Sheathing braced design of cold-formed steel structural members subjected to torsional buckling

Structures 20 (2019) 489–509

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Sheathing braced design of cold-formed steel structural members subjected to torsional buckling Sivaganesh Selvaraj, Mahendrakumar Madhavan

T

⁎

Department of Civil Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502 285, Telangana, India

ARTICLE INFO

ABSTRACT

Keywords: Sheathing Stiffness Bracing Cold-formed steel Wall panel Buckling Design method Application

The objective of this work is to examine the bracing effect of sheathing boards in inhibiting the instability failure modes of cold-formed steel (CFS) studs in the wall panel construction. A development of accurate and robust sheathing braced design concepts for CFS wall panels will eliminate the need for additional lateral steel bracing, thereby leading to efficient use of construction materials. The current design method by the American Iron and Steel Institute lacks in accurately predicting the design strength of the sheathed CFS stud. Therefore, the current investigation endeavors to fill the gap by carrying out experiments that simulate the behavior of the CFS studs subjected to out-of-plane loading. A total of sixty-seven experiments were carried out with seven different sheathing board types and ten different CFS studs to accomplish the objective. The experiments were carried out using a newly devised test set-up that simulates the worst case failure mode of the sheathing board. The experimental results indicate that the strength, stiffness and failure modes of the sheathing boards vary depending on the following; (i) fiber composition and material properties of the sheathing board; (ii) dimensions of the CFS stud. In addition, the test results also indicated that the stiffness of the sheathing board against the pull-through failure was not influenced by the thickness of the sheathing boards. Based on the inferences (trend of sheathing stiffness and failure modes) from the test results, a new expression is formulated to determine the stiffness of the sheathing board on a function of the tensile modulus of the sheathing board (Es) and dimensions of the CFS stud (d/2). The validation study indicates that the new expression is accurate in terms of both statistical and design application.

1. Introduction The key objective of a structural engineer is to use the materials efficiently in the design to arrive at the optimum dimension. As the construction industry deals with large varieties of materials and different types of structural components, it is necessary to carry out design optimization in every structural element to achieve the maximum structural economy. An approach that can lead to design optimization in light gage steel construction is to consider the use of sheathing board (external cover) as a structural component in sheathed CFS wall panel design. Previous research on CFS wall panels indicated that the sheathing board could increase the strength of the CFS wall stud tremendously by restraining the global instability (flexural torsional and lateral torsional buckling) of the CFS studs especially for the highly slender ones [1–7]. However, the sheathing's bracing effect depends on the specification of the sheathing board (material property and thickness) and fastener connection spacing (center-to-center distance between the fastener connections - df) (Fig. 1a). It should also be noted

⁎

that the current CFS structural member design methods are overly conservative for the highly slender CFS structural members especially the Direct Strength Method (DSM) by American Iron and Steel Institute [8,9]. Therefore, the consideration of sheathing board as a structural component in the design strength calculation would benefit the structural engineering community due to the increase in member strength by decreasing the global slenderness (reduced unbraced length) of the CFS stud resulting in an efficient design. The structural contribution of the sheathing boards in the CFS wall panels is not widely considered in the design of CFS wall studs due to the non-availability of robust design specifications that considers the sheathing's bracing effect accurately. The sheathing stiffness requirements of EN (2006) [15] and AS/NZS [16] were not included in the present study as the calculation procedures are based on the steel profiled sheeting, which is typically used in roof purlins. The use of profiled steel sheeting in the present studies will result in excessive restraint than is required to prevent torsional buckling of the CFS stud. Though, there are other design procedures by AISI (2013) [10] (based

Corresponding author at: Department of Civil Engineering, Indian Institute of Technology (IIT) Hyderabad, Kandi, Sangareddy 502 285, Telangana, India. E-mail addresses: [email protected] (S. Selvaraj), [email protected] (M. Madhavan).

https://doi.org/10.1016/j.istruc.2019.04.015 Received 28 January 2019; Received in revised form 19 March 2019; Accepted 24 April 2019 2352-0124/ © 2019 Published by Elsevier Ltd on behalf of Institution of Structural Engineers.

Structures 20 (2019) 489–509

S. Selvaraj and M. Madhavan

ng athi She ard bo

df No.6 type Fastener

(b) B lp D t

(a)

(c)

(d)

C/S Twist

Lateral deformation

(e) Pull-through failure

(f)

Bearing failure in the sheathing

Fig. 1. (a) Sheathing board in CFS wall panels; (b) Sheathing fastener connection; (c) Self-drilling fastener (No.6 Type) with steel cum rubber washer; (d) C shaped CFS stud (with notations); (e) Pull-through failure of self-drilling fastener at sheathing-fastener connections; (f) Bearing failure of sheathing at sheathing-fastener connections.

on sheathing stiffness and DSM approach) and AISI (2016) [11] (all steel design) to consider the sheathing effect in the structural design of sheathed CFS wall studs, the previous investigations [7,9,12] indicates that the design strength calculations by AISI (2013) [10] and AISI (2016) [11] are unconservative due to the incorrectly predicted failure modes. Particularly, the observation from the experimental investigation by [2,9,and,12–14] shows that the gypsum sheathing board can restrain the lateral torsional buckling of the CFS stud only when both the global and local slenderness of the CFS stud is higher than unity (λe > 1 and λl > 1). Whereas the design procedure by AISI [10] predicted that the gypsum sheathing could arrest the LTB failure mode for all CFS studs irrespective of the slenderness and led to reach the next possible failure mode (LTB to local buckling or yielding). Further, the investigation by Selvaraj and Madhavan [9] revealed that the unreliable design prediction by the current provisions of AISI (2013) [10] may be attributed to the fact that the expressions used to predict the actual sheathing stiffnesses (which quantifies the magnitude of

sheathing bracing effect in terms of stiffness) were formulated based on the very limited experimental test results [carried out using only one type of CFS stud (C shaped stud with single dimension)] and implicitly recommended for all CFS members (various slenderness and various shapes) and all loading cases (axial compression and out-of-plane bending). Therefore, it is necessary to formulate a correct and robust design procedure for the consideration of the sheathing board's bracing effect in the structural strength of the CFS wall stud for the efficient use of construction materials. Although the required bracing stiffness to arrest the LTB failure of CFS studs can be obtained from the Winter [1] and Yura [17] approach, as per authors knowledge, no study was carried out to investigate the actual stiffness offered by sheathing-fastener connection with respect to the CFS stud geometry. Therefore, the present investigation endeavors to determine (formulate an expression) the stiffness provided by the various types of sheathing boards against the worst-case failure mode of sheathing-fastener connection. The objective is to develop a simple 490

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Table 1 Common failure modes of sheathing boards. Sheathing type

Axial compression

In-plane shear

Out-of-plane loading

Soft sheathing (Gypsum board or cement board - sheathing board that made of particle materials)

Sheathing board fails in bearing failure (Shear force in self-drilling fasteners) or pull-through failure - (diagonal force in the sheathing) [2]

Severe cracking or pull-through of sheathing boards [18–24]

Hard sheathing (steel sheeting or sheathing board made of fiber materials)

Sheathing board resist the forces developed at each sheathing connection thereby brace the instability failures of the CFS studs and let the CFS stud to fail in the next governing failure mode (local buckling or reduces the unbraced length or shifts from minor axis bending to major axis bending) [2,5,6]

Steel sheeting - Screw breaking (single shear) or diagonal tension field action in sheathing [25] Plywood sheathing - Block shear type of sheathing failure when plies are perpendicular to load or breaking failure of plies when plies are parallel to load [24]

CFS studs with singly symmetric crosssections: Sudden pull-through at the sheathing fastener connections [2,7 and 12] CFS studs with point symmetric crosssections: Sheathing (Gypsum) restrains the CFS from biaxial bending [13] CFS studs with doubly symmetric cross-sections: Sheathing (Gypsum) restrains the CFS from LTB failure [26] No investigation was carried out previously

ed C Sheath

l

ll pane

FS wa

Alignment of loading plates Taking one sheathing-fastener connection

(a)

Bolting to ensure rigidity Packing woods Loading plate (b)

(c)

(d)

Fig. 2. Proposed test setup to examine the pull-through failure of self-drilling fastener in sheathing-fastener connection: (a) View of Sheathed CFS wall panel; (b) Single sheathing-fastener cconnction of the wall panel (one segment from actual wall panel); (c) Application of load to twist the CFS stud; (d) View of proposed test setup.

design approach for a sheathed CFS panels thereby an appropriate sheathing board type and thickness can be chosen by the designer to satisfy the bracing stiffness requirements. In addition, if the sheathing is designed to brace the torsional buckling of the highly slender CFS stud the need for additional steel braced can be eliminated thereby achieving the structural economy.

magnitude of the load than the bearing of sheathing (sheathing force in the sheathing – through the width of the board) (Fig. 1f). However, as per authors knowledge, no research work was carried out previously to examine or codify this worst-case scenario of failure mode in sheathed CFS wall panel design accurately with respect to various CFS stud dimensions and various sheathing materials, which could be the fundamental reason for the unreliable design strength prediction by the current AISI [10] design procedures described in [7 and 9]. Therefore, determining the pull-through strength of sheathing-fastener connection and codifying the sheathing stiffness with respect to various sheathing board materials and various sizes of the CFS studs shall lead to robust design guidelines. To accomplish this objective, various design parameters such as five different sheathing board materials (gypsum board, particle cement board, fiber cement board, plywood and gypsum cum LGSS sheet sheathing) and ten different CFS stud types are experimentally examined for the worst case sheathing-fastener connection failure modes.

1.1. Governing failure mode of sheathing-fastener connection The sheathing boards in the CFS wall may undergo various failure modes with respect to the loading conditions as described in Table 1. However, it should be noted that the common failure mode among the soft sheathing board is a pull-through failure of the fastener (rotation of the self-drilled fastener) from the sheathing board due to the torsional buckling of the CFS stud [18–26]. In addition, the pull-through failure of sheathing-fastener connection is the worst case of failure since it leads to sudden failure of the sheathed CFS studs [7,9,12]. It should also be noted that the pull-through failure (diagonal force in the sheathing board – through thickness) (Fig. 1e) could occur at a much lesser 491

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(a)

(b)

Fig. 3. (a) View of test sample in the universal testing machine; (b) Pull-through failure in sheathing-fastener connection due to twist of CFS stud.

2. Experimental test setup for examining the pull-through failure in sheathing-fastener connections

contact between the bearing boards and loading plates, thereby the failure mode or the load magnitude of the sheathing fastener connection is not influenced.

The pull-through failure means that the self-drilling fastener pulls through the thickness of the sheathing board either transversely or diagonally without the development of full bearing or tensile strength of the sheathing board i.e. the magnitude of pull through force will be low compared to the bearing strength or tensile rupture strength of sheathing board. It should be noted that in the sheathed CFS wall panels the pull-through failure occurs when the CFS studs in the wall panel fail in flexural-torsional buckling or lateral-torsional buckling (CFS stud rotates in cross-sectional and creates a diagonal force at the fastener connections – Fig. 1e). Therefore, to simulate this pulling through of self-drilled fastener in the sheathed CFS wall panels, a test setup is proposed such that the CFS stud rotates as a whole about its longitudinal axis and develops a diagonal force at sheathing-fastener connections. It should be noted that the proposed test setup represents one sheathing-fastener connection segment of the CFS wall panel component as shown in Figs. 2(a-c). The newly developed test set-up to examine the pull-through failure of sheathing boards is shown in Fig. 2d. The test was carried out by pulling the sheathing boards attached to the CFS studs in the opposite direction resulting in a cross-sectional rotation of the CFS studs and development of diagonal force at the sheathingfastener connection. The pull-through experimental test was carried out in a universal testing machine (Fig. 3a) by displacement control mode. The rate of displacement is 0.6 mm/min. It should be noted that the bearing boards are attached/inserted in between the sheathing boards and the loading plates to align the load axis to the center of the CFS stud as shown in Fig. 2d. However, it should be noted that the attached bearing board are connected with a two parallel series of bolts (6 numbers) to ensure that neither displacement nor rotation occurs at the

2.1. Validation for the proposed test setup Although, the proposed test setup seems to be viable to create a pullthrough failure at the sheathing-fastener connections, a preliminary investigation was carried out with two different CFS stud dimensions to verify the following: (i) to ensure that the sheathing-fastener connections undergo worst case failure mode that occurred in the full-scale testing of sheathed CFS wall panels (Fig. 1e) [7,9 and 12], (ii) the variation in the magnitude of sheathing stiffness with respect to the geometry of CFS stud. Such preliminary investigation is necessary to devise the experimental setup accurately since the findings from the experiments may be applicable to the codification of the design method to predict the strength of the sheathing braced CFS wall panels. It should be noted that the self-drilling fastener of type No.6 as per ASME [27] [Fig. 1(b-c)] with steel cum rubber washer is used in the testing work. The self-drilling washer of type No.6 with steel cum rubber washer (EPDM - Ethylene Propylene Diene Terpolymer) was chosen based on its performance [26]. The results of the preliminary investigation including stiffness trend and failure modes are shown in Figs. 4(a-c), respectively. The experimental results indicate that the tested specimens with two different CFS studs that simulate the torsional buckling of the sheathed CFS stud failed due to the occurrence of pull-through as shown in Figs. 3b and 4(b-e). In addition, the test result also proves that the stiffness of the sheathing-fastener connection against the rotation of the CFS stud varies depending on the dimensions of the CFS studs as shown in Fig. 4a. More specifically, the strength and stiffness of the sheathing492

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t = 1.5 mm

smaller depth (higher slenderness − L/rx) than the CFS studs with higher depths (low slenderness − L/rx), for a given type of sheathing. This result is in line with the experimental results of [7,9,12], and where the lateral torsional buckling of the CFS studs with smaller depths are restrained by the sheathing (Fig. 5a) while the CFS stud with higher depth failed in LTB due to the inadequate sheathing bracing effect (Fig. 5b). Since both the failure mode of the test specimens (Fig. 4(b-c)) and the stiffness trends (Fig. 4a) are in accordance with the full-scale test results (Fig. 4a(d-e)), it can be concluded that the proposed test setup can be used for examining the behavior of the sheathing-fastener connection in sheathed CFS walls panels subjected to twist (lateral torsional buckling).

CFS Stud 2

3. Examination of the pull-through capacity of various sheathing boards

1000

600 B = 40 mm

400 D = 50 mm

B = 60 mm

200

t = 1.5 mm

CFS Stud 1

D = 97 mm

Load (kN)

800

0

(a)

0

5

10

15

20

3.1. Test parameters

25

Displacement (mm)

After validating the newly devised test setup, a total of sixty-seven experiments were carried out including seven types of sheathing boards (Table 2) and ten different dimensions of CFS studs (Table 3) to determine the trend of sheathing stiffnesses. It should be noted that the various sheathing board types which are commonly used in the coldformed steel construction are investigated in this work. To be specific, the sheathing boards were chosen based on the tensile modulus and material composition; both the stiff (plywood - fiber) and soft (gypsum board - fiberless) sheathing boards were tested. In addition to this, a combination of soft sheathing (gypsum) with a layer of steel sheeting is also used. The material specifications of the various sheathing boards and dimensions of the CFS studs are summarized in Tables 2 and 3, respectively.

Pull-through failure Pull-through failure

(b)

(c)

Pull-through failure in sheathing-fastener connection simulated test setup with single self-drilling fastener

3.2. General trend in failure modes, stiffness and strength of sheathingfastener connections The strength and stiffness response of the various sheathing boards and failure modes against the CFS stud rotation (displacement of two flanges in the opposite direction) are summarized in Tables 4-5 and Figs. 6-11. In general, the experimental results indicate that the stiffness provided by the sheathing against the twist of the CFS stud primarily depends on the depth of the CFS stud (d) and material properties of the sheathing board [tensile modulus (Es), and fiber composition)]. More specifically, the resistance offered by the sheathing board with a fiber composition (plywood and fiber cement board) against the twist of the CFS stud is significantly higher than the sheathing boards made of particles (fiberless - cement board and gypsum board) as shown in Figs. 6a, 7(a-b), 8(a-b) and 10. In addition, to the resistance offered (strength and stiffness), the failure modes of sheathing-fastener connection of fiberless sheathing boards are also unpredictable (sudden) and undesirable. It was observed that for fiber less sheathing boards (gypsum and PCB) with the same thickness and material properties, the failure mode of the sheathing-fastener connections vary depending on the dimensions of the CFS stud (Figs. 8(c-j), 9 and 11(a-f)). For example, in the failure modes of the sheathing fastener connections with sheathing boards made of particles (PCB and gypsum boards - no fiber), the experimental results showed an explicit variation between the CFS studs with lower and higher depth. The smaller depth CFS studs (S1-5060-U-1.5) exhibited failure due to breakage of sheathing boards (Figs. 8(c-d), 9(a-b) and 11(a-b)) whereas, the deeper CFS studs (S6-8040-10-1.5, S7-80-50-25-1.5 and S10-120-40-U-1) exhibited pullthrough failure (Figs. 8(e-j), 9(c-h) and 11(c-f)). As mentioned previously, the variation in the sheathing-fastener connection failure modes should be attributed to the lever arm (d/2) of the CFS stud which influences the magnitude of the rotation causing deformation at the sheathing-fastener connection between the CFS stud and sheathing. However, this was not the case for sheathing boards with fiber content

(d)

Pull-through failure in sheathed CFS wall panels subjected to LTB

(e)

Fig. 4. (a) Pull-through strength and stiffness response of sheathing board against the varying CFS stud dimensions; Failure mode validation of proposed test setup: (b-c) Pull-through failure of self-drilling fastener in sheathing fastener connection; (d) Occurrence of pull-through in actual sheathed CFS wall panel; (e) Zoomed view of pull-through failure.

fastener connection significantly vary depending on the depth (lever arm - d/2) that induces the rotation of the CFS stud. The amount of cross-sectional twist of the CFS stud during the LTB depends on the depth of the CFS stud (higher lever arm – higher twist) [28–33]. Therefore, the rate of deformation at the sheathing-fastener connection for the deeper sheathed CFS studs will be higher (for the small magnitude of load) which leads to a much lesser sheathing stiffness compared to the smaller depth CFS studs (small lever arm). As shown in Fig. 4a, the sheathing fastener connection stiffness (initial slope) and strength of the stud 1 (depth is 50 mm) is significantly higher than the stud 2 (depth is 97 mm). This means that the LTB restraining effect of sheathing board will be high for CFS studs with 493

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(a)

(b)

D = 50 mm; B = 65 mm; t = 1.5 mm; Gypsum sheathing 12.5 mm with df = 300 mm LTB of the CFS stud Restrained

D = 80 mm; B = 50 mm; t = 2.5 mm; Gypsum sheathing 12.5 mm with df = 300 mm Failure due to Pull-through

Fig. 5. Effect of sheathing vs CFS stud dimensions: (a) Sheathing restrained the LTB failure of C shaped CFS stud (sufficient bracing stiffness for small depth CFS stud); (b) Pull-through failure in sheathing board (insufficient bracing stiffness for larger depth CFS stud). Table 2 Specifications and Material property of the sheathing boards. Sheathing type

Thickness (tb) (mm)

Tensile modulus* (Es) (MPa)

Density (kg/m3)

Material composition

Gypsum Gypsum + LGSS

12.5 12.5 0.45 8 12 6

2100 2100 215,000 2707

771.7 771.7 7850 1250

Gypsum slurry placed between two paper layers The LGSS sheeting is attached as an external cover

Gypsum LGSS Particle Cement Board Plywood

12 Fiber cement board

12

a

7983.3 3701.2b 7983.3a 3701.2b 6274.4

a

910–1100

Comprised of wood particle (28%) and cement (62%) mixture, where the cement plays a role of a bonding agent Manufactured using layered wood veneers

1355.8

Cellulose pulp fibers and cement

b

*obtained from the tensile test; longitudinal direction; transverse direction; Es - Tensile modulus of a sheathing board obtained from the tensile test. Table 3 Cross sectional dimensions and Material property CFS studs. Stud ID

d (mm)

b (mm)

t (mm)

Lip (lp) (mm)

E (GPa)

fy (MPa)

fu (MPa)

εf

S1–50-60-U-1.5 S2–70-30-U-1.5 S3–70-37.5-18-1.5 S4–70-55-U-2 S5–80-30-25-2.5 S6–80-40-10-1.5 S7–80-50-25-1.5 S8–90-60-U-1.5 S9–100-55-U-1 S10–120-40-U-1

50 70 70 70 80 80 80 90 100 120

60 30 37.5 55 30 40 50 60 55 40

1.5 1.5 1.5 2 2.5 1.5 1.5 1.5 1 1

– – 18 – 25 10 25 – –

202.7 217.9 202.7 211.5 214.8 217.9 212.2 212.2 221.3 210.93

378.3 376.4 378.3 330 329.6 376.4 377.4 377.4 330.1 365.2

442.8 439.2 442.8 425 417.3 439.2 440 440 425 426.4

18.2 18.3 18.2 18 18 18.3 16.1 16.1 18 17.6

d - out-to-out depth of CFS stud (web); b - breadth of the CFS stud (flange); t – thickness of the CFS stud. lp – depth of the lip in CFS stud (refer Fig. 1d for notations of the dimensions); E - Young's modulus of steel. fy - yield strength of steel; fu - ultimate tensile strength; εf - strain at fracture.

(plywood and fiber cement board) where the specimens exhibited a single failure mode (Figs. 6(b-i), 7(c-m)). It was further observed that the increase in the thickness of the sheathing board by 1.5 or two times does not increase the strength and stiffness by the same amount, but will depend on the failure mode of the

sheathing against the twist of the CFS stud. In particular, the thickness of PCB and plywood are varied in the present investigation. Fig. 12 shows the variation in initial stiffness and strength for the same type of sheathing with increased thickness. The results indicate that the increase in the PCB sheathing board thickness from 8 mm to 12 mm (1.5 494

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56.42 24.08 33.00 29.83 21.55 22.73 15.44 8.69 8.52 4.51

318.93 198.19 281.81 319.47 243.98 233.33 204.56 236.17 244.76 149.09

Table 5 Summary of the sheathing-fastener connection failure modes. Sheathing type

Depth of the CFS stud (≤50)

Depth of the CFS stud (50 to 120)

Depth of the CFS stud (≥120)

FCB 12 mm (Fig. 6(b-i)) Ply 6 mm (Fig. 7(c-g)) Ply 12 mm (Fig. 7(h-m))

Partial pullthrough Sheathing breakage Withdrawal of Self-drilling screws Sheathing breakage Sheathing breakage Sheathing breakage Sheathing breakage

Partial pullthrough Sheathing breakage Withdrawal of Self-drilling screws Pull-through

Withdrawal of Self-drilling screws Sheathing breakage Withdrawal of Self-drilling screws

PCB 8 mm (Fig. 8(c-j)) PCB 12 mm (Fig. 9) Gypsum 12.5 mm (Fig. 11(a-f)) Gypsum + LGSS (Fig. 11(g-j))

88.40 31.69 – 52.61 – – 33.48 14.30 9.76 6.85

580.16 317.80 – 441.03 – – 329.20 301.29 312.85 187.57

F (N) kp (N/mm) F (N)

Pull-through

Pull-through (sudden) Pull-through (sudden) Pull-through

Sheathing breakage

Sheathing breakage

Pull-through

239.95 73.53 65.39 106.03 64.16 42.54 63.08 49.10 10.79 6.80

1235.84 810.99 786.96 833.87 600.11 495.12 868.77 1084.62 726.60 458.23

174.81 39.56 74.26 104.84 71.69 50.53 69.94 34.36 11.43 8.28

2108.06 923.02 1102.21 1681.90 1243.43 1084.43 1175.89 1521.61 542.52 529.64

117.64 26.54 46.89 51.46 49.55 35.58 38.60 30.32 9.27 5.56

1073.42 595.60 853.07 672.74 780.73 865.77 686.35 597.65 576.53 299.60

132.76 44.66 61.63 73.82 47.44 38.03 59.45 34.81 11.13 5.28

1229.66 737.73 684.65 826.57 613.63 475.37 646.15 643.00 711.82 414.72

118.93 35.99 54.90 73.14 45.57 32.68 41.87 32.31 10.51 4.80

812.95 493.21 547.27 646.44 467.84 471.78 512.97 336.98 461.34 405.67

times) did not improve the strength and stiffness of the sheathing-fastener connection by 1.5 times as shown in Fig. 12d and f. Similar behavior was observed in the sheathing-fastener connection of plywood boards in which the thickness was doubled (6 mm to 12 mm) (Fig. 12a and c). It should be noted that the improvement in the sheathing stiffness after increasing the thickness is negligible (minimum – 1%, maximum – 42% and mean 13%) for PCB (Fig. 12e) and considerable for plywood sheathing (minimum – 13%, maximum – 104% and mean 51%) (Fig. 12b). However, both these sheathing boards response against the twist of the CFS stud cannot be treated in the same fashion, since there is a distinct change in the failure mode behavior of PCB and plywood sheathing. It should be noted that even after changing the thickness of the PCB sheathing board from 8 mm to 12 mm, the failure mode of the sheathing-fastener connection remains same (pull-through) for a constant CFS stud as shown in Figs. 8-9. However, in the case of plywood sheathing, the failure mode of the sheathing-fastener connection shifts from breakage of sheathing (Fig. 7(c–g) – 6 mm) to the withdrawal of fastener from the CFS stud (Fig. 7(h-m) – 12 mm). Therefore, based on the test results the following can be ascertained: (i) Fiber less sheathing board (gypsum and PCB) should not be considered to offer resistance against the torsional buckling of the CFS stud (ii) the resistance offered by the plywood sheathing of 6 mm is sufficient to prevent the torsional buckling of the CFS stud or in other words the required bracing stiffness is attained by employing a plywood sheathing of 6 mm thereby no failure was observed in the plywood sheathing of 12 mm (Fig. 7(h-m)). The above inferences are counterintuitive to the common design perception that the strength and stiffness of the bracing can be increased linearly by increasing the thickness [bearing area in the shearing direction − bearing stiffness (P/δ) depends of the area − (P/ δ) = (AE/L)] of the sheathing board. This deviation of results from the common wisdom indicates that the pull-through failures in the sheathing boards is catastrophic and requires a different design treatment compared to the shear and bearing design of sheathing boards. In addition, it should also be noted specifically that the presence of the LGSS sheet in the sheathing configuration (gypsum + LGSS sheet) significantly contributed to the initial stiffness magnitudes compared to the gypsum board for few CFS studs (S1-50-60-U-1.5, S4-70-55-U-2 and S7-80-50-25-1.5). However, it was observed during the experiments that the failure in the gypsum begins at the initial loading stage which led to a sudden breakage at the ultimate load. Such behavior of the gypsum + LGSS sheet sheathing configuration indicates that the additional provision of the LGSS may not be successful for resisting the twist of the CFS stud. Therefore, all these above sheathing stiffness trends and failure modes deviation from the conventional wisdom were considered fastidiously in the formation of the generalized sheathing stiffness predictor expression.

S1–50-60-U-1.5 S2–70-30-U-1.5 S3–70–37.5-18-1.5 S4–70-55-U-2 S5–80–30-25-2.5 S6–80–40-10-1.5 S7–80–50-25-1.5 S8–90-60-U-1.5 S9–100-55-U-1 S10–120-40-U-1

kp (N/mm) F (N) kp (N/mm) F (N) kp (N/mm) F (N) kp (N/mm) F (N) kp (N/mm) F (N) kp (N/mm)

Plywood – 6 mm Plywood – 12 mm Fiber cement board (FCB) – 12 mm Stud ID

Table 4 Experimental results of a pull-through capacity of various sheathing boards.

Particle cement board (PCB) – 12 mm

Particle cement board (PCB) – 8 mm

Gypsum board 12.5 mm + LGSS 0.5 mm

Gypsum board 12.5 mm

S. Selvaraj and M. Madhavan

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1500

Pull-through strength (N)

S1-50-60-U-1.5 S2-70-30-U-1.5 1200 S3-70-37.5-18-1.5 S4-70-55-U-2 900 S5-80-30-25-2.5 S6-80-40-10-1.5 600 S7-80-50-25-1.5 S8-90-60-U-1.5 300 S9-100-55-U-1 S10-120-40-U-1 0

(a) 0

20

40

60

80

Displacement (mm)

(c)

(b) S1-50-60-U-1.5

(d)

(e) S7-80-50-25-1.5

(g)

(f) S6-80-40-10-1.5

(h)

(i) S10-120-40-U-1

Fig. 6. (a) Pull-through strength vs. displacement of response of fiber cement board (FCB) sheathing against the various CFS stud dimensions; Pull-through failure of FCB sheathing board against the various CFS studs (b-c) Stud ID – S1–50-60-U-1.5; (d-e) Stud ID – S7–80–50-25-1.5; (f-g) Stud ID – S6–80–40-10-1.5; (h-i) Stud ID – S10–120-40-U-1.

4. Formulation of expression for sheathing stiffness prediction

accuracy in the predictor expression mean that it should accommodate all the design parameters of sheathed CFS wall panel (CFS stud dimensions, the material property of the sheathing boards) and it should also avoid undesirable or catastrophic failure modes of the sheathingfastener connections. Having determined the behavior of the sheathing-

The primary objective of this investigation is to formulate an accurate and robust expression for predicting the sheathing stiffness (kp) for the design of a sheathed CFS wall panel. The robustness and 496

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2400

1200

Plywood – 12 mm

2100

Pull-through strength (N)

Pull-through strength (N)

Plywood – 6 mm 1000 800 600 400 200

1800 1500 1200 900 600 300

0

0 0

(a)

50

100

(b)

Displacement (mm)

0

20

40

60

80

100

Displacement (mm)

S1-50-60-U-1.5

S2-70-30-U-1.5

S3-70-37.5-18-1.5

S4-70-55-U-2

S5-80-30-25-2.5

S6-80-40-10-1.5

S7-80-50-25-1.5

S8-90-60-U-1.5

S9-100-55-U-1

S10-120-40-U-1

(c) S1-50-60-U-1.5

(d)

(f) (e) S7-80-50-25-1.5

(g) S10-120-40-U-1

(k)

(h) S1-50-60-U-1.5

(i)

(j) S6-80-40-10-1.5 (l)

(m) S10-120-40-U-1

Fig. 7. Pull-through strength vs. displacement of response plywood sheathing against the various CFS stud dimensions: (a) Plywood sheathing 6 mm thickness; (b) Plywood sheathing 12 mm thickness; (c-g) Failure modes of plywood (6 mm) sheathing board against the various CFS studs (shown in ascending order of depth of CFS stud) – failure mode is constant – Breakage of sheathing board; (h-m) Failure modes of plywood (12 mm) sheathing board against the various CFS studs (shown in ascending order of depth of CFS stud) – failure mode is common – Withdrawal of self-drilling fastener from CFS stud.

fastener connection against the rotation of the CFS stud, the next step is to calculate the stiffness for each type of sheathing. Although there are other approaches to calculate the stiffness such as considering the slope of the load-displacement plot up to 40% of the load [34], an alternate method is used here by considering the limit state of serviceability. As the design criteria for serviceability limits the deflection of the CFS stud under the elastic limit (L/384), the stiffness of the sheathing-fastener connection is chosen as the initial stiffness of the load versus

displacement curve [response of the sheathing board against the rotation of the CFS stud - Fig. 7(a-b), 8(a-b), and 10. Similar calculation approach was followed by Vieira [5] for lateral-translational sheathing stiffness formulation. The determined initial stiffnesses for the various sheathing boards are summarized in Table 4. As mentioned previously, the stiffness magnitudes of the sheathing boards show a trend with the depth of the CFS stud; (i.e.) the magnitude of initial stiffness reduces as the depth of the CFS stud increases. The variation in the magnitude of

497

Structures 20 (2019) 489–509

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1400

1200

PCB – 8 mm

Pull-through strength (N)

Pull-through strength (N)

1400

1000 800 600 400 200

PCB – 12 mm

1000 800

600 400 200 0

0

(a)

1200

0

20

40

60

80

(b)

0

20

40

60

80

Displacement (mm)

Displacement (mm) S1-50-60-U-1.5

S2-70-30-U-1.5

S3-70-37.5-18-1.5

S4-70-55-U-2

S5-80-30-25-2.5

S6-80-40-10-1.5

S7-80-50-25-1.5

S8-90-60-U-1.5

S9-100-55-U-1

S10-120-40-U-1

(f)

(c) S1-50-60-U-1.5

(d)

(e) S7-80-50-25-1.5

(g)

(i) S10-120-40-U-1

(h) S6-80-40-10-1.5

(j)

Fig. 8. Pull-through strength vs. displacement of response particle cement board (PCB) sheathing against the various CFS stud dimensions: (a) PCB 8 mm; (b) PCB 12 mm; Failure modes of particle cement board (8 mm) sheathing board against the various CFS studs (shown in ascending order of depth of CFS stud) – failure mode is varying: (c–d) Breakage of FCB sheathing; (e–h) Pull-through of fastener; (i–j) Sudden pull-through of fastener.

498

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(d)

(a)

(c)

(b)

S1-50-60-U-1.5

S7-80-50-25-1.5

(e)

(f)

(h)

(g)

S6-80-40-10-1.5

S10-120-40-U-1

Fig. 9. Failure modes of particle cement board (12 mm) sheathing board against the various CFS studs (shown in ascending order of depth of CFS stud) – failure mode is varying: (a–b) Breakage of FCB sheathing; (c–f) Pull-through of fastener; (g–h) Sudden pull-through of fastener.

400

600

Pull-through strength (N)

Pull-through strength (N)

Gypsum 12. 5 mm 300

200

100

400 300 200 100 0

0

(a)

Gypsum 12. 5 mm + LGSS 0.5 mm

500

0

20

40

60

(b) 0

Displacement (mm)

20

40

60

Displacement (mm)

S1-50-60-U-1.5

S2-70-30-U-1.5

S3-70-37.5-18-1.5

S4-70-55-U-2

S5-80-30-25-2.5

S6-80-40-10-1.5

S7-80-50-25-1.5

S8-90-60-U-1.5

S9-100-55-U-1

S10-120-40-U-1

Fig. 10. Pull-through strength vs. displacement of response gypsum board sheathing against the various CFS stud dimensions: (a) Gypsum 12.5 mm; (b) Gypsum 12.5 mm + LGSS – 0.5 mm (external addition). 499

Structures 20 (2019) 489–509

S. Selvaraj and M. Madhavan

(b)

(e) (a)

S1-50-60-U-1.5

(c)

(d)

(f)

S7-80-50-25-1.5

S10-120-40-U-1

(j)

(h)

(g)

S1-50-60-U-1.5

(i)

S7-80-50-25-1.5

(k)

(l)

S10-120-40-U-1

Fig. 11. Failure modes of gypsum (12.5 mm) sheathing board against the various CFS studs (shown in ascending order of depth of CFS stud) – failure mode is varying: (a–b) Breakage of FCB sheathing; (c–f) Pull-through of fastener; (g–l) Failure modes of gypsum (12.5 mm) sheathing board + 0.5 mm LGSS external sheet against the various CFS studs (shown in ascending order of depth of CFS stud) – failure mode is constant – Breakage of gypsum board.

the sheathing stiffness (kp) with respect to the depth of the CFS stud for different sheathing boards are shown in Fig. 13. Although, the sheathing stiffness (kp) shows an exponentially decreasing trend with respect to the depth of the CFS stud for each sheathing type (Eqs. (1)-(7) in Table 6), it should be noted that in general the following design parameters influence the bracing stiffness of the sheathed CFS wall panel; (i) geometry of the CFS stud, (ii) material property of the CFS stud; and (iii) material property of the sheathing board. Therefore, an attempt has been made to include all the above-mentioned design parameters in the formulation of the sheathing stiffness predictor equations by introducing two different variable coefficients A and B with respect to the type of the sheathing boards. In addition, it should be noted that the generalized form of the sheathing stiffness expression as well as the variable coefficients are made such that it can accommodate many other sheathing board types used in the construction practices. The step-by-step procedure used to formulate the generalized sheathing stiffness expression [(Eq. (15))] and the variable coefficients [Eqs. (16)-(17)] is described in Table 6. The empirical-generalized sheathing stiffness predictor expression is shown below.

kp =

( )e E 58.4

A.

(

A = 3112.4 Es B=

)e

(Bd/2)

0.0437

(16)

(17)

The proposed Eqs. (15)–(17) for predicting the magnitude sheathing stiffness is valid only in SI units, where E and Es are Young's modulus of steel in N/mm2 (Table 3) and tensile modulus of sheathing board in N/ mm2 (Table 2), respectively; d is the depth of the CFS stud (Fig. 1d) in millimeters. 4.1. Validation study for the sheathing stiffness predictor expression Although, the preliminary trend between the sheathing stiffness and CFS stud dimensions (Eqs. (1–7)) which were used to develop the generalized expression ((Eq. (15))) for predicting the sheathing stiffness appears to display a good correlation with the actual stiffness magnitudes (Fig. 13), it is necessary to carry out the validation study for each sheathing type to increase the degree of confidence in the proposed generalized expression [(Eq. (15))]. The validation study is carried out in two different ways; the first method of validation is based on statistics [35,36] and the other method is based on the direct comparison with the full-scale experiments (design and application-oriented validation).

( 0.106(d /2))

6274.40 Es

Es 142857.1

0.909

(15)

500

Structures 20 (2019) 489–509

S. Selvaraj and M. Madhavan

200

2

2.5

Plywood - 12 mm

Plywood - 12 mm

Plywood - 6 mm

Plywood - 6 mm

125 100 75 50

2.0

1.5

Strength (kN)

150

kp 12 mm / kp 6 mm

Stiffness kp (N/mm)

175

1

0.5

Min - 13% Max - 104% Mean - 51%

25 0 30

40

50

60

70

Depth / 2 (mm)

150

0.0 20

(b)

1.0 0.5

0 20

(a)

1.5

30

40

50

60

70

Depth / 2 (mm)

(c)

20

40

1.50

2

PCB - 12 mm

PCB - 8 mm

75 50

1.5

Strength (kN)

100

1

0.5

Min - 1% Max - 42% Mean - 13%

25 0

(d)

0 20

30

40

50

60

PCB - 8 mm

1.25

kp 12 mm / kp 8 mm

Stiffness kp (N/mm)

PCB - 12 mm

125

60

Depth / 2 (mm)

70

Depth / 2 (mm)

(e)

20

30

40

50

60

Depth / 2 (mm)

1.00 0.75

0.50 0.25 0.00

70

(f)

20

30

40

50

60

70

Depth / 2 (mm)

Fig. 12. Investigation on effect of sheathing board thickness vs pull-through strength and stiffness.

the residual validation indicating that the proposed generalized expression from (Eqs. (15)-(17)) is adequate for predicting the stiffness provided by the sheathing against the pull-through failure. However, it should be noted that the predicted stiffness magnitudes are under-predicted for the sheathing board types plywood 12 mm (Fig. 14c), PCB 12 mm (Fig. 15a), PCB 8 mm (Fig. 15c) and gypsum 12.5 mm + LGSS (Fig. 16c) compared to the actual stiffness magnitudes (kp - Table 4). This is because the values of coefficients A and B are formulated such that the magnitudes of sheathing stiffness will be underpredicted for the sheathing types which exhibits a sudden failure in the sheathing-fastener connection due to the twist of the CFS stud (Figs. 7b, 8a-b, and 10b – a sudden drop in the load magnitudes can be observed after reaching ultimate load) and the thickness of the sheathing board is not considered as a parameter since it does not significantly influence the sheathing stiffness as explained in Fig. 12.

300 FCB - 12 mm Plywood - 12 mm

Stiffness (kp) (N/mm)

250

Plywood - 6 mm PCB - 12 mm

200

PCB - 6 mm Gypsum - 12 mm + LGSS - 0.5 mm

Gypsum - 12 mm

150

100

50

0 20

30

40

50

60

70

4.1.2. Application and design-oriented verification of generalized sheathing stiffness equation - comparison with the full-scale experimental results To further verify the application of the predicted sheathing stiffness magnitudes from the proposed generalized equation (Eq. (15)) with the actual CFS wall design procedures, twelve full-scale (2250 mm long specimens) testing results of the sheathed CFS wall panels subjected out-of-plane bending is used herein (Table 7). The full-scale test setup used in the present study is similar to the ones used by Selvaraj and Madhavan [7]. The experimental test results include various CFS studs and three different sheathing materials (plywood, PCB and gypsum). This application-oriented verification method is straightforward, the sheathing stiffness that is required to arrest the lateral torsional buckling (cross-sectional twist) of the CFS stud is calculated using Yura's method [17] and it is compared against the actual sheathing stiffness

Depth / 2 (mm) Fig. 13. Sheathing stiffness magnitudes versus dimensions of CFS stud.

4.1.1. Residual method Figs. 14-16 illustrates the comparison between of sheathing stiffness predictor equation [Eq. (15)] with the actual sheathing stiffness magnitudes obtained from the experiments and the residuals (e) (e-difference between actual observed stiffness and predicted stiffness). It can be observed that the residuals of the generalized expression do not have any identifiable structure/pattern. Therefore, Eq. (15) comply with the statistical principle that the residuals of the fitted models should not have any pattern to avoid having a systematic bias [35,36]. Therefore,

501

502

Definition of the variables

Step 1: Determine the stiffness curve for each sheathing board with respect to the geometric property of the CFS stud from Fig. 13 Step 2: Determination of trend of difference between sheathing stiffness magnitudes (highest stiffness magnitudes (FCB) to the corresponding stiffness magnitudes (others)) (Eq. (1) / Eq. (x)) x = 2 to 7 Step 3: Process of making the sheathing stiffness predictor expression as a generalized one Step 4: Generalized form of the sheathing stiffness predictor expression

Description

()

0.106 d 2

Eq . (1) Eq . (2)

()

0.011 d 2

()

0.095 d 2

= 1.656e

Eq. (2)

kp = 2197.7e

Plywood – 12 mm

Eq . (1) Eq . (3)

()

0.01 d 2

()

0.096 d 2

= 1.907e

Eq. (3)

kp = 1909e

Particle cement board – 12 mm

Eq . (1) Eq . (4)

()

0.011 d 2

()

0.095 d 2

= 2.255e

Eq. (4)

kp = 1614.3e

Particle cement board – 8 mm

Eq . (1) Eq . (5)

0.018 d 2

()

()

0.088 d 2

= 3.210e

Eq. (5)

kp = 1133.8e

Plywood – 6 mm

Eq . (1) Eq . (6)

() 0.026 d 2

() 0.08 d 2

= 5.286e

Eq. (6)

kp = 688.5e

Gypsum board 12.5 mm + LGSS 0.5 mm

Eq . (1) Eq . (7)

() 0.028 d 2

() 0.078 d 2

= 8.588e

Eq. (7)

kp = 423.8e

Gypsum board 12.5 mm

3639.5e 0.106 (d/2) 1.656 e 0.011(d/2)

Eq. (14)

( ) to accommodate the material property of the CFS

Es 142857.1

0.0437 Eq. (17)

Eq. (16)

Eq. (15)

E 58.4

kp - Stiffness of the sheathing board against the pull-through failure; d - out-to-out depth of the CFS stud; E - Young's modulus of a CFS stud material obtained from the tensile test; Es - Tensile modulus of a sheathing board obtained from the tensile test; A and B – Coefficients based on the sheathing board type respectively shown in Eq. (16) and Eq. (17).

B=

0.909

(E / 58.4)e 0.106(d/2) 6274.40 (Bd/2) A. e Es

A = 3112.4 Es

kp =

stud. Where E is the Young's modulus of a CFS stud material obtained from the tensile test.

sheathing boards for which the sheathing stiffness is being determined. In addition, the constant in the expression (Eq. (1)) 3639.5 is equated to the ratio of

To arrive at a generalized expression to evaluate the stiffness provided by sheathing boards, an empirical equation based on a curve fit of experimental data collated from 67 tests are formulated. This was carried out by replacing the numerical coefficient in the expressions (Eqs. (8)-(13) using terms A and B that was formulated as a function of the ratio between tensile modulus of the highest sheathing to the other

kp(plywood) =

Eq. (8) Eq. (9) Eq. (10) Eq. (11) Eq. (12) Eq. (13) Now the equations (Eqs. (8–13)) ascertained from the differences between the sheathing stiffness magnitudes of highest to the corresponding one can be directly used as a divider to the expression (Eq. (1)) which is the exponential trend of the highly stiff fiber cement board sheathing with respect to the d/2 to determine the stiffnesses of the other sheathing boards. For example the sheathing stiffness predictor expression for the plywood sheathing board of thickness 12 mm (Eq. (2)) is equal to (Eq.(1) / Eq. (8))

–

Eq. (1)

kp = 3639.5e

Fiber cement board – 12 mm

Table 6 Formulation of generalized expression sheathing stiffness prediction.

S. Selvaraj and M. Madhavan

Structures 20 (2019) 489–509

Structures 20 (2019) 489–509

S. Selvaraj and M. Madhavan

30

300 Experimental Predicted [Eqs. (15-17)]

200

Residual e

Stiffness (N/mm)

250

FCB – 12 mm

150

100

0

50

FCB – 12 mm -30

0 20

30

(a)

40

50

60

20

70

30

(b)

Depth / 2 (mm)

200

40

50

60

70

Depth / 2 (mm)

50 Experimental

Residual e

Stiffness (N/mm)

Predicted [Eqs. (15-17)]

150 Plywood – 12 mm

100

0

50 Plywood – 12 mm -50

0

(c)

20

40

60

80

20

(d)

40

200

60

80

Depth / 2 (mm)

Depth / 2 (mm) 30

PW6

Predicted [Eqs. (15-17)]

150

Residual e

Stiffness (N/mm)

Experimental

Plywood – 6 mm

100

0

50 Plywood – 6 mm -30

0

(e) 20

30

40

50

60

70

(f)

Depth / 2 (mm)

20

30

40

50

60

70

Depth / 2 (mm)

Fig. 14. Validation of generalized stiffness equations (Eqs. (15)-(17)) for Fiber cement board (FCB) sheathing: (a) Actual sheathing stiffness vs. Predicted sheathing stiffness; (b) Residual distribution; Validation of generalized stiffness equations (Eqs. (15)-(17)] for Plywood sheathing: (a) Actual sheathing stiffness vs. Predicted sheathing stiffness (Plywood 12 mm); (b) Residual distribution; (c) Actual sheathing stiffness vs. Predicted sheathing stiffness (Plywood 6 mm); (d) Residual distribution;

magnitude determined using the generalized equation [Eq. (15)]. It can be assumed that the sheathing will arrest the LTB of the CFS stud, when the determined actual sheathing stiffness magnitudes (kp) using Eq. (15) are higher than the required bracing stiffness (βi) determined using Yura's method [Eq. (18)]. This result can be further directly compared with the failure modes (whether the sheathing restrains the LTB failure of the CFS stud or not) of the sheathed CFS stud obtained from the fullscale testing results shown in Figs. 17-19 [7] and Table 7. A similar method of bracing stiffness check was previously used by Refs. [24] and [37] for sheathing bracing requirements. The Yura's method [17] of required bracing stiffness calculation is from Winter's [1 and 34] ideal lateral brace stiffness method which was developed for sheathed CFS columns. The Winter's method [1 and 34]

of bracing stiffness calculation is based on the elastic buckling stiffness of the column, where an increase in buckling load results in a corresponding increase in the stiffness required to brace the column. However, the Winter's method [34] has been modified by Yura [17] to account for different loading cases (uniform and concentric), a number of bracings, single or double curvature and top flange loading. The modified formula for required bracing stiffness (βi∗) is given in Eq. (18). i

=2

Ni Cb Pf Lb

Cd CL

(18)

where numerical 2 is a factor of safety as suggested by Yura [17]; Ni = coefficient depending on number of braces (n), as recommended by Winter [34], for discrete bracing Ni = 4 − (2/n) and for relative

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150

30 Experimental Predicted [Eqs. (15-17)]

100

Residual e

Stiffness (N/mm)

125

PCB – 12 mm

75 50

0

25

PCB – 12 mm

0

-30 20

(a)

30

40

50

60

70

Depth / 2 (mm)

20

(b)

150

30

40

50

60

70

Depth / 2 (mm)

30 Experimental Predicted [Eqs. (15-17)]

100

Residual e

Stiffness (N/mm)

125

PCB – 8 mm

75 50

0

25

PCB – 8 mm

0

-30 20

(c)

30

40

50

60

70

Depth / 2 (mm)

20

(d)

30

40

50

60

70

Depth / 2 (mm)

Fig. 15. Validation of generalized stiffness equations (Eqs. (15)-(17) for Particle cement board (PCB) sheathing: (a) Actual sheathing stiffness vs. Predicted sheathing stiffness (PCB 12 mm); (b) Residual distribution; (c) Actual sheathing stiffness vs. Predicted sheathing stiffness (PCB 8 mm); (d) Residual distribution;

100

30 GYP

80

Predicted [Eqs. (15-17)]

60

Gypsum – 12.5 mm

Residual e

Stiffness (N/mm)

Experimental

40

0

20

Gypsum – 12.5 mm

0

-30 20

(a)

30

40

50

60

70

Depth / 2 (mm)

(b)

20

30

40

50

Experimental

80

GYP+LGSS

Predicted [Eqs. (15-17)]

Residual e

Stiffness (N/mm)

70

30

100

Gypsum – 12.5 mm + LGSS 0.5 mm

60 40

0

20

Gypsum – 12.5 mm + LGSS 0.5 mm

0

(c)

60

Depth / 2 (mm)

-30 20

30

40

50

60

70

Depth / 2 (mm)

(d)

20

30

40

50

60

70

Depth / 2 (mm)

Fig. 16. Validation of generalized stiffness equations (Eqs. (15)-(17)) for Gypsum sheathing: (a) Actual sheathing stiffness vs. Predicted sheathing stiffness (Gypsum 12.5 mm); (b) Residual distribution; (c) Actual sheathing stiffness vs. Predicted sheathing stiffness (Gypsum 12.5 mm + LGSS 0.5 mm); (d) Residual distribution;

504

Structures 20 (2019) 489–509 The prediction by Eq. (15) is correct

βi > kp indicating sheathing will fail in pullthrough βi < kp indicating sheathing will not fail βi > kp indicating sheathing will fail in pull-through 150 300 150 300

300

Gypsum

2100

2707.8 PCB

CL06

C05

CL04

CL03

Br – Breakage; NF – No failure; PT – Pull-through; LTB – Lateral Torsional Buckling; Y – Yielding; LB – Local buckling; Tb – thickness of the sheathing board.

Figs. 17(c-e) Fig. 17(f) Figs. 17(g-i) Fig. 17(j) Figs. 18(c-d) Fig. 18(e) Figs. 18(f-h) Fig. 18(i) Figs. 19(c-e) Fig. 19(f) Figs. 19(g-h) Fig. 19(i) Y Y LTB Y Y Y LTB Y LB LB LTB LTB CL02

bracing Ni = 1; n = number of bracings (sheathing fastener connections); Cb = bending coefficient, for uniform loading Cb = 1 and for three-point loading Cb = 1.75; Pf = (π2EIyc)/L2; E = young's modulus of the CFS steel beam (Table 3); Iyc = moment of inertia of the compression flange; L = unbraced length of the CFS structural member requires bracing; Cd = additional modification factor to account the number of inflection points (single or double curvature), equal to unity for single curvature and Cd = 1 + (MS/ML)2 for double curvature; MS and ML are the moments causing compression in the top and bottom flanges respectively; CL = modification factor to account the top flange loading effect, equal to unity for normal loading and CL = 1 + (1.2/n) for top flange loading; Lb = is taken as the distance between the two bracing points along the length of the CFS stud (df). It should be noted that the stiffness required (βi∗) should be matched by the sheathing stiffness (kp) in order to restrain the CFS stud from failure due to LTB. The actual stiffness (kp) of the various sheathing types determined from Eq. (15) is compared with the required bracing stiffness (βi) obtained using Eq. (18) to inhibit the LTB of the CFS stud as per Yura's method in Table 7. In general, the comparison indicates that the actual stiffness magnitudes predicted by the generalized expression Eq. (15) is either accurate or conservative. In particular, the full-scale test results show that the CFS stud sheathed with plywood sheathing of 6 mm thickness failed in LTB (specimen CL02) or slightly above the yield moment capacity (specimen CL01) (MEXP ≤ My – Fig. 17a-b) and the sheathing boards failed in breakage (Figs. 17(c-e), (g-i)). This experimental failure mode was accurately predicted by the stiffness equation Eq. (15) shows that the actual stiffness (kp) of the 6 mm plywood sheathing is less than the required stiffness (βi) (Table 7CL01 and CL02) whereas, in the case of plywood sheathing with 12 mm, the stiffness prediction by Eq. (15) was conservative. This conservative prediction shall be attributed to the fact that the coefficients used Eq. (15)(A and B) were formulated such that the sudden withdrawal of fastener from CFS stud (Figs. 7b and 7(h-m)) will be avoided. The full-scale test results showed that all the CFS wall panels fabricated with particle cement board (PCB) experienced pull-through failure at the sheathing fastener connection [Figs. 18(c-i)]. This again was accurately predicted by the generalized sheathing stiffness predictor expression (Eq. (15)) by showing that the actual stiffness (kp) of the PCB sheathing is less than the required sheathing stiffness (βi). Nevertheless, it should be noted that three out of four PCB CFS panels (CL03 - PCB – 8 mm – 300 mm, CL03 - PCB – 12 mm – 300 mm, and CL04 - PCB – 12 mm – 300 mm) reached yield moment capacity [MEXP > My – Figs. 18(a-b)] in spite of the occurrence of pull-through in PCB sheathing during loading (load magnitudes at which the pullthrough occurred is marked with dotted circles in Figs. 18(a-b)). This yielding failure of CFS stud should be attributed to the fact that the sheathing fastener connection away from the mid-span of the CFS studs did not fail during loading. However, the accurate prediction of failure mode by Eq. (15) will avoid any damage of sheathing during loading and lead to a conservative design strength prediction of sheathed CFS wall panel. The comparison of bracing stiffness prediction for the gypsum sheathing boards with the full-scale test results shows that the generalized sheathing predictor expression (Eq. (15)) is reliable for the design of sheathed CFS wall panels. It was accurately predicted that the bracing effect of gypsum sheathing is sufficient to arrest the LTB of the unlipped CFS stud (C05) and insufficient for the lipped CFS stud (CL06). It should be noted from Fig. 19a that the experimental moment magnitudes are higher than the design moment magnitudes predicted by direct strength method for the braced beam as per AISI 2016, which increases the degree of confidence in the bracing stiffness prediction by the proposed expression (Eq. (15)). Whereas for the CL06 studs, it was correctly predicted that the gypsum sheathing would fail in a pull-

The prediction by Eq. (15) is correct The prediction by Eq. (15) is correct

The prediction by Eq. (15) is conservative

35.05 35.05 14.86 14.86 25.50 25.50 11.58 11.58 59.64 59.64 18.79 18.79 Sheathing

Br NF Br NF PT PT PT PT NF NF PT PT 300

6 12 6 12 8 12 8 12 12.5 12.5 12.5 12.5 3701 Plywood

1.5 1.5 2 2 1.5 1.5 2 2 1.5 1.5 1.5 1.5 26 26 22 22 25 25 25 25 – – 10 10 50 50 55 55 50 50 58 58 45 45 43.5 43.5 80 80 100 100 80 80 100 100 50 50 80 80 CL01

B

lp

t

Tensile modulus (Es) Material D

Tb (mm)

Fastener Spacing (mm)

Failure mode

Stud

Reference Figure

55.66 55.66 93.14 93.14 55.66 55.66 111.52 111.52 17.20 18.40 25.44 27.22

Bracing stiffness required as per Eq. (18) (βi) (N/mm) Sheathed CFS wall panel - Full-scale experimental Results Sheathing configuration CFS stud Dimensions (mm) Specimen ID

Table 7 Verification of the generalized expression for sheathing stiffness prediction.

βi > kp indicating sheathing will fail in Breakage

Comments Result

Predicted stiffness as per generalized Eq. (15) (kp) (N/ mm)

Comparison results - Full-scale experiments vs. predicted failure mode

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Moment (kN-mm)

Moment (kN-mm)

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CL01 Plywood - 6 mm - 300 mm Plywood - 12 mm - 300 mm My

1000

(a)

0 0

10

20

30

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(b)

60

Out-of-plane deflection (mm)

(c)

(d)

(f)

Plywood - 6 mm - 300 mm Plywood - 12 mm - 300 mm My

0 0

10

20

30

40

50

60

Out-of-plane deflection (mm)

(g)

CL01 - Plywood – 6 mm – 300 mm

Breakage

CL02

2000

CL02 - Plywood – 6 mm – 300 mm

Breakage

(e)

(h)

(j)

CL01 - Plywood – 12 mm – 300 mm

(i)

CL02 - Plywood – 12 mm – 300 mm

Fig. 17. Application and design oriented verification of generalized sheathing stiffness equation (Eqs. (15)-(17)) for Plywood sheathing: (a) Load vs Displacement curve for CL01 CFS stud; (b) Load vs Displacement curve for CL02 CFS stud; (c–f) Effect of sheathing for CL01 CFS stud; (g–j) Effect of sheathing for CL02 CFS stud;

through, which can be observed in the actual failure mode figures of sheathed CFS wall panels (CL06) (Figs. 19 (g-i)). Therefore, the above validation study indicates that the generalized expression can be used to check the ability of sheathing board to inhibit the lateral torsional buckling of the CFS stud.

particles (fiberless – particle cement board and gypsum board). 3. The failure modes of fiberless sheathing boards (particle cement board and gypsum board) are undesirable (sudden pull-through and breakage) and vary for different dimensions of CFS studs. Therefore, fiberless sheathing should not be considered as a bracing element in the design of CFS wall panels. 4. More importantly, the experimental evidence indicates that the thickness of the sheathing boards does not influence the stiffness against pull-through failure. However, the failure modes of sheathing < 8 mm is undesirable and hence it can be conservatively recommended not to use the sheathing boards < 12 mm thickness when the bracing effect of sheathing is considered in the design.

5. Conclusions The new method to determine the sheathing stiffness against the torsional buckling of the CFS stud is presented. The actual stiffness of the sheathing boards against the worst-case failure mode was determined using a newly devised test setup. Prior to the stiffness determination, a thorough validation was carried out to ensure that the newly devised test setup is accurate in simulating the behavior of the sheathed CFS wall panels subjected to out-of-plane loading (torsional buckling). A total of sixty-seven experiments including seven different sheathing types and ten different CFS studs were carried out. Based on the test results the following conclusions can be drawn:

Based on the inferences obtained from the experimental results, a generalized expression (Eqs. (15)-(17)) to predict the stiffness of the various sheathing boards is formulated fastidiously. The generalized expression is formulated such that it can accommodate the design parameters of sheathed CFS wall panel (CFS stud dimensions, the material property of the sheathing boards) and inhibit the undesirable or catastrophic failure modes of the sheathing fastener connections. A statistical, and experimental (application and design oriented) validations indicate that the generalized expression can be used to examine the bracing ability of sheathing boards.

1. The strength and stiffness of the sheathing boards against the pullthrough failure primarily depend on the tensile modulus of sheathing board and depth of the CFS stud. 2. The resistance offered by the sheathing board with a fiber composition (plywood and fiber cement board) against the twist of the CFS stud is significantly higher than the sheathing boards made of

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7000

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Moment (kN-mm)

6000

Occurrence of pull-through

4000

3000

2000

CL03 PCB - 8 mm - 300 mm PCB - 12 mm - 300 mm My

1000

5000 4000 3000

PCB - 8 mm - 300 mm PCB - 12 mm - 300 mm My

1000 0

0

10

20

30

40

50

60

(b)

Out-of-Plane deflection (mm)

(c)

CL04

2000

0

(a)

Occurrence of pull-through

0

10

20

30

40

50

60

Out-of-Plane deflection (mm)

(f)

CL03 – PCB – 8 mm – 300 mm

CL04 – PCB – 8 mm – 300 mm Occurrence of pull-through

Occurrence of pull-through

(d)

(e)

(h)

(g)

(i)

CL03 – PCB – 12 mm – 300 mm

CL04 – PCB – 12 mm – 300 mm

Fig. 18. Application and design oriented verification of generalized sheathing stiffness equation [Eqs. (15–17)] for PCB sheathing: (a) Load vs Displacement curve for CL03 CFS stud; (b) Load vs Displacement curve for CL04 CFS stud; (c–f) Effect of sheathing for CL03 CFS stud; (g-j) Effect of sheathing for CL04 CFS stud;

Notations

lp MS ML Ni n Pf tb t εf βi

The following symbols are used in this paper A and B Coefficients based on the sheathing board [Eq. (16) and Eq. (17)] a or df Fastener spacing; b Breadth of the CFS stud (flange) (Table 3); Fending coefficient; Cb CL Modification factor to account the top flange loading effect; Additional modification factor to account the number of inCd flection points; d Out-to-out depth of CFS stud (web) (Table 3); Es Tensile modulus of sheathing board; E Young’s modulus of steel; F Pull-through strength of the sheathing board; fy Yield stress of the CFS stud (Table 3); fu Ultimate stress of the CFS stud (Table 3); k Effective length coefficient; kp Stiffness of the sheathing board against the pull-through failure [Eq. (15)]; L Center to center length of the CFS stud (unbraced length); Lb Distance between two bracing points along the length of the

CFS stud (df); Depth of CFS stud’s lip (Table 3); Moment causing compression in the top flange; Moments causing compression in the bottom flange; Coefficient depending on number of braces; Number of bracings (sheathing fastener connections); Elastic critical buckling load; Thickness of the sheathing board; Thickness of the CFS stud; Strain at fracture; Stiffness required to brace the CFS stud;

Acknowledgments The investigation reported in this paper was funded by Science Engineering and Research Board (SERB) Research Grant (SB/S3/CEE/046/ 2014) from the Department of Science and Technology (DST), Government of India. The first author would like to acknowledge the financial assistance received from this project. The authors would like to gratefully acknowledge Pennar Engineered Building Systems Ltd., Hyderabad for their help in fabricating the test specimens required for experimental investigation.

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1500

1000

500

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C05

CL06

Gypsum - 12.5 mm - 150 mm

Gypsum - 12.5 mm - 150 mm

Gypsum - 12.5 mm - 300 mm

Gypsum - 12.5 mm - 300 mm My

M-DSM

0

0

(a)

(c)

(d)

(f)

0

20 40 60 Out-of-plane deflection (mm)

80

C05 – Gypsum – 12.5 mm – 150 mm

LTB – Restrained Local buckling

(e)

(b)

20 40 Out-of-plane deflection (mm)

(g)

LTB – Restrained Local buckling

C05 – Gypsum – 12.5 mm – 300 mm

0

CL06 - Gypsum– 12.5 mm – 150 mm

(h)

(i)

60

Failed in LTB Pull-through failure

CL06 - Gypsum– 12.5 mm – 300 mm

Fig. 19. Application and design oriented verification of generalized sheathing stiffness equation (Eqs. (15)-(17) for Gypsum sheathing: (a) Load vs Displacement curve for C05 CFS stud; (b) Load vs Displacement curve for CL06 CFS stud; (c–f) Effect of sheathing for CL05 CFS stud; (g–j) Effect of sheathing for CL06 CFS stud;

References

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