brace force, the analogy of the AISI S211 / S240 wall stud bridging rule is used: 0.02·P per stud (the AISI S100 general single-point brace rule is 0.01; the more conservative 0.02 has been chosen for wall studs). In a wall without sheathing the forces accumulate along the bridging line: F = 0.02·(nint·Pint + P) (the intermediate studs and one edge stud; as if the anchorage were at one end only, on the safe side). In a sheathed wall there is no accumulation (AISI RP20-4): F = 0.02·P. P is the largest stud compression (including the combination magnified by D for the edge stud). The connection is checked with the TBDY 10.3.4 screw shear (t1 bridging, t2 stud; φ = 0.5 / Ω = 3.0) and, if the strap width has been entered, the bridging is checked in tension according to HCBTİE 4.4 (deducting one screw hole); if the width is not entered, the required area F/(φt·Fy) is reported. The HCBTİE 6 (b)–(f) conditions are checked with the details entered; a detail that is not entered is not checked and an information row is given. If the long edge of the sheathing is marked horizontal and there is no bridging, a TBDY 10.3.1.4 error is given. In a panel with bridging entered, the HCBTİE 6 (a) warning “h/d > 50: orta yükseklikte kuşak gerekli” (h/d > 50: bridging required at mid-height) is not given; the note in the stud report states the number of bridging rows.

Information checks. A warning is given if the track web height differs from the stud web height by more than 10 mm (the stud does not seat inside the track). If the track wall thickness is smaller than that of the stud, a reminder is given that the TBDY Table 10.5 screw / stud wall thickness condition must also be satisfied in the track.

Transfer of the track wall thickness to other checks. If a track profile has been selected, the shear anchorage check (bolt hole bearing HCBTİE 8.3.2; t1 in the screw-type storey connection, HCBTİE 8.2.2) uses the wall thickness of the bottom track, and the floor–top track screw (Section 11) uses that of the top track. If no profile is selected, the track thickness in the anchorage tab is used, and if that is not entered either, the stud thickness; the automatic profile is also chosen from the U sections closest to this thickness. If there is no exact match in the catalogue (if the thickness of the automatic profile differs from this value), an information row is given.

14. Assumptions and limits

• Since ASD is not defined in HCBTİE, it is applied with the AISI S100 safety factors and the ASCE 7 ASD combination logic; LRFD should be taken as the basis in official project approval.
• In distortional buckling the moment gradient (β > 1) is not taken into account (safe side).
• In axial tension the net area is taken equal to the gross area; hole and connection limit states must be checked separately.
• The calculation path is for the predefined C, Z, U, C+, Sigma and Sigma+ sections. For the Z section, only bending about the axis perpendicular to the web is calculated.
• Wind bending and out-of-plane deflection are applied only to walls marked with an edge axis (exterior walls); internal pressure/suction and corner zone increases are not modelled.
• The lateral support that the sheathing provides to the stud is idealized with the assumption of a buckling length equal to the stud spacing.
• In the floor joist, the sheathing and blocking bracing are user declarations. Cb is taken as 1 for a cantilever and for a length with intermediate bracing. The vibration frequency is a simple-beam estimate. Web crippling is limited to the scope of TS EN 1993-1-3 6.1.7.2 (Sigma web, r/t > 6 and hw/t > 200 are out of scope).
• Cold-formed steel floor generation works only in quadrilateral slabs with edges parallel to the axis; the load width distribution is exact in the classical transfer, and in the shell model the sheathing shares load between beams.
• In the floor diaphragm there is no code value for vn (the default is the TBDY Table 10.5 wall panel analogy). The chord and collector are assumed braced in compression at the floor joist spacing (Lx = Ly = Lz = Lb, Section 11); a collector portion spanning an opening must be checked separately; the chord force comes from the simple beam model; columns do not enter the line force (they enter the net force of the level); the opening ratio is calculated when the irregularity checks are on. For definitions where floor joists have not been generated, the detailed diaphragm table is not printed; the results appear in the level row, in the analysis warnings and in the project checklist.
• Panel track and bridging forces (Section 13) are interpretation models with no equation in the codes (sawtooth track force, 2%·P bridging brace force); the top track collector check is performed only at levels with a cold-formed steel floor diaphragm. Track bending under out-of-plane load, web crippling in the floor joist caused by the edge stud compression in the upper storey, and track splices are not calculated.