Finite Element Investigation of a Bolted Extended End-Plate Moment Connection Subjected to Variation of Temperature

Although beam to beam joints are a critical part of steel structures and connection strength varies with temperature considerably, regrettably very few works have been conducted under elevated temperature conditions on end plate moment connection. The strength and stiffness properties degrade with increase of temperature. This paper presents an investigation of a bolted extended end-plate beam to beam joint subjected to variation of temperature. 20°C, 204°C, 316°C, 427°C, 649°C temperatures were considered for finite element analysis and their effects on end-plate moment connection were discussed. It has been found that with the increase of temperature, end plate thickness does not vary but stiffness of end plate reduces considerably. Finally, the effects of the changes of different beam parameters on the end-plate moment connection were discussed. *Corresponding author: Md Manik Mia, Concordia University Montreal, Quebec, Canada, Tel: +1 514-848-2424; E-mail: manik08ce@gmail.com Received January 25, 2016; Accepted April 25, 2016; Published April 27, 2016 Citation: Mia MM, Amanat KM (2016) Finite Element Investigation of a Bolted Extended End-Plate Moment Connection Subjected to Variation of Temperature. J Civil Environ Eng 6: 225. doi:10.4172/2165-784X.1000225 Copyright: © 2016 Mia MM, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


Introduction
An extended end-plate connection is one in which the endplate protrudes beyond the flanges of the beam section to allow for the placement of exterior bolts. Moment connections are usually designed to transfer bending moments, shear forces and sometimes normal force. The strength of end plate will change with temperature which will cause reduction of strength of connection. When the steel elements and structures are subjected to high temperatures (fire) they progressively lose their stiffness and carrying capacity because Young's modulus and yield strength are decreasing. The ability of connections to withstand force during a fire weakens as a result of strength and stiffness reduction [1]. Connections play a very important role to survive extreme fires without progressively collapsing [2]. Lawson [3] first examined the fire resistance of beam-to-column connection experimentally. Al-Jabri [4] conducted a series of fire tests to establish the moment-rotation temperature relationships for semi-rigid joints. When temperature exceeds 100°C, the stress-strain curve begins to become nonlinear, gradually eliminating well-defined yield point. The modulus of elasticity, yield strength and tensile strength all reduce as temperature increases. After 500°C, the rate of decrease is maximum [5].
Stress and strain values of a mild steel (Yield strength 275 MPa) were obtained from tension test performed in Structural Mechanics Laboratory of Bangladesh University of Engineering and Technology, Dhaka, Bangladesh. Then using the guidelines proposed by NIST [5], corresponding yield strength, ultimate strength, elastic modulus, stress and strain values were calculated at 20°C, 204°C, 316°C, 427°C, 649°C . Finally in order to investigate adequate end plate thickness and corresponding end plate reaction with change of temperature, finite element software ANSYS 11.0 was used.

Methodology Finite element model
A finite element model was developed to describe the behavior of the joint in a beam-to-beam extended end-plate moment connection at elevated temperatures. Among different finite element analysis packages, ANSYS 11.0 was chosen for modeling and analysis. In order to analyze the bolted extended end-plate moment connection, large deflection and plastic material properties (material nonlinearity) were used. A typical situation where end-plate type beam splice is used is shown in Figure 1. For finite element analysis of the moment capacity, a part of the beam on one side of the joint was modeled with appropriate load and boundary connections. Separate elements had been used for the modeling of the beam flange, beam web, end-plate, load plate, bolts and contact surface. SHELL181 had been used for the beam flange, beam web, end-plate and load plate. COMBIN39 was used for the contact surface and the bolts. A load plate had been used in order to avoid the local yielding of the beam, at the point of the application of load. The behavior of the bolts and the contact surface was described by COMBIN39 spring element. The behavior of nonlinear stress-strain materials can be simulated accurately in ANSYS.
Multilinear isotropic hardening is one such option to describe such material behaviors. W12x58 section and A325 bolt having yield strength 90ksi (620 MPa) and ultimate strength 120 ksi (827 MPa) were used in the analysis. When the beam is subjected to external load then a reaction is created in end-plate to resist corresponding enddisplacement which is termed end-plate reaction and that displacement is termed as end-displacement.

Meshing
SHELL181 was used to model the entire beam. The meshing was done in such a way that more intense meshing reamained near the endplate. This is because the effect of bending is greater in that region.

Meshing of the end-plate
SHELL181 was used to model the end-plate. BKIN option was used in order to describe the behavior of the bilinear isotropic steel. The meshing was done in such a way to ensure that nodes exist at the desired locations of the bolts, as shown in Figure 4. Here, beam width a and a4 = a3 b weld where weld = min (flange thickness, endplate thickness) The meshing of the load plate is identical to the meshing of the end-plate.

Properties of the bolt
COMBIN39 link element was used to simulate the behavior of bolts. Figure 5 shows the force-deflection behavior of bolts. The values of both K c and K t are equal here. K c and K t represent the stiffness of the bolt and were calculated as follows:

Properties of the contact element
Contact element was used to describe the behavior of two end-plates in contact with each other. The same COMBIN39 spring element was used for this purpose. The nodes of the end-plate are extruded along the axis of the beam, in the opposite direction of the beam, to generate the COMBIN39 contact elements. The stress-strain relationship for the   Page 3 of 5 element was described so that it can resist compression but remains very weak in tension. Figure 6 shows the force-deflection behavior of contact springs. The value of K c is large while that of K t is very small.

Boundary conditions
The free ends of the COMBIN39 link elements, which simulate the contact surface, were restrained in all directions. To protect against sliding, one node of the end-plate was restrained in the vertical direction and two nodes were restrained in the horizontal direction. It would help the COMBIN39 elements to resist the displacement both in horizontal and vertical direction or to give stability to the end-plate. A point load is applied at the load plate end of the beam. The point load is applied at the intersection of the top flange of the beam with the web as shown in Figure 7. The magnitude of the load is such that it ensures that yielding of steel occurs. This is of importance for determining the corresponding thickness of end-plate for a particular dimension of beam.

Stress-strain data input
Stress and strain values of a mild steel (Yield strength 275 MPa) were obtained from tension test performed in Structural Mechanics Laboratory of Bangladesh University of Engineering and Technology, Dhaka, Bangladesh. The stress-strain curves were prepared and used for finite element analysis (Figures 8-10).

Convergence of the solution
The objective of the finite element study is to determine the endplate thickness for W12x58 section considering temperature effects. The required end-plate thickness is that thickness for which the failure is just initiated by the yielding of the beam. This thickness can be determined by a trial and error solution involving the force-deflection relationship of the structure. From the Figure 11 given below it was found that after increasing end-plate thickness to 50 mm, end-plate reaction does not change which indicates that at this thickness failure will be just initiated by the yielding of the beam.

Temperature effect on end plate reaction
Using the Table 1 proposed by NIST [5], corresponding yield      From the values obtained from finite element analysis, it had been found that end-plate thickness does not change with the increase of temperature but stiffness of plate had been found to decrease considerably. Here the value just after which nonlinearity begins was taken as end-plate reaction. Stiffness is termed as resisting force per unit deflection. Stiffness of end-plate at 20°C was taken as 1.0 and stiffness of end-plate at other temperatures were compared with it and a relative stiffness curve had been drawn.

Effects on end-plate reaction with the change of beam parameters
The effects of the changes of different beam parameters on the end plate reactions are shown in the curves in Figures 12a-12d. It had been found that end-plate reaction increases with increase of beam height, flange thickness, web thickness, and beam width. This is because increasing any one of these parameters results in an increased moment capacity of the beam. Thus to counter the increase in moment, a greater end-plate thickness is required and as a result end-plate reaction also increases.

Conclusion
This study originated with the aim to provide an idea about temperature effects on end-plate connection. How end-plate reaction varies with temperature was the problem. The conclusions are mentioned below, ■ The end-plate reaction at 204°C is found very close to reaction found at 20°C.
■ At temperature 316°C, end-plate reaction is found 61% of reaction found at temperature 20°C.