# Study on In-Plane Initial Rotational Stiffness of Eccentric RHS Beam-Column Joints

^{*}

## Abstract

**:**

## 1. Introduction

_{u}: Ultimate bending moment,

_{1}: Length of plate corresponding to stiffening,

_{y}: The yield strength of the steel,

## 2. Construction and Finite Element Model

#### 2.1. Construction

#### 2.2. Finite Element Model

_{y}) was 450 MPa, the ultimate stress (f

_{u}) was 650 MPa, the elastic modulus (E) was 2.08 × 10

^{5}MPa, the tangential modulus (E′) was 0.005E, and Poisson’s ratio (ν) was 0.3.

## 3. Initial Stiffness of the Joint

#### 3.1. Eccentric RHS Joints without Stiffeners

_{0}of the T-shaped square tube intersecting joints was provided from the literature [2], as shown in Formula (1). It considers the deformation coefficient of the main panel k

_{cf}, the tensile deformation coefficient of the web k

_{cw}, and the shear deformation coefficient of the web k

_{sh}. The tensile deformation coefficient of the web can be calculated using Formulas (2) to (4).

_{eff}= 2.5T and bringing it into Equation (4), because the wall thickness (T) is approximately equal to the wall thickness of the beam (t), and the column height (H) is much greater than (t), according to the forms of Formula (2)~Formula (5), the initial rotational stiffness K

_{0}of the eccentric RHS joint can be written in the form of Formula (6). The coefficient (k) can be obtained through parameter analysis.

_{0}of the joint increased linearly with an increase in η(h/B). The influence of η(h/B) can be fitted by a linear function. In Figure 4b, with an increase in the beam–column width ratio correction value β*(2b/B − 1), the width of the beam increased, and the bending moment was distributed more to the non-eccentric side. The initial rotational stiffness K

_{0}of the joint increased non-linearly with an increase in β*(2b/B − 1). In Figure 4c,d, the failure mode of eccentric RHS joints was related to the thickness of the tube wall. Therefore, increasing the column diameter-thickness ratio γ(B/2T) is beneficial for enhancing the initial rotational stiffness K

_{0}. To some extent, increasing the beam-column wall thickness ratio τ(t/T) can also improve the initial rotational stiffness K

_{0}. The initial rotational stiffness K

_{0}of the joint increased non−linearly with the γ(B/2T) and τ(t/T). The influence of β*(2b/B − 1), γ(B/2T), and τ(t/T) can be fitted by a quadratic function. The final coefficient (k) can be written in the form of Formula (7), where C

_{1}~C

_{8}are undetermined constants. Using the data of 60 finite element models for parameter fitting, the fitting results are shown in Formula (8); most of the errors are less than 10%, and the maximum error is about 17%, which can obtain the initial rotational stiffness of the joint more accurately.

#### 3.2. Eccentric RHS Joints with Stiffeners

_{0}) resulting from the presence of a stiffener in the eccentric RHS joints. By analyzing the parameters that influence the increase in bearing capacity, the main factors affecting ΔK

_{0}can be determined. The geometric parameters, namely the stiffener thickness (t

_{l}), beam height (h), and length (l), were investigated, as shown in Figure 5. It was observed that ΔK

_{0}is directly proportional to t

_{l}and l, indicating that larger dimensions of the gusset plate lead to a more pronounced enhancement in joint stiffness through the stiffener. Furthermore, ΔK

_{0}exhibits a linear relationship with the beam height (h), with a positive intersection point on the x-axis. This signifies that the stiffener’s ability to improve the joint stiffness may be limited when the beam height is small. This can be attributed to the reduced longitudinal deformation along the beam direction, which hinders the effective contribution of the stiffeners.

_{0}). Conversely, changes in other geometric parameters of the beam-column members and modifications to the stiffener shape exhibited a relatively smaller effect on ΔK

_{0}. Notably, the parameter η was primarily achieved by altering the beam height (h), which was not explicitly considered in the final formula to avoid redundancy.

_{0}) of the joint is expressed by Formula (10), and a parameter fitting was performed using the data from 50 finite element models established in this research. The fitting result is presented in Formula (10). When calculating the effect of the stiffener on the rotational stiffness, the contribution of the stiffener was ignored if the calculated ΔK

_{0}was negative. The effect of the stiffener on the joint rotational stiffness was calculated using Formula (11), while the initial rotational stiffness of the joint without a stiffener was calculated using Formula (8). These two values were then added together to obtain the initial rotational stiffness of the joint with a stiffener. The maximum error (Δ

_{max}) was −11.21%, and the average error (Δ

_{avg}) was −0.24%, demonstrating that the results met the engineering accuracy requirements.

## 4. Spatial Effect

#### 4.1. Geometric Effect

#### 4.2. Load Effect

_{2}of the adjacent side beam, the bending capacity M

_{u1}and initial rotational stiffness K

_{1}of the joint in the main stress direction were analyzed. The bending capacity M

_{u}represents the joint’s ultimate bearing capacity when only a single beam of the joint is subjected to load. The results of this analysis are shown in Figure 12.

## 5. Mathematical Model of Eccentric RHS Beam-Column Joint

#### 5.1. Selection of Mathematical Model

#### 5.2. Joint-Level Finite Element Verification

#### 5.3. Structure-Level Finite Element Verification

## 6. Conclusions

- (1)
- The rotational stiffness (K
_{0}) of eccentric RHS joints is primarily influenced by the tension-compression deformation stiffness (k_{cw}) of the web. It increases with the height-to-column flange width ratio (η) and the beam-to-column wall thickness ratio (τ). Meanwhile, the column’s wall width-to-thickness ratio (γ) increases with these ratios’ increments. - (2)
- The rotational stiffness (K
_{0}) does not change significantly when the beam-column flange width ratio (β) is less than 0.5. It increases significantly with an increase in (β) when (β) is greater than 0.5, indicating that the bending moment distribution form of the joint changes. - (3)
- Considering the force mechanism of the eccentric RHS joint, the side plate connected to the stressed beam and the web plate on the eccentric side bear most of the load, while the plates on the other two sides of the rectangular tubular column member are minimally affected. Therefore, for a T-shaped space joint with a 90° included angle, the mutual influence between the two stressed beams can be disregarded.
- (4)
- To simulate the semi-rigid effect of the joint, this study adopted a nonlinear corner spring model. Compared with the solid element analysis, the ultimate bending moment error of the joint is only 1.0%, the average lateral displacement error in the frame structure is only 2.5%. The finite element analysis confirmed the accuracy of the power function model in accurately simulating the static load behavior of the joint, particularly the bending moment-angle relationship.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Notation | Implication |

η | Beam height to column flange width ratio |

β^{*} | Beam-column width ratio correction |

γ | Column tube wall width–thickness ratio |

τ | Beam-column section wall-thickness ratio |

β | Beam-column width ratio |

M_{u} | Ultimate bending moment |

t_{l} l | The cross-sectional area of the plate corresponding to the stiffener |

f_{y} | The yield strength of the steel |

K_{0} | The rotational stiffness |

ΔK_{0} | The increment of the initial rotational stiffness |

k_{cw} | The tension-compression deformation stiffness |

P | The vertical load at the loading point at the beam end |

Δ | The vertical displacement at the loading point at the beam end |

h | Indicates the moment arm provided by the upper and lower stiffeners |

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**Figure 1.**Models of joints. (

**a**) Eccentric RHS joint without stiffeners; (

**b**) Eccentric RHS joint with stiffeners.

**Figure 2.**Meshes of finite element models. (

**a**) Eccentric RHS joint without stiffeners; (

**b**) Eccentric RHS joint with stiffeners.

**Figure 5.**Effects of different stiffeners on joint rotational stiffness increments ΔK

_{0}; (

**a**) Effect of t

_{1}on ΔK

_{0}; (

**b**) Effect of l on ΔK

_{0}; (

**c**) Effect of h on ΔK

_{0}.

**Figure 6.**The effects of geometric parameters on the rotational stiffness increment ΔK

_{0}. (

**a**) Effect of β* on ΔK

_{0}; (

**b**) Effect of η on ΔK

_{0}; (

**c**) Effect of γ on ΔK

_{0}; (

**d**) Effect of τ on ΔK

_{0}.

**Figure 17.**Calculation results of the beam system finite element model. (

**a**) deformation diagram; (

**b**) bending moment diagram.

Maximum Mesh Size | Ultimate Bending Moment M_{u}/(kN/m) | Error/% |
---|---|---|

80 | 96.18 | 0.81 |

90 | 96.43 | 1.07 |

100 | 98.12 | 2.84 |

110 | 101.53 | 6.41 |

120 | 106.23 | 11.34 |

Model Number | Column Size | Beam Size | |||
---|---|---|---|---|---|

Width B/mm | Thickness T/mm | Width b/mm | Height h/mm | Thickness t/mm | |

J-β-200-130 | 200 | 8 | 130 | 250 | 6 |

J-β-200-140 | 200 | 8 | 140 | 250 | 6 |

J-β-200-150 | 200 | 8 | 150 | 250 | 6 |

J-β-200-160 | 200 | 8 | 160 | 250 | 6 |

J-β-200-170 | 200 | 8 | 170 | 250 | 6 |

J-β-150-80 | 150 | 8 | 80 | 200 | 6 |

J-β-150-90 | 150 | 8 | 90 | 200 | 6 |

J-β-150-100 | 150 | 8 | 100 | 200 | 6 |

J-β-150-110 | 150 | 8 | 110 | 200 | 6 |

J-β-150-120 | 150 | 8 | 120 | 200 | 6 |

J-β-250-160 | 250 | 8 | 160 | 300 | 6 |

J-β-250-175 | 250 | 8 | 175 | 300 | 6 |

J-β-250-190 | 250 | 8 | 190 | 300 | 6 |

J-β-250-200 | 250 | 8 | 200 | 300 | 6 |

J-β-250-210 | 250 | 8 | 210 | 300 | 6 |

J-γ-200-6 | 200 | 6 | 150 | 250 | 6 |

J-γ-200-7 | 200 | 7 | 150 | 250 | 7 |

J-γ-200-8 | 200 | 8 | 150 | 250 | 8 |

J-γ-200-9 | 200 | 9 | 150 | 250 | 9 |

J-γ-200-10 | 200 | 10 | 150 | 250 | 10 |

J-γ-150-6 | 150 | 6 | 100 | 200 | 6 |

J-γ-150-7 | 150 | 7 | 100 | 200 | 7 |

J-γ-150-8 | 150 | 8 | 100 | 200 | 8 |

J-γ-150-9 | 150 | 9 | 100 | 200 | 9 |

J-γ-150-10 | 150 | 10 | 100 | 200 | 10 |

J-γ-250-8 | 250 | 8 | 180 | 300 | 8 |

J-γ-250-9 | 250 | 9 | 180 | 300 | 9 |

J-γ-250-10 | 250 | 10 | 180 | 300 | 10 |

J-γ-250-11 | 250 | 11 | 180 | 300 | 11 |

J-γ-250-12 | 250 | 12 | 180 | 300 | 12 |

J-η-200-200 | 200 | 8 | 150 | 200 | 6 |

J-η-200-225 | 200 | 8 | 150 | 225 | 6 |

J-η-200-250 | 200 | 8 | 150 | 250 | 6 |

J-η-200-275 | 200 | 8 | 150 | 275 | 6 |

J-η-200-300 | 200 | 8 | 150 | 300 | 6 |

J-η-150-150 | 150 | 8 | 100 | 150 | 6 |

J-η-150-175 | 150 | 8 | 100 | 175 | 6 |

J-η-150-200 | 150 | 8 | 100 | 200 | 6 |

J-η-150-225 | 150 | 8 | 100 | 225 | 6 |

J-η-150-250 | 150 | 8 | 100 | 250 | 6 |

J-η-250-250 | 250 | 8 | 200 | 250 | 6 |

J-η-250-275 | 250 | 8 | 200 | 275 | 6 |

J-η-250-300 | 250 | 8 | 200 | 300 | 6 |

J-η-250-325 | 250 | 8 | 200 | 325 | 6 |

J-η-250-350 | 250 | 8 | 200 | 350 | 6 |

J-τ-200-4 | 200 | 8 | 150 | 250 | 4 |

J-τ-200-5 | 200 | 8 | 150 | 250 | 5 |

J-τ-200-6 | 200 | 8 | 150 | 250 | 6 |

J-τ-200-7 | 200 | 8 | 150 | 250 | 7 |

J-τ-200-8 | 200 | 8 | 150 | 250 | 8 |

J-τ-150-4 | 150 | 8 | 100 | 200 | 4 |

J-τ-150-5 | 150 | 8 | 100 | 200 | 5 |

J-τ-150-6 | 150 | 8 | 100 | 200 | 6 |

J-τ-150-7 | 150 | 8 | 100 | 200 | 7 |

J-τ-150-8 | 150 | 8 | 100 | 200 | 8 |

J-τ-250-4 | 250 | 8 | 200 | 250 | 4 |

J-τ-250-5 | 250 | 8 | 200 | 250 | 5 |

J-τ-250-6 | 250 | 8 | 200 | 250 | 6 |

J-τ-250-7 | 250 | 8 | 200 | 250 | 7 |

J-τ-250-8 | 250 | 8 | 200 | 250 | 8 |

Model Number | Column Size | Beam Size | Stiffener Size | ||||
---|---|---|---|---|---|---|---|

Width B/mm | Thickness T/mm | Width b/mm | Height h/mm | Thickness t/mm | Thickness t _{l}/mm | Length l/mm | |

J-t_{1}-200-4+ | 200 | 8 | 150 | 250 | 8 | 4 | 100 |

J-t_{1}-200-5+ | 200 | 8 | 150 | 250 | 8 | 5 | 100 |

J-t_{1}-200-6+ | 200 | 8 | 150 | 250 | 8 | 6 | 100 |

J-t_{1}-200-7+ | 200 | 8 | 150 | 250 | 8 | 7 | 100 |

J-t_{1}-200-8+ | 200 | 8 | 150 | 250 | 8 | 8 | 100 |

J-l-200-60+ | 200 | 8 | 150 | 250 | 6 | 6 | 60 |

J-l-200-80+ | 200 | 8 | 150 | 250 | 6 | 6 | 80 |

J-l-200-100+ | 200 | 8 | 150 | 250 | 6 | 6 | 100 |

J-l-200-120+ | 200 | 8 | 150 | 250 | 6 | 6 | 120 |

J-l-200-140+ | 200 | 8 | 150 | 250 | 6 | 6 | 140 |

J-β-200-130+ | 200 | 8 | 130 | 250 | 6 | 6 | 100 |

J-β-200-140+ | 200 | 8 | 140 | 250 | 6 | 6 | 100 |

J-β-200-150+ | 200 | 8 | 150 | 250 | 6 | 6 | 100 |

J-β-200-160+ | 200 | 8 | 160 | 250 | 6 | 6 | 100 |

J-β-200-170+ | 200 | 8 | 170 | 250 | 6 | 6 | 100 |

J-β-150-80+ | 150 | 8 | 80 | 200 | 6 | 6 | 100 |

J-β-150-90+ | 150 | 8 | 90 | 200 | 6 | 6 | 100 |

J-β-150-100+ | 150 | 8 | 100 | 200 | 6 | 6 | 100 |

J-β-150-110+ | 150 | 8 | 110 | 200 | 6 | 6 | 100 |

J-β-150-120+ | 150 | 8 | 120 | 200 | 6 | 6 | 100 |

J-η-200-200+ | 200 | 8 | 150 | 200 | 6 | 6 | 100 |

J-η-200-225+ | 200 | 8 | 150 | 225 | 6 | 6 | 100 |

J-η-200-250+ | 200 | 8 | 150 | 250 | 6 | 6 | 100 |

J-η-200-275+ | 200 | 8 | 150 | 275 | 6 | 6 | 100 |

J-η-200-300+ | 200 | 8 | 150 | 300 | 6 | 6 | 100 |

J-η-150-150+ | 150 | 8 | 100 | 150 | 6 | 6 | 100 |

J-η-150-175+ | 150 | 8 | 100 | 175 | 6 | 6 | 100 |

J-η-150-200+ | 150 | 8 | 100 | 200 | 6 | 6 | 100 |

J-η-150-225+ | 150 | 8 | 100 | 225 | 6 | 6 | 100 |

J-η-150-250+ | 150 | 8 | 100 | 250 | 6 | 6 | 100 |

J-γ-200-6+ | 200 | 6 | 150 | 250 | 6 | 6 | 100 |

J-γ-200-7+ | 200 | 7 | 150 | 250 | 6 | 6 | 100 |

J-γ-200-8+ | 200 | 8 | 150 | 250 | 6 | 6 | 100 |

J-γ-200-9+ | 200 | 9 | 150 | 250 | 6 | 6 | 100 |

J-γ-200-10+ | 200 | 10 | 150 | 250 | 6 | 6 | 100 |

J-γ-150-6+ | 150 | 6 | 100 | 200 | 6 | 6 | 100 |

J-γ-150-7+ | 150 | 7 | 100 | 200 | 6 | 6 | 100 |

J-γ-150-8+ | 150 | 8 | 100 | 200 | 6 | 6 | 100 |

J-γ-150-9+ | 150 | 9 | 100 | 200 | 6 | 6 | 100 |

J-γ-150-10+ | 150 | 10 | 100 | 200 | 6 | 6 | 100 |

J-γ-200-6+ | 200 | 6 | 150 | 250 | 6 | 6 | 100 |

J-τ-200-4+ | 200 | 8 | 150 | 250 | 4 | 4 | 100 |

J-τ-200-5+ | 200 | 8 | 150 | 250 | 5 | 4 | 100 |

J-τ-200-6+ | 200 | 8 | 150 | 250 | 6 | 4 | 100 |

J-τ-200-7+ | 200 | 8 | 150 | 250 | 7 | 4 | 100 |

J-τ-200-8+ | 200 | 8 | 150 | 250 | 8 | 4 | 100 |

J-τ-150-4+ | 150 | 8 | 100 | 200 | 4 | 4 | 100 |

J-τ-150-5+ | 150 | 8 | 100 | 200 | 5 | 4 | 100 |

J-τ-150-6+ | 150 | 8 | 100 | 200 | 6 | 4 | 100 |

J-τ-150-7+ | 150 | 8 | 100 | 200 | 7 | 4 | 100 |

J-τ-150-8+ | 150 | 8 | 100 | 200 | 8 | 4 | 100 |

Model Number | Beam–Column Flange Width Ratio β | Rotational Stiffness K _{0}/(kN·m·rad^{−1}) | ||
---|---|---|---|---|

Finite Element | Formula | Error/% | ||

J-β-200-130 | 0.65 | 8435.53 | 8108.01 | −3.88 |

J-β-200-140 | 0.70 | 8681.78 | 8423.72 | −2.97 |

J-β-200-150 | 0.75 | 9004.52 | 8870.70 | −1.49 |

J-β-200-160 | 0.80 | 9549.81 | 9448.95 | −1.06 |

J-β-200-170 | 0.85 | 10,651.09 | 10,158.47 | −4.63 |

J-β-150-80 | 0.53 | 5386.18 | 5526.39 | 2.60 |

J-β-150-90 | 0.60 | 5508.9 | 5555.64 | 0.85 |

J-β-150-100 | 0.67 | 5710.09 | 5748.51 | 0.67 |

J-β-150-110 | 0.73 | 6156.72 | 6105.02 | −0.84 |

J-β-150-120 | 0.80 | 7090.71 | 6625.16 | −6.57 |

J-β-250-160 | 0.64 | 12,403.06 | 11,312.82 | −8.79 |

J-β-250-175 | 0.70 | 12,123.24 | 11,822.41 | −2.48 |

J-β-250-190 | 0.76 | 12,589.15 | 12,597.31 | 0.06 |

J-β-250-200 | 0.80 | 13,458.62 | 13,261.29 | −1.47 |

J-β-250-210 | 0.84 | 14,268.36 | 14,043.19 | −1.58 |

Model Number | Beam Height to Column Flange Width Ratio η | Rotational Stiffness K _{0}/(kN·m·rad^{−1}) | ||
---|---|---|---|---|

Finite Element | Formula | Error/% | ||

J-η-200-200 | 1.00 | 5655.36 | 5376.64 | −4.93 |

J-η-200-225 | 1.13 | 6909.83 | 7016.18 | 1.54 |

J-η-200-250 | 1.25 | 9004.52 | 8870.70 | −1.49 |

J-η-200-275 | 1.38 | 10,786.44 | 10,940.21 | 1.43 |

J-η-200-300 | 1.50 | 13,237.56 | 13,224.70 | −0.10 |

J-η-150-150 | 1.00 | 3121.51 | 3022.32 | −3.18 |

J-η-150-175 | 1.17 | 4228.32 | 4278.00 | 1.17 |

J-η-150-200 | 1.33 | 5703.28 | 5748.51 | 0.79 |

J-η-150-225 | 1.50 | 7100.36 | 7433.88 | 4.70 |

J-η-150-250 | 1.67 | 8818.22 | 9334.08 | 5.85 |

J-η-250-250 | 1.00 | 8602.05 | 8799.27 | 2.29 |

J-η-250-275 | 1.10 | 11,142.91 | 10,917.69 | −2.02 |

J-η-250-300 | 1.20 | 13,189.28 | 13,261.29 | 0.55 |

J-η-250-325 | 1.30 | 15,711.35 | 15,830.08 | 0.76 |

J-η-250-350 | 1.40 | 18,475.05 | 18,624.04 | 0.81 |

Model Number | Column Tube Wall Width–Thickness Ratio γ | Rotational Stiffness K _{0}/(kN·m·rad^{−1}) | ||
---|---|---|---|---|

Finite Element | Formula | Error/% | ||

J-γ-200-6 | 16.67 | 7164.19 | 7262.48 | 1.37 |

J-γ-200-7 | 14.29 | 7785.08 | 7999.25 | 2.75 |

J-γ-200-8 | 12.50 | 9004.52 | 8870.70 | −1.49 |

J-γ-200-9 | 11.11 | 9973.64 | 9862.26 | −1.12 |

J-γ-200-10 | 10.00 | 11,492.77 | 10,965.21 | −4.59 |

J-γ-150-6 | 12.50 | 4347.77 | 4415.37 | 1.55 |

J-γ-150-7 | 10.71 | 4694.31 | 5035.76 | 7.27 |

J-γ-150-8 | 9.38 | 5710.09 | 5748.51 | 0.67 |

J-γ-150-9 | 8.33 | 6901.66 | 6547.09 | −5.14 |

J-γ-150-10 | 7.50 | 8195.46 | 7427.57 | −9.37 |

J-γ-250-8 | 15.63 | 12,335.87 | 12,051.23 | −2.31 |

J-γ-250-9 | 13.89 | 14,203.56 | 13,124.57 | −7.60 |

J-γ-250-10 | 12.50 | 14,641.01 | 14,333.68 | −2.10 |

J-γ-250-11 | 11.36 | 16,173.1 | 15,668.97 | −3.12 |

J-γ-250-12 | 10.42 | 17,516.66 | 17,124.04 | −2.24 |

Model Number | Beam–Column Section Wall–Thickness Ratio τ | Rotational Stiffness K _{0}/(kN·m·rad^{−1}) | ||
---|---|---|---|---|

Finite Element | Formula | Error/% | ||

J-τ-200-4 | 0.50 | 7085.27 | 7919.16 | 11.77 |

J-τ-200-5 | 0.63 | 8310.69 | 8394.87 | 1.01 |

J-τ-200-6 | 0.75 | 9004.52 | 8870.70 | −1.49 |

J-τ-200-7 | 0.88 | 9389.58 | 9346.63 | −0.46 |

J-τ-200-8 | 1.00 | 9683.7 | 9822.67 | 1.44 |

J-τ-150-4 | 0.50 | 4863.35 | 5131.88 | 5.52 |

J-τ-150-5 | 0.63 | 5318.5 | 5440.16 | 2.29 |

J-τ-150-6 | 0.75 | 5703.28 | 5748.51 | 0.79 |

J-τ-150-7 | 0.88 | 5983.3 | 6056.94 | 1.23 |

J-τ-150-8 | 1.00 | 6110.39 | 6365.43 | 4.17 |

J-τ-250-4 | 0.50 | 6695.22 | 7855.39 | 17.33 |

J-τ-250-5 | 0.63 | 8124.95 | 8327.28 | 2.49 |

J-τ-250-6 | 0.75 | 8602.05 | 8799.27 | 2.29 |

J-τ-250-7 | 0.88 | 9223.87 | 9271.37 | 0.51 |

J-τ-250-8 | 1.00 | 9604.13 | 9743.58 | 1.45 |

Model Number | Rotational Stiffness K _{0}/(kN·m·rad^{−1}) | ||
---|---|---|---|

Finite Element | Formula | Error/% | |

J-t_{1}-200-4+ | 14,880.21 | 14,915.25 | 0.24 |

J-t_{1}-200-5+ | 15,987.88 | 16,223.14 | 1.47 |

J-t_{1}-200-6+ | 17,373.82 | 17,531.02 | 0.90 |

J-t_{1}-200-7+ | 18,650.79 | 18,838.91 | 1.01 |

J-t_{1}-200-8+ | 19,533.17 | 20,146.8 | 3.14 |

J-l-200-60+ | 13,313.45 | 13,712.91 | 3.00 |

J-l-200-80+ | 15,567.45 | 15,282.38 | −1.83 |

J-l-200-100+ | 16,579.87 | 16,851.84 | 1.64 |

J-l-200-120+ | 18,229.8 | 18,421.31 | 1.05 |

J-l-200-140+ | 19,216.52 | 19,990.77 | 4.03 |

J-β-200-130+ | 16,367.13 | 16,282.85 | −0.51 |

J-β-200-140+ | 16,712.04 | 16,529.1 | −1.09 |

J-β-200-150+ | 16,579.71 | 16,851.84 | 1.64 |

J-β-200-160+ | 17,218.84 | 17,397.13 | 1.04 |

J-β-200-170+ | 18,244.75 | 18,498.41 | 1.39 |

J-β-150-80+ | 9700.97 | 10,332.07 | 6.51 |

J-β-150-90+ | 10,422.72 | 10,639.5 | 2.08 |

J-β-150-100+ | 10,790.95 | 10,840.69 | 0.46 |

J-β-150-110+ | 11,720.02 | 11,271.38 | −3.83 |

J-β-150-120+ | 12,227.62 | 12,173.72 | −0.44 |

J-η-200-200+ | 11,217.62 | 10,785.96 | −3.85 |

J-η-200-225+ | 13,943.22 | 13,398.79 | −3.90 |

J-η-200-250+ | 16,579.71 | 16,851.84 | 1.64 |

J-η-200-275+ | 20,414.23 | 19,992.13 | −2.07 |

J-η-200-300+ | 23,653.88 | 23,801.61 | 0.62 |

J-η-150-150+ | 5941.52 | 5535.377 | −6.84 |

J-η-150-175+ | 9010.61 | 8000.551 | −11.21 |

J-η-150-200+ | 11,452.97 | 10,833.88 | −5.41 |

J-η-150-225+ | 13,742.02 | 13,558.85 | −1.33 |

J-η-150-250+ | 16,379.9 | 16,607.65 | 1.39 |

J-γ-200-6+ | 15,002.93 | 15,011.51 | 0.06 |

J-γ-200-7+ | 16,023.23 | 15,632.4 | −2.44 |

J-γ-200-8+ | 16,579.71 | 16,851.84 | 1.64 |

J-γ-200-9+ | 18,122.54 | 17,820.96 | −1.66 |

J-γ-200-10+ | 19,006.86 | 19,340.09 | 1.75 |

J-γ-150-6+ | 9189.39 | 9478.365 | 3.14 |

J-γ-150-7+ | 9952.77 | 9824.905 | −1.28 |

J-γ-150-8+ | 11,309.46 | 10,840.69 | −4.14 |

J-γ-150-9+ | 12,203.30 | 11,972.49 | −1.89 |

J-γ-150-10+ | 12,361.27 | 13,326.06 | 7.80 |

J-γ-200-6+ | 15,002.93 | 15,011.51 | 0.06 |

J-τ-200-4+ | 12,715.51 | 12,316.82 | −3.14 |

J-τ-200-5+ | 13,780.39 | 13,542.24 | −1.73 |

J-τ-200-6+ | 14,287.32 | 14,236.07 | −0.36 |

J-τ-200-7+ | 14,777.89 | 14,621.13 | −1.06 |

J-τ-200-8+ | 15,225.99 | 14,915.25 | −2.04 |

J-τ-150-4+ | 7711.47 | 8283.747 | 7.42 |

J-τ-150-5+ | 8991.67 | 8738.897 | −2.81 |

J-τ-150-6+ | 9129.09 | 9123.677 | −0.06 |

J-τ-150-7+ | 9533.8 | 9403.697 | −1.36 |

J-τ-150-8+ | 9640.53 | 9530.787 | −1.14 |

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## Share and Cite

**MDPI and ACS Style**

Guo, X.; Li, W.; Xv, Z.
Study on In-Plane Initial Rotational Stiffness of Eccentric RHS Beam-Column Joints. *Materials* **2023**, *16*, 5103.
https://doi.org/10.3390/ma16145103

**AMA Style**

Guo X, Li W, Xv Z.
Study on In-Plane Initial Rotational Stiffness of Eccentric RHS Beam-Column Joints. *Materials*. 2023; 16(14):5103.
https://doi.org/10.3390/ma16145103

**Chicago/Turabian Style**

Guo, Xiaonong, Weixin Li, and Zeyu Xv.
2023. "Study on In-Plane Initial Rotational Stiffness of Eccentric RHS Beam-Column Joints" *Materials* 16, no. 14: 5103.
https://doi.org/10.3390/ma16145103