## 1 Introduction  
Wind turbine generators (WTGs) have gained much attention because they utilize one of the cleanest and most environmentally friendly energy resources as an alternative to fossil fuels [1]. A modern wind turbine typically consists of blades, a nacelle including a generator and gearbox, and a substructure such as a tower. The two or three blades are coupled to the rotatable hub through a pitch bearing system by the blade root joint connection [2].  
Currently, two types of root joint connections are widely used in commercial wind turbine blades: steel insert type and T-bolt (also referred to as \"IKEA\" connection) type, as shown in Figure 1[3, 4]. Traditionally, T-bolts or IKEA connections have been a popular choice for connecting a blade to the hub of the wind turbine due to the relatively easy manufacturing process and convenience of replacement. T-bolt joints have cross-bolts positioned perpendicular to the root cylinder surface, and longitudinal bolts connect the hub to the cross-bolt [5]. [PERSON] investigated the T-bolt joint both numerically and with experiments and concluded that the T-bolt joint is reliable and inexpensive [6]. As blade length has increased, however, a couple of issues have come up such as a transportation difficulty and excessive material usage due to the increased blade circle diameter (BCD) and increased root layer thickness to ensure structural durability [7, 8].  
During the last decade, the insert joint technology has been applied, especially to large offshore blades, which could reduce the BCD and weight as an alternative to T-bolted connections [9]. The advantage of the insert joint is that compared to the conventional T-bolt connection about 35% more bolts can be implemented. Further, no damage is caused by drilling, and another potential advantage is that inserts can be included as prefabricated parts in a root infusion [10].  
As blade size becomes larger, a fatigue failure in the root region becomes an increasing problem due to the higher-gravity-induced edgewise loads [11, 12]. That is, as the effect of the higher edgewise fatigue loading on the blade root region becomes critical, the stress concentration factor (SCF) at the bolt thread root that is sensitive to fatigue also becomes an important parameter in addition to the structural integrity of root laminate [13, 14, 15]. Many experiments were performed to ensure the quality of laminated root insert joint, for example, the bonding failure mechanism and manufacturing quality experimentally and numerically [16]. [PERSON] et al. recently performed a failure analysis of a fractured high-strength bolt used in a MW Class wind turbine blade connection system, and concluded that the bolt failure was caused by insufficient tightening and improper manufacturing procedure [17]. There is, however, little work on the stress concentration factor of a bolt-nut joint and a bolt-insert joint connection that depends on the varying geometric parameters of bolts, nut, and insert. Therefore, the comprehensive understanding of SCFs at the thread interface both between the insert and bolt and between the bolt and nut are important to avoid unwanted structural failure, especially for a large blade with M42 bolts.  
In this work, the stress concentration factors on bolted joint connections will be fully investigated with two-dimensional and three-dimensional linear finite element models with contact elements according to the changes of the geometric parameters, including shank diameter, nut height, nut type, and relief cone angle. Based on close investigation, guidelines for choosing the proper connection type for an offshore wind blade root connection will be provided. This work will be also beneficial for designing bolted joint connections of segment or modular blades [18, 19].