# Mechanical Properties of Prefabricated Cold-Formed Steel Stud Wall Panels Sheathed with Fireproof Phenolic Boards under Out-of-Plane Loading

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Program

#### 2.1. Experimental Parameters and Plan

#### 2.2. Test Specimen

^{2}. The cold-formed light-gauge steel studs have a length of 3110 mm, and the cross-section size is 89 mm × 41 mm × 0.8 mm. The tracks have a length of 1200 mm, and the section size is 90.6 mm × 41 mm × 0.8 mm. The detailed dimensions of the steel frame are shown in Figure 4. The fireproof phenolic boards were then pasted on the upper and lower surfaces of the steel frame with the silicone sealant, as shown in Figure 4b. Subsequently, the gypsum board was pasted on the outside of the fireproof phenolic board, and the inner space of the wall was filled with aluminum silicate cotton, as presented in Figure 4b. Finally, the LSF wall panel was connected to the steel beam through the connector and bolts, as shown in Figure 4b.

#### 2.3. Material Properties

#### 2.4. Loading Plan

^{2}following the GB50009-2012 [46], which could meet the design requirements in most areas of China. Subsequently, 1.57, 1.4, and 1.42 were selected for the gust factor, the structural shape factor of wind load, and the height variation coefficient of wind pressure under the worst condition, respectively. The standard value of wind load is calculated according to Equation (1).

_{gz}is the gust factor, μ

_{s}

_{1}is the structural shape factor of wind load, μ

_{z}is the height variation coefficient of wind pressure, ω

_{01}is the basic wind pressure, and w

_{k}

_{1}is the standard value of wind load, which is 3.121 KN/m

^{2}. In this study, the load levels corresponding to different displacements of each specimen can be compared with the wind load standard value of 3.121 KN/m

^{2}for checking the serviceability limit state.

^{2}. A gap of 20 mm was maintained between the bags to prevent the arching effect of weights. Each bag was paved to ensure uniform contact with the wall panel. During loading, each level of load lasted 5 min, and the last level of load lasted 30 min. During unloading, the step-by-step method was adopted until the load was zero and the interval time of the step was 3 min. In addition, the applying maximum load of each specimen and loading levels are determined according to the above calculated standard value of wind load, estimated bearing capacity of the wall and connector, and the safety of the test process. The applying maximum loads of all specimens except for specimen QB2-I-Y-2.5-4-3 are larger than the calculated standard value of wind load of 3.121 KN/m

^{2}to check the serviceability limit state of the specimen. For specimen QB2-I-Y-2.5-4-3, its estimated bearing capacity connector is relatively low because of the small thickness of its connector and fewer screws connected to steel beams, so its applying maximum load is set to be relatively low to avoid the possible danger caused by sudden connector failure. Specimens QB1-I-L-2.5-5-1, QB2-I-Y-2.5-4-3, QB3-I-L-1.5-3-1, QB4-I-Y-2.5-4-2, QB5-II-L-2.5-3-1, and QB6-II-Y-2.5-4-3 implemented 8-levels loading (3.216 KN/m

^{2}), 12-levels loading (4.824 KN/m

^{2}), 4-levels loading (1.608 KN/m

^{2}), 10-levels loading (4.020 KN/m

^{2}), 8-levels loading (3.216 KN/m

^{2}), and 12-levels loading (4.824 KN/m

^{2}), respectively. All tests were conducted in the structural laboratory of the School of Civil Engineering, Zhengzhou University. In this study, a total of 150 bags were prepared and the mass of a dry gravel bag was 10 kg. The typical images of the specimen before and after loading are shown in Figure 6. It is worth noticing that under the wind load carried by building structures as specified in the GB50009-2012 [46], wall panels need to meet the requirements of the normal service stage, while the wall panels are commonly in the elastic stage. Thus applying maximum load was designed within the elastic range.

#### 2.5. Measuring Instrument Arrangement

## 3. Results and Discussion

#### 3.1. Experimental Phenomena

#### 3.2. Load-Span Deflection Curve

^{2}), I is the equivalent moment of inertia of the mid-span section of the wall (m

^{4}), k is the coefficient that characterizes the restraint at both ends and load form (dimensionless), w is the applied area load of each level (KN/m

^{2}), b is the width of the specimen (m), l is the effective span of the specimen (m), and f is the measured mid-span deflection of the specimen (mm).

#### 3.3. Bending Stiffness

#### 3.3.1. Arrangement of Light-Gauge Steel Studs

#### 3.3.2. Connection Mode

#### 3.4. Strain Distribution

## 4. Theoretical Study of the Stress of LSF Wall Panels

#### 4.1. Symmetric Slip Theory

#### 4.1.1. The Basic Assumptions

- (1)
- Fireproof phenolic boards, silicone sealant, and cold-formed light-gauge steel studs are all elastomers. Phenolic boards and the light-gauge steel studs are in continuous and uniform contact through the silicone sealant in the longitudinal direction and maintain the same curvature. Furthemore, the longitudinal slip is a linear elastic process.
- (2)
- Under the condition of small elastic deformation, the top and lower interfaces are stressed symmetrically.
- (3)
- The out-of-plane stiffness, the bending moment, and the shear stress of the fireproof phenolic board can be ignored.

#### 4.1.2. Differential Equation of Symmetrical Slip

_{i}is the total bonding width of wall width, and N

_{f}(x) is the axial stress of single-sided phenolic boards. According to Assumption (1), τ(x) is expressed as:

_{f}(x) is the longitudinal strain of the phenolic board, and ε

_{s}(x) is the longitudinal strain of the light-gauge steel studs. According to Assumption (3), the longitudinal strain at the centroid of the fireproof phenolic board at the top compression position can be expressed as follows:

_{f}is the elastic modulus of the phenolic board, and A

_{f}is the cross-section area of the single side phenolic board. Because the axial forces of the top and lower fireproof phenolic boards are self-balanced, the longitudinal strain at the top flange of cold-formed light-gauge steel studs is expressed as follows:

_{s}is the elastic modulus of the light-gauge steel studs, I

_{s}the total moment of inertia of the section of light-gauge steel studs, h

_{s}is the height of the section of light-gauge steel studs, and M

_{s}(x) is the total bending moment of the section of light-gauge steel studs. The simultaneous of Equations (7)–(9) is expressed as follows:

_{c}is the distance between the centroid of the section of light-gauge steel studs and the centroid of the phenolic board section. The differential equation of elastic slip of LSF wall can be expressed by Equation (12), which can be obtained by the simultaneous of Equations (6), (10) and (11).

#### 4.1.3. Solution of the Mechanical Characteristic Quantity of Interface Slip under Load

#### 4.1.4. Composite Section Stiffness and Sheathing Effect Coefficient of LSF Wall Panels

_{f}is the moment of inertia of the whole section of the top and lower phenolic board to the centroid of the composite section after conversion according to the elastic modulus.

_{0}is the mid-span deflection of the wall without considering slip. The expression of sheathing effect coefficient is obtained by the inverse solution:

_{0i}can then be calculated by substituting B

_{0i}into Equation (23).

#### 4.2. Calculation of Elastic Deflection of LSF Wall Panels and Bending Normal Stress of Longitudinal Light-Gauge Steel Studs under Wind Load

#### 4.2.1. Calculation of Mid-Span Elastic Deflection of LSF Wall Panels

#### 4.2.2. Calculation of Elastic Bending Normal Stress of Longitudinal Light-Gauge Steel Studs

#### 4.2.3. Strength Checking of the Adhesive Layer between Phenolic Boards and Light-Gauge Steel Studs

#### 4.3. Comparison between the Proposed Method and the Existing Methods

#### 4.3.1. Transformed-Section Method without Considering Interface Slip

_{0}is the width of the top flange of the beam without panel support, b

_{1}and b

_{2}are the calculated width of the flange plate on both sides of the beam, and the smaller value of 1/6 of the beam span l and 6 times of the flange plate thickness h

_{1}is taken as b

_{1}and b

_{2}, respectively. The calculation equation for the converted width of the flange plate is as follows:

_{E}is the ratio of elastic modulus of beam material E

_{s}to the elastic modulus of flange plate material E

_{f}. When the combined section of the two materials is converted into the section of the beam material, the deflection and section stress can be calculated according to the material mechanics method.

#### 4.3.2. Reduced Stiffness Method Considering Interface Slip

_{s}is the elastic modulus of beam material, I

_{eq}is the moment of inertia of the converted section, and ζ is the stiffness reduction coefficient, which is calculated according to the following equation:

_{cf}is the flange plate section area within the effective width, A is the beam cross-section area, I is the moment of inertia of the beam section, I

_{cf}is the moment of inertia of flange plate section within the effective width, d

_{c}is the distance between the centroid of the beam section and the centroid of the flange plate section, h is the height of the composite section, l is the calculated span, k is the stiffness coefficient of the connector between the flange plate and the beam, p is the average spacing of connectors, and n

_{s}is the number of longitudinal columns of connectors. In the elastic stage, the elastic resistance moment of the reduced section considering the interface slip [45] is as follows:

_{eq}is the elastic resistance moment of the section calculated according to the transformed-section method and ζ is the stiffness reduction coefficient, which is calculated as follows:

_{w}is the section area of steel beam web; A

_{ft}and A

_{fs}are the section area of the top and lower flange of steel beam, respectively; h

_{f1}and h

_{f2}are the thickness of the top and lower flange, respectively.

#### 4.3.3. Comparison of Calculated Results

## 5. Conclusions

- In the elastic stress stage under out-of-plane loads, the asymmetric arrangement of light-gauge steel studs of the LSF wall does not affect the overall elastic bending stiffness of wall panels. Thus, the symmetrical arrangement is recommended for practical applications.
- In the elastic stress stage under out-of-plane loads, increasing the thickness of the L-shaped connect-or and the number of self-tapping screws can improve the out-of-plane stiffness of the prefabricated LSF wall system. The overall out-of-plane stiffness of the prefabricated LSF wall system and the stiffness contribution of a single special-shaped connector can be increased by increasing the number of special-shaped connectors from two to three. The symmetrical arrangement of light-gauge steel studs of LSF wall is beneficial to improving the out-of-plane stiffness of the connectors. In addition, special-shaped connectors have greater out-of-plane stiffness than L-shaped connectors.
- Based on the sheathing effect of the wall panel and the symmetric slip theory of the interface between the fireproof phenolic board and light-gauge steel studs, the equations for calculating the elastic deflection in span and the elastic bending stress of light-gauge steel studs of the LSF wall are derived theoretically under out-of-plane loading. Compared with the transformed-section method and the reduced stiffness method in China’s steel structure design standards, the results obtained from the calculation of the method proposed in this paper are closer to the experimentally measured data.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**LSF walls section and stud section. (

**a**) Type-I walls section structure (symmetrical arrangement of light-gauge steel studs). (

**b**) Type-II walls section structure (asymmetric arrangement of light-gauge steel studs). (

**c**) Cross-section of light-gauge steel stud.

**Figure 2.**Dimension of L-shaped connector and hole positions (mm). (

**a**) Hole positions of L-shaped connector connected with steel beam by three self-drilling screws. (

**b**) Hole positions of L-shaped connector connected with steel beam by five self-drilling screws. (

**c**) Section dimension of L-shaped connector.

**Figure 3.**Dimension of special-shaped connector and hole positions (mm). (

**a**) Hole positions of special-shaped connector. (

**b**) Section dimension of special-shaped connector.

**Figure 15.**Strain distribution curves of mid-span section. (

**a**) QB1-I-L-2.5-5-1 (

**b**) QB5-II-L-2.5-3-1.

**Figure 16.**Strain load curves. (

**a**) Strain of top flanges of light-gauge steel studs and top phenolic board of QB1-I-L-2.5-5-1; (

**b**) Strain of lower flanges of light-gauge steel studs and lower phenolic board of QB1-I-L-2.5-5-1; (

**c**) Strain of top flanges of light-gauge steel studs and top phenolic board of QB5-II-L-2.5-3-1; (

**d**) Strain of lower flanges of light-gauge steel studs and lower phenolic board of QB5-II-L-2.5-3-1.

**Figure 19.**Distribution of mechanical parameters of slip along wall span. (

**a**) Slip shear stress distribution. (

**b**) Slip distribution. (

**c**) Slip strain distribution.

Specimen | Wall Type | Connector Section | Thickness of Connector (mm) | Number of Single Side Connectors | Number of Single Side Screws Connected to Steel Beams |
---|---|---|---|---|---|

QB1-I-L-2.5-5-1 | Type I | L-shape | 2.5 | 1 | 5 |

QB2-I-Y-2.5-4-3 | Type I | Special-shaped | 2.5 | 3 | 12 |

QB3-I-L-1.5-3-1 | Type I | L-shape | 1.5 | 1 | 3 |

QB4-I-Y-2.5-4-2 | Type I | Special-shaped | 2.5 | 2 | 8 |

QB5-II-L-2.5-3-1 | Type II | L-shape | 2.5 | 1 | 3 |

QB6-II-Y-2.5-4-3 | Type II | Special-shaped | 2.5 | 3 | 12 |

Material | Yield Stress (Mpa) | Ultimate Stress (Mpa) | Young’s Modulus (GPa) | Poisson’s Ratio |
---|---|---|---|---|

Cold-formed steel | 302.4 | 377.3 | 178.3 | 0.32 |

Fireproof phenolic board | / | 424.8 | 33.76 | 0.27 |

Silicone sealant | / | 1.13 | 0.00067 | 0.50 |

Loading Series | Loading Uniform Area Load (KN/m^{2}) | Unloading Uniform Area Load (KN/m^{2}) |
---|---|---|

0-level | 0 | 4.824 |

1-level | 0.402 | 4.422 |

2-level | 0.804 | 4.020 |

… | … | … |

11-level | 4.422 | 0.402 |

12-level | 4.824 | 0 |

Specimen | Applying Maximum Load (KN/m^{2}) | Loading Bending Stiffness of Specimen (KN·m^{2}) | Unloading Bending Stiffness of Specimen (KN·m^{2}) | Mid-Span Deflection (mm) |
---|---|---|---|---|

QB1-I-L-2.5-5-1 | 3.216 | 40753 | 47535 | 9.75 |

QB2-I-Y-2.5-4-3 | 4.824 | 45166 | 52295 | 13.26 |

QB3-I-L-1.5-3-1 | 1.608 | 23492 | 33666 | 8.68 |

QB4-I-Y-2.5-4-2 | 4.020 | 42865 | 48616 | 11.70 |

QB5-II-L-2.5-3-1 | 3.216 | 38882 | 47691 | 10.25 |

QB6-II-Y-2.5-4-3 | 4.824 | 45662 | 52517 | 13.00 |

Wall Specimen | Applying Maximum Load (KN/m ^{2}) | Mid-Span Deflection (mm) | Loading Bending Stiffness (KN·m ^{2}) | Unloading Bending Stiffness (KN·m ^{2}) |
---|---|---|---|---|

QB1-I-L-2.5-5-1 | 3.216 | 7.11 | 48866 | 52570 |

QB2-I-Y-2.5-4-3 | 4.824 | 12.18 | 42980 | 46449 |

QB3-I-L-1.5-3-1 | 1.608 | 4.96 | 31274 | 48852 |

QB4-I-Y-2.5-4-2 | 4.020 | 9.73 | 45129 | 49175 |

QBn-I average value | / | / | 42062 | 49262 |

QB5-II-L-2.5-3-1 | 3.216 | 7.33 | 47463 | 47470 |

QB6-II-Y-2.5-4-3 | 4.824 | 11.64 | 44029 | 47862 |

QBn-II average value | / | / | 45746 | 47666 |

Specimen | Elastic Bending Stiffness of Specimen (KN·m ^{2}) | Elastic Bending Stiffness of Wall Panel (KN·m^{2}) | Ratio of Bending Stiffness of Specimen to the Wall Panel |
---|---|---|---|

QB1-I-L-2.5-5-1 | 47535 | 52570 | 0.904 |

QB2-I-Y-2.5-4-3 | 52295 | 46449 | 1.126 |

QB3-I-L-1.5-3-1 | 33666 | 48852 | 0.689 |

QB4-I-Y-2.5-4-2 | 48616 | 49175 | 0.987 |

QB5-II-L-2.5-3-1 | 47691 | 54131 | 0.881 |

QB6-II-Y-2.5-4-3 | 52517 | 47862 | 1.097 |

Specimen | Measured Bending Stiffness B _{0i} (KN·m^{2}) | Measured Conversion m _{0i} | Calculated Value m | Ratio of Calculated Value to Measured Value |
---|---|---|---|---|

QB1-I-L-2.5-5-1 | 684.5 | 0.699 | 0.549 | 0.79 |

QB2-I-Y-2.5-4-3 | 604.8 | 0.588 | 0.93 | |

QB3-I-L-1.5-3-1 | 636.1 | 0.631 | 0.87 | |

QB4-I-Y-2.5-4-2 | 640.3 | 0.637 | 0.86 | |

QB5-II-L-2.5-3-1 | 618.1 | 0.606 | 0.91 | |

QB6-II-Y-2.5-4-3 | 623.2 | 0.613 | 0.90 | |

Average value | 634.5 | 0.629 | 0.88 |

Load (KN/m^{2}) | f_{0} (mm) | f_{1}/f_{0} | f_{2}/f_{0} | f_{3}/f_{0} |
---|---|---|---|---|

0.402 | 0.81 | 0.805 | 3.030 | 1.255 |

0.804 | 1.74 | 0.750 | 2.824 | 1.169 |

1.206 | 2.69 | 0.728 | 2.740 | 1.135 |

1.608 | 3.65 | 0.715 | 2.695 | 1.116 |

2.010 | 4.43 | 0.736 | 2.772 | 1.148 |

2.412 | 5.41 | 0.725 | 2.729 | 1.130 |

2.814 | 6.37 | 0.718 | 2.703 | 1.119 |

3.216 | 7.41 | 0.705 | 2.655 | 1.100 |

3.618 | 8.57 | 0.686 | 2.583 | 1.070 |

4.020 | 9.64 | 0.677 | 2.551 | 1.056 |

4.422 | 10.77 | 0.667 | 2.511 | 1.040 |

4.824 | 11.91 | 0.658 | 2.478 | 1.026 |

Average value | / | 0.714 | 2.689 | 1.114 |

_{1}represents the mid-span deflection calculated by the transformed-section method; f

_{2}represents the mid-span deflection calculated by the reduced stiffness method; f

_{3}represents the mid-span deflection calculated by the method presented in this paper; f

_{0}represents the average measured mid-span deflection of 6 wall panel specimens.

**Table 9.**Comparison of compressive stress at top flange of longitudinal light-gauge steel studs in mid-span.

Load (KN/m^{2}) | σ_{sc}_{0} (MPa) | σ_{sc}_{1}/σ_{sc}_{0} | σ_{sc}_{2}/σ_{sc}_{0} | σ_{sc}_{3}/σ_{sc}_{0} |
---|---|---|---|---|

0.402 | −7.84 | 0.656 | 7.166 | 1.023 |

0.804 | −16.30 | 0.631 | 6.888 | 0.984 |

1.206 | −24.21 | 0.637 | 6.959 | 0.994 |

1.608 | −30.34 | 0.678 | 7.404 | 1.057 |

2.010 | −35.98 | 0.714 | 7.803 | 1.114 |

2.412 | −42.29 | 0.730 | 7.968 | 1.138 |

2.814 | −49.80 | 0.723 | 7.893 | 1.127 |

3.216 | −57.18 | 0.719 | 7.857 | 1.122 |

3.618 | −62.28 | 0.743 | 8.115 | 1.159 |

4.020 | −67.54 | 0.761 | 8.314 | 1.187 |

4.422 | −77.63 | 0.728 | 7.956 | 1.136 |

4.824 | −88.80 | 0.695 | 7.588 | 1.083 |

Mean value | / | 0.701 | 7.659 | 1.094 |

_{sc}

_{1}represents the compressive stress at top flange of longitudinal light-gauge steel studs in mid-span calculated by the transformed-section method; σ

_{sc}

_{2}represents the compressive stress at top flange of longitudinal light-gauge steel studs in mid-span calculated by the reduced stiffness method; σ

_{sc}

_{3}represents the compressive stress at top flange of longitudinal light-gauge steel studs in mid-span calculated by the method presented in this paper; σ

_{sc}

_{0}represents the average measured compressive stress at top flange of longitudinal light-gauge steel studs in mid-span of six specimens.

**Table 10.**Comparison of tensile stress at the lower flange of longitudinal light-gauge steel studs in mid-span.

Load (KN/m^{2}) | σ_{st}_{0} (MPa) | σ_{st1}/σ_{st0} | σ_{st2}/σ_{st0} | σ_{st3}/σ_{st0} |
---|---|---|---|---|

0.402 | 9.04 | 0.569 | 6.214 | 0.887 |

0.804 | 17.44 | 0.590 | 6.440 | 0.920 |

1.206 | 25.91 | 0.595 | 6.502 | 0.928 |

1.608 | 31.89 | 0.645 | 7.044 | 1.006 |

2.010 | 39.50 | 0.651 | 7.107 | 1.015 |

2.412 | 48.88 | 0.631 | 6.893 | 0.984 |

2.814 | 56.83 | 0.633 | 6.916 | 0.988 |

3.216 | 63.84 | 0.644 | 7.037 | 1.005 |

3.618 | 69.73 | 0.664 | 7.248 | 1.035 |

4.020 | 76.21 | 0.675 | 7.368 | 1.052 |

4.422 | 87.45 | 0.647 | 7.064 | 1.009 |

4.824 | 98.12 | 0.629 | 6.867 | 0.981 |

Mean value | / | 0.631 | 6.892 | 0.984 |

_{st}

_{1}represents the tensile stress at the lower flange of longitudinal light-gauge steel studs in mid-span calculated by the reduced section method; σ

_{st}

_{2}represents the tensile stress at the lower flange of longitudinal light-gauge steel studs in mid-span calculated by the reduced stiffness method; σ

_{st}

_{3}represents the tensile stress at the lower flange of longitudinal light-gauge steel studs in mid-span calculated by the method presented in this paper; σ

_{st}

_{0}represents the average measured tensile stress at the lower flange of longitudinal light-gauge steel studs in mid-span of six specimens.

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## Share and Cite

**MDPI and ACS Style**

Zhao, G.; Chen, W.; Zhao, D.; Li, K.
Mechanical Properties of Prefabricated Cold-Formed Steel Stud Wall Panels Sheathed with Fireproof Phenolic Boards under Out-of-Plane Loading. *Buildings* **2022**, *12*, 897.
https://doi.org/10.3390/buildings12070897

**AMA Style**

Zhao G, Chen W, Zhao D, Li K.
Mechanical Properties of Prefabricated Cold-Formed Steel Stud Wall Panels Sheathed with Fireproof Phenolic Boards under Out-of-Plane Loading. *Buildings*. 2022; 12(7):897.
https://doi.org/10.3390/buildings12070897

**Chicago/Turabian Style**

Zhao, Gengqi, Wanqiong Chen, Dapeng Zhao, and Ke Li.
2022. "Mechanical Properties of Prefabricated Cold-Formed Steel Stud Wall Panels Sheathed with Fireproof Phenolic Boards under Out-of-Plane Loading" *Buildings* 12, no. 7: 897.
https://doi.org/10.3390/buildings12070897