Analysis of Cold Formed Sections of Steel Angle under Tensile Load by Numerical Method

GRD Journals- Global Research and Development Journal for Engineering | Volume 4 | Issue 1| December 2018 ISSN: 2455-5703

Analysis of Cold Formed Sections of Steel Angle under Tensile Load by Numerical Method A Paul Makesh Research Scholar Department of Civil Engineering Dr.M.G.R Educational and Research Institute Maduravoyal, Chennai, Tamilnadu India

Dr. S Arivalagan Dean and Professor Department of Civil Engineering Dr.M.G.R Educational and Research Institute Maduravoyal, Chennai, Tamilnadu India

Abstract The effective sectional area concept was adopted to conduct the analysis of cold-formed Tension members. ANSYS software was utilized to simulate the behavior of cold formed steel angle under tension load. The paper describes the results from a finite element investigation into the load capacity tension members of single angle sections and double angles sections of 1.5 mm and 1.6 mm under plain (without Lipped) and with Lipped conditions subjected to tension. Results were recorded as the load carrying capacity increases for connected to the opposite side of the gusset than the connected to same side. It observed load vs deflection, Analyses are compared with experimental results.

Keywords- ANSYS, Tension members, Cold-formed steel, FEM, Angle sections, Non-Linear Analysis

I. INTRODUCTION Cold formed steel member are less weight and thinner than hot- rolled sections. They can be used to produce and forming of almost any shapr and section to any desired geometry and length. Openings of cold formed steel beams used to facilitate sanitary, electrical and mechanical works. These openings should have size, shape and location, as far as possible; have no effect on the structural strength requriments. The main disadvantages of opening in cold formed steel sections are the local buckling due to high width of open to thickness ratios. Recent codes of practice and standards have suggested simplified methods and processes for the design of steel members with perforation.

However, numerical and experimental researches have been published to investigated the effect of openings on the load capacity of cold formed steel (CFS) members subjected to monitonic axial load. An extensive parametric study have helped to enhance the understanding the behaviour and buckling of wide range of opening angle sections under different combinations of axial tension load moment. Numercial modeling is one of the important features in finite element analysis. This chapter discusses the finite element modeling of the cold formed steel angles, the finite element analysis program ANSYS is used to create the model of the tested specimens under these models, ultimate loads and total deformation of cold formed angles are compared with experimental results angles.

II. LITERATURE REVIEW In order to understand flexural behavior of CFS members and why there is need of this study, a through literature review was undertaken. This literature review included review of the characteristics, design methods and numerical methods to analyze and accurate modeling of CFS sections followed by a summary which presents main findings and gaps in the literature.

Alireza Bagheri et.al [1] (2012) are presented the Cyclic behavior of bolted cold – formed angles. In this paper a finite element (FE) procedure is described for simulating hysteretic moment – rotation behavior and failure deformations of bolted cold- formed steel ( CFS).

K.F. Chung and K.H,Ip [2] (2012) are presented the Finite element investigation on the structural behavior of cold formed steel bolted connections. A finite element model with three-dimensional soild elements established to investigate the bearing failure of cold- formed steel bolted connections.

Valdier Francisco et al.[3] presented details of 66 experiments carried out on cold formed steel fastened with bolts subjected to tension. They examined the reduction coefficient performance based upon the new tests and data available in the literature, comprising of 108 tests.

Chi-Ling Pan[4] investigated the effect of shear lag on the angles cold formed steel sections, by testing 54 specimens with different cross sectional dimensions. The Indian code for use of cold formed steel IS: 801[5] does not any provision for the design of tension members. Hence during the code revision, experiments were conducted at CSIR-SERC on cold formed angle tension members for the inclusion of design provisions.

Moen et.al[6] 2008 through analytical models showed that the variation of residual stress through the thickness is rather complex and nonlinear similar finding was made by Shafter and Pekoz earlier in experimental analysis.

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Analysis of Cold Formed Sections of Steel Angle under Tensile Load by Numerical Method (GRDJE/ Volume 4 / Issue 1/ 002)

III. EXPERIMENTAL INVESTIGATION A total of 72 specimens have been tested by varying the angle sizes, number of bolts and the bold pitch distance. All the specimens have been designed to undergo net section rupture failure or block failure. The specimens are equal angles 50x50, 60x60 and 70x70mm, and unequal angles are 50x25,60x30 and 70x35mm they have equal length and thickness of 1.5 and 1.6mm respectively. The angles are connected to the gusset plate under eccentric tensile loads on single and double angle specimen.

IV. FINITE ELEMENT ANALYSIS The goal of the Finite Element Analysis was to develop a model that could study the effect of connection eccentricity and connection length on tension member. In order to test the validity, the results obtained from the analysis were used to compare with the test results from the experiments. The Finite Element Analysis was performed using the commercial Finite Element Program ANSYS, version 15.0.

FEM is best understood from its practical application, known as finite element analysis (FEA). FEA as applied in engineering is a computational tool for performing engineering analysis. It includes the use of mesh generation techniques for dividing a complex problem into small elements, as well as the use of software program coded with FEM algorithm. In applying FEA, the complex problem is usually a physical system with the underlying physics such as the Euler-Bernoulli beam equation, the heat equation, or the Navier-Stokes equations expressed in either PDE or integral equations, while the divided small elements of the complex problem represent different areas in the physical system.

FEA is a good choice for analyzing problems over complicated domains (like cars and oil pipelines), when the domain changes (as during a solid state reaction with a moving boundary), when the desired precision varies over the entire domain, or when the solution lacks smoothness. FEA simulations provide a valuable resource as they remove multiple instances of creation and testing of hard prototypes for various high fidelity situations.

A. Non-Linear Analysis To perform the non-linear analysis, the single and double angle specimens are modeled based on the experimental set up incorporating geometric imperfections. As the nonlinear problem is path dependant, the solution process requires a step by step load incremental analysis. In the analysis, the solution usually converged very slowly after yielding, and the increment for each load step had to be made very small. The geometric imperfections included the thickness of the section, width of the connected leg, width of unconnected leg in case of single plain angles and it includes width of lip in case of lipped angles. Yielding is determined using von-Mises yield criteria. A static structural analysis determines the displacements, stresses, strains, and forces in structures or components caused by loads that do not induce significant inertia and damping effects. Steady loading and response conditions are assumed.

A static structural analysis determines the displacements, stresses, strains, and forces in structures or components caused by loads that do not induce significant inertia and damping effects. Steady loading and response conditions are assumed. The loads and the response of the structure are assumed to differ slowly in time. Using ANSYS 15, a static structural load can be carried out. ANSYS uses Newton- Raphson balance equilibrium and the solution obtained at the last converged load step was used as the ultimate numerical load of the specimen.

V. NUMERICAL INVESTIGATION To validate the experimental results, a finite element analysis package ANSYS (15.0) was used for the modeling and analysis. A non-linear analysis was performed and the materials are assumed to behave as an isotropic hardening material. From the experimental tension test results, the static material modeling was done. The element type used to model the test specimens is SHELL 63. It is a 4-noded 3 dimensional quadratic shell element. This element has six degrees of freedom at each node. Finite element mesh of size 2x2mm was implied and used in all the simulations. The friction or contact between connected leg of the specimen and the gusset plate was ignored.

Numerical investigations on structural behavior of cold formed steel angle sections subjected to tensile loading are presented in this paper. The ultimate strength capacity is arrived for cross section dimension with varying eccentricity load under tension loading condition through Numerical analysis ANSYS 15 work bench. The effect of compressive stress was observed more in the outstanding leg and therefore the outstanding leg experiences local buckling. From the figures, it is observed that the lip experiences local buckling and the stress concentration is more nearer to the bolt holes as expected.It is seen that the separation of angles take place in the connected portion.

S.No 1 2

Table 1: Comparison of Experimental load and Numerical load of thickness 1.5mm Size of specimen Exp load (kN) Description Ansys load (kN) % increase in load (mm) 50x50xt 27.54 29.12 5.74 Equal size Single angle without Lip 60x60xt 32.45 34.28 5.64

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Analysis of Cold Formed Sections of Steel Angle under Tensile Load by Numerical Method (GRDJE/ Volume 4 / Issue 1/ 002)

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Single angle with Lip

Double angle opposite side without Lip Double angle same side without Lip

Double angle opposite side with Lip

Double angle same side with Lip Unequal size Single angle without Lip Single angle with Lip Double angle opposite side

without Lip

Double angle same side without Lip

Double angle opposite side with Lip

Double angle same side with Lip

70x70xt 50x50x10xt 60x60x10xt 70x70x10xt 50x50xt 60x60xt 70x70xt 50x50xt 60x60xt 70x70xt 50x50x10xt 60x60x10xt 70x70x10xt 50x50x10xt 60x60x10xt 70x70x10xt 50x25xt 60x30xt 70x35xt 50x25x10xt 60x30x10xt 70x35x10xt 50x25xt 60x30xt 70x35xt 50x25xt 60x30xt 70x35xt 50x25x10xt 60x30x10xt 70x35x10xt 50x25x10xt 60x30x10xt 70x35x10xt

36.75 36.28 42.58 48.56 59.78 64.58 79.86 56.78 64.58 78.54 69.74 74.58 97.87 68.74 80.47 96.47 18.27 22.47 28.47 23.47 30.79 33.48 38.78 49.78 58.47 37.48 49.72 58.78 50.43 54.58 70.59 51.58 60.72 70.58

38.32 37.98 44.32 51.28 63.25 68.15 83.78 59.42 68.18 82.37 72.87 76.89 102.72 71.82 83.51 99.72 19.28 23.81 30.12 24.58 32.18 35.28 40.91 51.89 61.29 39.72 52.41 61.29 52.38 56.27 73.45 53.48 63.72 73.82

4.27 4.69 4.09 5.60 5.80 5.53 4.91 4.65 5.57 4.88 4.49 3.10 4.96 4.48 3.78 3.37 5.53 5.96 5.80 4.73 4.51 5.38 5.49 4.24 4.82 5.98 5.41 4.27 3.87 3.10 4.05 3.68 4.94 4.59

Table’s 1 to 2 shows comparison between the experimental loads and ANSYS load of cold formed steel single angle sections and double angle section under tension.

Numerical results shown that the ultimate strength of single equal plain angle sections without lip 5% higher than the experimental loads under tension. To examine that the single equal angle lipped section under tension load is increase 4% times greater than experimental loads.

In the case of Double angles specimens connected to opposite side without Lip 6% higher than the experimental loads.

Also it was observed that Double angles specimens connected to same side without Lip 5% higher than the experimental loads.

In the case of Double angles specimens connected to opposite side without Lip 5% higher than the experimental loads. Also it was observed that Double angles specimens connected to same side without Lip 6% higher than the experimental loads.

Numerical results shown that the ultimate strength of single unequal plain angle sections without lip 4% higher than the experimental loads under tension. To examine that the single unequal angle lipped section under tension load is increase 5% times greater than experimental loads. In the case of Double unequal angles specimens connected to opposite side without Lip 6% higher than the experimental loads.

Also it was observed that Double unequal angles specimens connected to same side without Lip 5% higher than the experimental loads. In the case of Double unequal angles specimens connected to opposite side without Lip 4% higher than the experimental loads. Also it was observed that Double unequal angles specimens connected to same side without Lip 5% higher than the experimental loads.

S.No 1 2 3 4 5 6 7 8

Table 2: Comparison of Experimental load and Numerical load of thickness 1.6mm Size of specimen Exp load (KN) Description Ansys load (KN) % increase in load (mm) 50x50xt 29.45 31.12 5.67 Equal size Single angle without Lip 60x60xt 34.56 36.41 5.35 70x70xt 40.58 42.89 5.69 50x50x10xt 39.15 41.28 5.44 Single angle with Lip 60x60x10xt 46.78 48.78 4.28 70x70x10xt 52.58 54.89 4.39 50x50xt 62.58 65.98 5.43 Double angle opposite side without Lip 60x60xt 68.41 71.28 4.20

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Analysis of Cold Formed Sections of Steel Angle under Tensile Load by Numerical Method (GRDJE/ Volume 4 / Issue 1/ 002)

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Double angle same side

without Lip

Double angle opposite side with Lip

Double angle same side

with Lip

Unequal size Single angle without Lip Single angle with Lip

Double angle opposite side without Lip

Double angle same side without Lip

Double angle opposite side with Lip

Double angle same side with Lip

70x70xt 50x50xt 60x60xt 70x70xt 50x50x10xt 60x60x10xt 70x70x10xt 50x50x10xt 60x60x10xt 70x70x10xt 50x25xt 60x30xt 70x35xt 50x25x10xt 60x30x10xt 70x35x10xt 50x25xt 60x30xt 70x35xt 50x25xt 60x30xt 70x35xt 50x25x10xt 60x30x10xt 70x35x10xt 50x25x10xt 60x30x10xt 70x35x10xt

84.59 62.58 76.24 84.25 76.28 82.58 103.56 76.42 88.48 106.58 21.58 25.46 32.45 28.11 31.44 39.58 40.48 57.48 67.41 41.33 52.58 68.47 58.45 68.45 81.54 56.18 67.28 81.59

88.47 65.21 79.34 87.87 79.89 86.45 108.78 79.89 92.89 111.28 22.75 26.91 34.12 29.71 32.76 41.75 42.79 60.48 70.13 43.51 55.18 72.26 61.81 72.29 86.28 59.13 71.28 85.89

4.59 4.20 4.07 4.30 4.73 4.69 5.04 4.54 4.98 4.41 5.42 5.70 5.15 5.69 4.20 5.48 5.71 5.22 4.04 5.27 4.94 5.54 5.75 5.61 5.81 5.25 5.95 5.27

A. Load vs Deflection Fig 1 to 5 shows the typical load versus deflection behavior for single angles with and without lips and double angles. The ultimate strength is the maximum stress that a material can withstand before it breaks or weakens. From the graphs, it is observed that the ultimate load of experimental valves is similar to numerical valves for specimens.

Fig. 1: Load vs Deflection behavior of single plain angle specimen (1.5mm)

Fig. 2: Load vs Deflection behavior of single unequal angle specimen t=1.5mm

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Analysis of Cold Formed Sections of Steel Angle under Tensile Load by Numerical Method (GRDJE/ Volume 4 / Issue 1/ 002)

Fig. 3: Load vs Deflection behavior of Double plain angle (opposite side) t=1.5mm

Fig. 4: Load vs Deflection behavior of Double plain angle (same side) t=1.5mm

Fig. 5: Load vs Deflection behavior of single plain angle specimen t=1.6mm

B. Comparison of Experimental load and ANSYS load Fig 6 to 8 shows comparison between Experimental load and ANSYS load of single angle sections and double angle sections. It was found that ultimate strength of ANSYS loads are 4% to 6% higher than the ultimate strength of Experimental loads.

Fig. 6: Comparison of ultimate load for single equal angle specimens (1.5mm)

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Analysis of Cold Formed Sections of Steel Angle under Tensile Load by Numerical Method (GRDJE/ Volume 4 / Issue 1/ 002)

Fig. 7: Comparison of ultimate load for single unequal angles specimens (1.5mm)

Fig. 8: Comparison of ultimate load for single unequal angles with Lip (1.6mm)

VI. CONCLUSION ANSYS software was utilized to calculate the strength behavior of cold formed steel angle under tension load. The numerical model developed using ANSYS to predict the behavior of single and double angles was found to simulate the experimental valves are closely.

Numerical results shown that the ultimate strength of single equal plain angle sections without lip 5% higher than the experimental loads under tension.

To examine that the single equal angle lipped section under tension load is increase 4% times greater than experimental loads. In the case of Double angles specimens connected to opposite side without Lip 6% higher than the experimental loads.

Also it was observed that Double angles specimens connected to same side without Lip 5% higher than the experimental loads.

In the case of Double angles specimens connected to opposite side without Lip 5% higher than the experimental loads.

Also it was observed that Double angles specimens connected to same side without Lip 6% higher than the experimental loads.

The ultimate strength is the maximum stress that a material can withstand before it breaks or weakens.

From the graphs, it is observed that the ultimate loads of experimental valves are similar to numerical valves for specimens.

It was found that ultimate strength of ANSYS loads are 4% to 6% higher than the ultimate strength of Experimental loads.

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Kulak, GL & Grondin, GY 2001, ‘AISC Rules for Block Shear in Bolted Connections’, Engineering Journal, vol. 5, no. 4, pp. 199-203 Li & Chen 2008, ‘An analytical model to predict the distortional buckling stress of cold formed steel sections’, Journal of Structural Division, ASCE, vol.

12, no. 5, pp. 1043-1049 Padma Priya, R 2015, ‘Experimental study on behavior of bolted cold formed steel angles under tension’, Asian Journal of Civil Engineering, vol. 6, no. 5, pp. 614-618 Schifferaw & Schafer 2007, ‘Inelastic bending capacity in cold formed steel members’, Construction research of steel structures, vol. 6, no. 5, pp. 571-553

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Analysis of Cold Formed Sections of Steel Angle under Tensile Load by Numerical Method (GRDJE/ Volume 4 / Issue 1/ 002) [5] [6] [7] [8] [9] [10] [11] [12] [13]

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