## 1 Introduction
[PERSON] [18; 19; 20; 21; 22] developed formulas for the stresses considering elastic and plastic adhesive material for balanced and unbalanced joints. [PERSON] [23] developed the formulas for balanced joints considering a non-deformable geometry, concluding that the shear stresses do not vary along with the adhesive. [PERSON] and [PERSON] [24; 25] investigates the shear and normal stresses applicable to various adhesive joint configurations and different adherents, with simplified formulas that are easy to apply. [PERSON] [26] following the work of [PERSON] and [PERSON], modified the formulas to estimate the stress of the adhesive, considering the thickness of the adhesive and different thicknesses of the adherents. [PERSON] [27] proposed easy-to-apply formulas for estimating adhesive joints only for balanced adherents. These explicit methods are applied for adherents and adhesives with isotropic properties and linear-elastic analysis. Implicit methods include the following: [PERSON] and [PERSON] [28] who developed an ordinary linear differential equation of the eighth order, where they consider anisotropic adherents and isotropic adhesive. [PERSON] [29], based on the [PERSON] and Reissner method, analyzed the influence of the thickness of the adhesive on the adhesive joint. [PERSON] and [PERSON] [30] included the influence of thermal loads on the adhesive bond and the modelling of the spring-loaded adhesive and presented formulas for the stresses on the top and bottom of the adhesive. [PERSON] [31] proposed formulas considering elastic anisotropic adherents and elastic-plastic isotropic adhesive. These methods recommend using numerical methods and/or finite elements depending on the case to complete the estimation of the stresses of the adhesive joints. The mentioned methods have proposed formulas to statically estimate the stresses and their distribution in the adhesive, however, they have not taken into consideration the behavior of the joint subjected to vibratory loads. These studies are presented by Det Norske Veritas (DNV) [32],[PERSON] [33], and [PERSON] et al. [34], allowing them to estimate the S-N curve of the joint based on the operating cycles. In this investigation, the methodology consists of using general formulas to calculate the stresses of adhesive joints applied in a tubular hybrid joint (see Figure 1), and the accomplishment of a failure criterion of interlaminar stresses in the laminates of the adherents. From the different tests performed with finite element analysis (FEA), it was proved that the tubular reinforcement laminate behaves like an adhesive single-lap joint. Bigwood and Crocombe [24] formulas are used due to different thicknesses and stiffness of the adherents of this joint. These formulas have been validated by [PERSON] and [PERSON] [35] and [PERSON] and [PERSON] [36] using FEA. [PERSON] [35] applied the method to select the epoxy and acrylate adhesive based on the mechanical performance of the bond and subjected to short-duration loads; this analytical method has shown good results with small deformations in the adhesive (30% of the maximum deformation). However, it loses accuracy with greater deformation compared with the nonlinear FEA results. [PERSON] [36] apply the Bigwood [24] method as it is of general use in adhesive joints; they used an L-shaped symmetric T-pull model modelled in FEA with four nodes 2D plane elements, finding satisfactory results in the extreme stress values and the distribution along with the adhesive. From the results of the different studies, we found that depending on the characteristics of the adhesive joint, the adhesive or the interface between the FRP laminates adherents 1 and 2 may fail [18]. For this reason, when studying a hybrid joint using tubular stiffeners, consideration should be given to the following:  
1. The limit of the interlaminar stresses of the adherents, [PERSON] [37]. 2. The fatigue on the joint to guarantee its useful life, [PERSON] [32].