Introduction
Wind power generation has been significantly increasing as a new and renewable energy across the world [
1] and have gained much attention according to the high reliability, maturity in technology and cost competitiveness compared to other renewable energies [
2]. Efficiency of wind power plants is a major issue of concern given the steady increase of the size of wind turbines during the last 25 years from approximately a rated power of 50kW and a rotor diameter of 10–15m up to today’s available 5MW machines with a rotor diameter of more than 120 m [
3,
4]. In other words, this change has forced researchers develop more accurate models to predict turbine’s responses and to design with more efficiency. Constructing wind turbine tower’s cost is 15%–20% of the total installation costs [
1] and studies conducted have shown that lattice towers have significantly lower construction costs and can result in 20%–30% reduction in the total project costs [
5,
6,
7].
Joint slip is defined as the relative displacement of jointed members in a bolted joint that is subject to a shear load [
8]. The bolt-holes are always oversized to provide erection tolerance. The relative positions of the bolts within them cause slippage and have some effects on deflection and structural stiffness [
9].
Many studies have been done on joint slip effects in the past years and many analytical models have been proposed based on experimental results. Kravitz and Samuelson [
10], Al-Bermani and Kitipornchai [
11], Santhakumar [
12] and Knight and Santhakumar [
13] concluded that the mismatch between tower deflection’s experimental and theoretical results is one of the results of joint slippage. Also, based on the report of Rao et al. [
14] deflections of towers with joint slippage effects are up to 1.9 times greater than the results obtained by linear analytical displacements. Also, He and Li [
15] concluded that neglecting possible cyclic loading and assuming the wind loading as the only dominant loading is not persuasive enough and would cause estimation errors. Nevertheless, Ungkurapinan et al. [
8] reported joint slip behavior in transmission towers in a specific single-leg angel and lap splice bolted joints with monotonic loading in an experimental study. They developed empirical mathematical expressions to describe the slippage effects.
Experimental study and results
Joint tests
According to Ungkurapinan et al. [
6], variables which can influence bolted joint deformation are: (a) applied load; (b) poor workmanship; (c) bolt properties; (d) number of bolts; (e) pitch of bolts; (f) bolt diameter; (g) bolt arrangement; (h) bolt length; (i) angle properties; (j) the ratio of the effective net area of steel angle, A
ne, and the shear area of the bolts, A
s; (k) the ratio of the effective net area of steel angle, A
ne, and the gross area of the steel angle, A
g; (l) extent of corrosion; (m) nature of faying surfaces; (n) bolt tightening method; (o) end distance and edge distance; (p) load type; and (q) single or multiple shear. Some of Ungkurapinan’s assumptions such as supposed clearance applied torque for friction bolts either had mismatches with the codes or were not general assumptions. The number of bolts varied from 1–4 bolts, loads are monotonically applied and the connected bolts had less capacity than the section.
In the experimental study, the applied load (a) was measured while the number of bolts (d), bolt diameter (f), and bolt arrangement (g), were changed. Moreover, it was assumed that the connected bolts have more capacity than the section does. The other parameters were held constant. For example, the parameters, i.e., angle property complied with CAN/CSA S6-06 [
16], (i), the end distance and the edge distance (o) were held constant due to AISC Specification [
17] in each experiment by using bolts of B 33.4 grade. Also, load type (p), is cyclic as it naturally is in wind turbines.
Classical lattice towers are constructed of angle sections or a group of angles typically connected with bolted joints which comprise several joint configurations in terms of geometry, continuity, and presence of gusset plates [
18]. In the experiments conducted in this study and for the test specimens, different types of single equal length angles to represent actual joint arrangement in a lattice tower were investigated (see Fig. 1(b) and Table 1).
Four electrical displacement transducers resting on a small steel plate and welded to the top bolt were set up set on each specimen as shown in Fig. 1(a). The focus of this report is on measurement of allowed joint slippage. Moreover, the specimens were tested using the 20L H85261A Hydraulic Testing Machine using a loading rate of 0.004 mm/s and they were placed centrally in the testing machine (as seen in Fig. 6).
Material properties
The results of standard tension tests on the pieces taken from the angles showed that the modulus of elasticity, yield strength, tensile strength and percentage of elongation are 205 GPa, 343 MPa, 507 MPa and 32.25 respectively which correspond to steel conforming to DIN17100-St37. Direct tension tests on bolts results indicate that tensile load and tensile strength are 136.2 kN and 883 MPa, respectively which correspond to B 33.4 grade 5 bolts.
Experimental list
Test specimens were placed in such a way that the load was applied to the corner of the angles (see Fig. 6) and they were bolted to the 50 mm plates as 50 mm plate transformation is negligible and joint slippage could be measured much more accurately and buckling would occur in the member not in the joints which are restrained from buckling. Incorporating 24 joint tests has been done and all tests have been replicated for 3 times for reducing the probable errors, and the curves are the average idealized of these replications. Details of tests specimens, including size and number of bolts and type of angel sections are shown in Fig. 1(b), and reported in Table 1.
Experimental results and discussion
Load versus joint deformation at various stages of loading can be defined in a general diagram as shown in Fig. 2 with a good approximation. This curve includes points 0 to 9. The idealized curves of the experimental study are shown in Figs. 3 to 4 and their values are reported in Tables 2 to 3.
The experimental results indicate that the smallest portion of load-displacement curve occurs before slippage and it is caused by the frictional load transfer. In addition, its elastic stiffness is between points 0 and 1 as shown in Fig. 2. Joint slip which is between points 1 and 2 in Fig. 2 is an early deformation that takes place at an approximately constant shear load or at very low stiffness levels [
8]. In fact, the two members start to slip over each other after reaching the threshold slippage load due to the clearance between the hole and the bolt [
14]. Furthermore, the results show that joint slip takes place during service loads [
14] (between 8kN to 75kN) and it is inversely proportional with the number of bolts. In other words, the more numbers of bolts, the less slippage in the bolts. The results show that if the connected bolts have more capacity than the section, slippage will reach 2 mm which is the standard clearance for bolt sizes up to 24mm in diameter [
14] in spite of Ungkurapina’s report that slip would not reach the maximum possible extents of 3.2 mm and 1.6 mm [
13]. After slippage starts, joint stiffness reduces dramatically until the joint reaches a bearing stage (between points 2 and 3 in Fig.2) [
14]. Furthermore, the slope of this portion is approximately near the elastic stiffness before slippage (between points 0 and 1 in Fig.2). Compression parts start from point 4 in Fig. 4. These parts are similar to the tension parts and consist of 4 portions. The viscous damping ratio (
z) which are often used to judge the capacity of energy dissipation [
19], of all types of connections can be calculated based on load-displacement curves. As it is given in Fig. 5, viscous damping ratio (
z) is
and it is reported in Table 4 Also it must be stated that the area of the elastic portion after slippage is negligible.
Numerical finite element simulation of the experimental tests
The experimental test specimens were modeled three-dimensionally using the Abaqus finite element program version 6.13-4. The specimens were bolted to the 50 mm plates as 50 mm plate transformation is negligible as mentioned before and shown in Fig. 6. Thus, joint slippage could be measured much more accurately and buckling would occur in the member and not in the joints which are restrained from buckling. In the Abaqus models, the bolts and the 50mm plates were modelled by using an 8-node linear brick reduced integration (C3D8R) and the angles were modelled by using an 8-node linear brick (C3D8). These elements have six or seven degrees of freedom at each node in the nodal x-, y-, and z-directions and the warping magnitude was neglected. Load magnitude was defined in such a way that the section had elastic deformation and it was applied to the corner of the angles. Furthermore, it is assumed that the 50mm plates which were welded to a rigid surface were fixed without any rotation and displacement (ENCASTRE U1= U2= U3= UR1= UR2= UR3=0 and the amount of torque applied to the bolts was defined as a bolt load in the computer program. Also, the interaction between the bolts, angles and the 50mm plates was defined as standard finite sliding and standard surface to surface, respectively using the discretization method. The contact property was defined as normally hard contact and allowed separation after contacts and 0.27 as tangential friction coefficient obtained by trial and error in such a way that it could be verified by the experimental results while directionality of the models was assumed isotropic. Three models are shown in Fig.7.
The experimental results (shown in Fig. 3 and Fig.4 and Tables 2–4) are compared with the numerical Abaqus results in Fig. 9 Given that the proposed numerical FE models can predict the real behavior of the prototype with negligible error, it was developed for some other types of angle connection (See Table 5) in order to determine the influence of angle length and thickness, the number of bolts, bolt diameter and the effective area of the connection for joint slip estimation. Details of the specimens, including the size and the number of bolts and the type of angel sections and number of elements used in Abaqus models are shown in Fig. 1(b), and Table 5. Also, the specimens Nos. 1–8 are tested experimentally, and modelled by Abaqus and they are also verified by experimental results while specimens Nos. 9–15 are just modelled by Abaqus. Also, In order to make sure that our reported results are insensitive to the number of elements, we performed mesh sensitivity analysis. As it can be observed from the results for a one representative case, it is clear that we included adequate number of elements and such that the results are clearly independent of the number of elements. Sensitivity analysis of specimen No. 5 (L60×6-4Bolt16) is shown in Fig. 8.
The results of the specimens can lead us to understand the influence and importance of parameters such as the number of bolts, bolt diameter, angle properties, bolt area and net area of section. For instance, the effect of angle thickness can be defined by comparing the results of specimens Nos. 4, 5 and 12; Nos. 2 and 10; Nos. 6, 13 and 14. The specimens which are used for determination of the influence of effective variables such as angle thickness (See Figs. 10(a), (b) and (c)), angle length (See Figs. 10(d) and (e)), number of bolts (See Figs. 10(f) and 10(g)) and bolt area (See Figs. 10(h), (i) and (j)) are listed in Table 6. The results are shown in Fig. 10.
After comparing the results we can conclude that joint behavior under cyclic loading is dependent on the number of bolts, bolt diameter, area of bolts, angle thickness and effective area. In addition, the influence of these parameters can be found. Each parameter has different effect on joint behavior in each part of Fig. 2, also, lattice tower designers sometimes prefer to use one specific bolt diameter according to performance and application simplicity, so they can limit and decrease joint slippage by changing other parameters according to these figures. Generally, bolt diameter is the most important parameter for predicting joint behavior. In other words, comparing the results can sow which parameters have more influence on the various parts of joint behavior.
Conclusions
The proposed results was assessed by verifying the Abaqus FE models with the experimental results and then comparing the verified Abaqus results together. The following should be emphasized regarding this investigation:
1) The comparisons between the predictions of the Abaqus results and the experimental results demonstrated an excellent agreement and the proposed models can predict various types of joint behavior accurately with a negligible error.
2) Joint behavior under cyclic loading is dependent on the number of bolts, bolt diameter, the area of the bolts, angle thickness and effective area. The results show that joint slip takes place during service loads and bolt diameter is the most important parameter for predicting joint behavior.
3) The results show that slippage will reach 2 mm which is the standard clearance for bolt sizes up to 24mm in diameter, if the connected bolts have more capacity than the section.
4) Damping ratio ( z) for all lattice connections can be supposed to be approximately 40 percent.
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