 Open Access
 Authors : Sanmati Vikas T L , Athrey S Katti
 Paper ID : IJERTV9IS060827
 Volume & Issue : Volume 09, Issue 06 (June 2020)
 Published (First Online): 03072020
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Design and Finite Element Analysis of Shear Fitting for the Vertical Tail of An Aircraft
Sanmati Vikas T L1 1Kaunas University of Technology,
Kaunas, Lithuania
Athrey S Katti 2
2Visvesvaraya Technological University Belagavi, Karnataka, India
Abstract – Aircraft consist of different types of components such as elevators, rudders, flaps, ailerons, winglets, spoilers, etc. The tail section of an aircraft or otherwise referred to as the empennage, plays an important role in the generation of pitch and yaw movements. This is generated by the elevators and rudder installed on the horizontal and vertical stabilizers respectively. These stabilizers experience different types of loads during flight. These loads are distributed to the fuselage through fittings. These fittings are also responsible for forming a connection between the empennage and the fuselage. Different types of fittings namely shear fitting, bending fitting, hinge fitting etc are used for this purpose. This paper is a case study and mainly focuses on the design methodology and finite element analysis of shear fitting for vertical tail of a small aircraft. Suitable method is followed to design the shear fitting which involves performing numerical calculation, creating a solid model and performing the finite element analysis. The results are compared and dimensions are finalized.
Keywords Aircraft, stabilizers, shear fitting, vertical tail, finite element analysis

INTRODUCTION
Different types of fittings are used in various parts of the aircraft. The attachment of all major primary structures like the wing, landing gear, horizontal tail, vertical tail etc is achieved through fittings. The basic function of an aircrafts structure is to transmit and resist the applied loads, provide and maintain the aerodynamic shape while protecting the passengers and cargo from the various forces which the aircraft is subjected to during flight. Most aircrafts use either the monocoque or semi monocoque type of construction. In the semimonocoque construction the outer surface or skin of the aircraft is usually supported by transverse frames and longitudinal stiffening members to enable it to resist the compressive, bending and torsional loads without buckling. In case of monocoque construction the skin has to resist both normal and shear loads. The main purpose of a fitting is to form the interface between two components and also transfer the loads from the larger component to the smaller component, a very good example for this is, the load transfer from the vertical tail to the fuselage. The empennage consists of the horizontal and vertical stabilizers which experience aerodynamic loads and these loads will be transferred to fuselage with the help of different types of fittings such as shear fitting, bending fitting and hinge fitting. The nomenclature of these depends on the type of loads they transfer to the fuselage. A Shear fitting transfers shear loads, whereas a bending fitting is responsible for transferring the banding loads. A fitting mainly consists of a lug and a flange with fastener holes. This paper is a case study of the design and analysis of the shear fitting of the vertical tail. The vertical tail
consists of ribs, spars, stringers and skin panels, each of these components experience different types of loads and the sum total effect of this has to be transferred to the fuselage via the various fitting combinations. The arrangement of the different types of fittings plays an important role in the transfer of loads. Fittings are placed on the bottom rib of the vertical tail with the arrangement of a shear fitting near the leading edge followed by two bending fittings, one in the middle and one in the trailing edge of the rib. The placement of fittings is done in conjunction with the location of spars. These fittings are primary structures and their failure may lead to the catastrophic failure of the entire aircraft.

LITERATURE SURVEY
In the paper Design and Analysis of Lug Joint in an Airframe Structure Using Finite Element Method author C V Rama Krishna et al. carried out a design and FEA approach for the typical lug joint which is a representative of an aircraft structure application. Design of lug in this paper provides a safety against lug failure and pin failure when the lug is under axial loading condition. Margin of safety for lug joint is computed using two methods max peak stress and stress averaged over the contact area but in the max peak stress the predicted margins were much less than those calculated from the theoretical calculations. The shear fitting transfers the shear loads but, it is critical due to axial loading, a shear fitting consists of two main parts, namely the lug and a flange. A lug, also known as a lifting lug or a pad eye, is essentially a plate with a hole in it where the hole is sized to fit a clevis pin. Lugs are used in combination with clevis pins to transmit load between different mechanical components. When axial load is applied on the shear fitting the lug can fail under different condition as mentioned below [1].

Tension failure;

Shear tearout;

Bearing failure.
Fig.1, represents the lug failure mode under the action of axial tensile force represented by the arrow and the failure occurs across the net section of the lug in the middle region of the lug, as highlighted below. Fig.2, represents the failure of the lug by shear tearout when being loaded axially. Shear tearout occurs when shear is predominant and the failure region is at 45 degrees from the loading axis, as shown above. Fig.3, represents the bearing failure of the lug under axial loading condition. This failure which occurs in the lug when the applied
load crosses the elastic limit, and it may also lead to shear tear out.
Fig 1. Represents the tension failure of the lug in axial loading condition.
Fig 2. Represents the shear tearout of lug under axial loading condition.
Fig 3. Represents the bearing failure of lug under axial loading condition.
According to author I S Raju et al. in his paper Structural Analysis of the Right Rear Lug of American Airlines Flight 587 have carried out a comparative case study using finite element analysis on a right rear lug of the American Airlines Flight 587
– Airbus A300600R.The evaluation of the load experiencing on the right rear lug is done by using global models of the vertical tail, local models near the right rear lug, and a globallocal analysis procedure. The analysis of lug is carried out in two approach where first is solidshell type modelling is used, and in the second approach, layeredshell type modelling is used. Both the approach is use to progressive failure analysis to determine the load, mode, and location of failure in the right rear lug under loading representative of an Airbus certification. Both analyses were in excellent agreement with each other on the predicted failure loads, failure mode, and location of failure. Finally, when the failure mode of the right rear lug for the 1985certification test, 2003subcomponent test, and the accident load case is identified as a cleavagetype failure. For the accident case, the predicted failure load for the right rear lug from the PFA is greater than 1.98 times the limit load of the lugs [2].
According to HIS ESDU 91008 strength analysis of the lug can be achieved when the lug is under in plane axial, transvers or oblique loading condition from a clearance fit pin. Other ESDU methods evaluate the stress concentration due to the hole, the stress due to an interferencefit bsh, the endurance of a lug under repeated loading and the stress intensity factors for cracks in loaded holes [3].
The lug analysis can be done in different methods as mentioned below:
Simplified analysis method – This method involves assuming the nature of failure and calculating the FOS (Factor of safety). This method seems to be easy but it doesnt give an exact result.
Air force method – This method considers most of the failure modes as mentioned above, and uses empirical curves to determine more accurate allowable loads. This method allows for lugs under axial loading, transverse loading, and oblique loading. This method also accounts for the interaction between the lug and the pin.
ASME BTH The American Society for Mechanical Engineers, method considers most of the failure modes above, and uses simplified equations with correction factors based on empirical data to determine more accurate allowable loads. This method is simpler than the Air Force Method, but it only allows for lugs under axial loading and does not account for the interaction between the lug and the pin [4].
The shear fitting is designed at the vertical tail and fuselage interface of an aircraft which is experiencing a suitable load. In this paper for the hand calculations ESDU 91008 method is followed which is closer to the air force method. Here the shear fitting is designed for the critical load case, after identifying the critical loads by performing the load case corelation, then with the help of finite element method analysis is carried out to see the behaviour of the fitting and improvise its design.
Vertical tail of an aircraft plays an important role since it controls the yawing motion of the aircraft, and its seen in all commercial aircrafts, except for some fighter aircrafts adopting the delta wing construction. Vertical tail of an aircraft experiences different types of loads when it is in air, or during takeoff, or when its taxing. It experiences the maximum loads when its in the air and performing a manoeuvre. A typical vertical tail for a 17seater aircraft is as shown in the Fig.4.
The ribs of the vertical tail predominantly receive the shear loads, whereas, the spars take up the bending loads. In order to transfer these loads an appropriate configuration of fittings is required. The load path is usually from the skin to the ribs followed by the spar and then to the fittings, and the fittings finally transfer the load to the fuselage. Ribs are discontinuous members and spars are long continuous members which run from the root rib to the tip of the vertical tail. The fittings are usually mounter onto the root rib of the vertical tail.
Fig.4, represents the finite element model and Fig.5, shows the dimensions of the vertical tail of a small aircraft. It consists of seven ribs, three spars and skin panels with stringers. According to the aircraft coordinate load is applied in the yaxis direction as shown in the figure.
Fig 4. Represents the FEA model of a vertical tail of an aircraft.
Fig 5. Represents the dimensions of a vertical tail of an aircraft.
After modelling the vertical tail, fittings points are created by taking spars as the reference points, because a majority of load is borne by the spars and the load transfer occurs from the spar to the fittings. The fitting configuration used in this vertical tail design is as shown in the figure below.
Fig 6. Represents the fitting configuration for the vertical tail of an aircraft.
Positions of the different types of fittings is represented in Fig.6, The shear fitting is located at the leading edge of the root rib, followed by two bending fittings located in the middle and the trailing edge of the root rib. This combination of fittings or
this arrangement is considered for the fact that a bending fitting is a combination of two shear fittings oriented in a different manner, another main advantage of this configuration is that even if the front fitting which is a shear fitting fails, it will not lead to a catastrophic failure as the two bending fittings will aid in taking up its load. If we went with a configuration of two shear fittings and only one bending fitting then, in case of failure of one of the shear fittings, the load in ydirection which has a predominant effect and creates large bending force, will not be diffused completely and ultimately lead to the failure of the entire vertical tail. A shear fitting though transfers shear loads, it is critical due to axial loading. In this study the failsafe design philosophy is adopted.


METHODOLOGY
Designing and analysis of the shear fitting involves performing the classical calculations of failure of lug under different loading conditions, creation of CAD model, performing finite element analysis with the twodimensional and threedimensional idealizations of the elements, and finalizing the minimum necessary dimensions for the fitting. Initially vertical tail is subjected to a limit load of 10000kg. The design load calculation is done in accordance with FAR 25.303, where the limit load is multiplied by a factor of 1.5. This yields a design load of 15000kg or 147105N. This load is applied as a pressure load on the surface of the vertical tail in the preprocesser, which distributes the load based on the surface area and ordinates. In order to obtain the critical loads acting on the fitting, a load case corelation has to be performed, for which load cases are to be created. Since there are three different fittings it is necessary to create six load cases which are as mentioned below.

First case – Intact case.

Second case – Front fitting failure (shear fitting) (FF).

Third case – Middle fitting left hand failure (bending fitting) (MFLH).

Fourth case – Middle fitting right hand failure (bending fitting) (MFRH).

Fifth case – Rear fitting left hand failure (bending fitting) (RFLH).

Sixth case Rear fitting right hand failure (bending fitting) (RFRH).
Fig 7. Represents the position of the fittings.
Fig.7, represents the positions of the fittings, where right hand side is abbreviated as RH and lefthand side as LH. From the figure it is clear that front fitting is at the leading edge of the root rib which is a shear fitting followed by middle and rear fittings which are bending fittings. Shear fitting consist of a
single lug, whereas, a bending fitting consist of two lugs so it is a combination of two shear fittings. The fitting points are idealized and analysis performed in order to generate the following load cases. It is necessary to study different cases
because the philosophy followed is fail safe design. When the analysis is carried out for the vertical tail load cases are generated and load case corelation performed, which, is as follows.
TABLE 1. REPRESENTS THE INTACT LOAD CASE.
Description
Case name
Fittings
Node No
Fx
Fy
Fz
Case 1 [Intact – Design
Loads]
Intact
FF
10001
19249.3
0
44140
MFLH
10002
0
127025
561837
MFRH
10003
0
57785.5
630335.4
RFLH
10004
0
23457.75
525297
RFRH
10005
0
11396.1
508319.5
TABLE 2. REPRESENTS THE FF FAIL LOAD CASE.
Description
Case name
Fittings
Node No
Fx
Fy
Fz
Case 2 [Fail Safe Case – Limit Loads]
FF Failed
FF
10001
0
0
0
MFLH
10002
0
70109.5
404307
MFCenter
10006
12832.9
0
0
MFRH
10003
0
53097.6
390476.5
RFLH
10004
0
4441.895
335161
RFRH
10005
0
18794.16
353911.8
TABLE 3. REPRESENTS THE MFLH FAIL LOAD CASE.
Description
Case name
Fittings
Node No
Fx
Fy
Fz
Case 3
FailSafe Condition
MF LH Failed
FF
10001
12832.9
0
137840
MFLH
10002
0
0
0
MFRH
10003
0
123207
264860.5
RFLH
10004
0
56043.36
699995
RFRH
10005
0
32807.4
577895
TABLE 4. REPRESENTS THE MFRH FAIL LOAD CASE.
Description
Case name
Fittings
Node No
Fx
Fy
Fz
Case 4
FailSafe Condition
MF RH Failed
FF
10001
12832.9
0
96154.77
MFLH
10002
0
123207
208240
MFRH
10003
0
0
0
RFLH
10004
0
31179.1
611887
RFRH
10005
0
54414.98
728892
TABLE 5. REPRESENTS THE RFLH FAIL LOAD CASE.
Description
Case name
Fittings
Node No
Fx
Fy
Fz
Case 5
FailSafe Condition
RF LH Failed
FF
10001
12832.9
0
34308.28
MFLH
10002
0
19727.5
724857
MFRH
10003
0
103480
641661.3
RFLH
10004
0
0
0
RFRH
10005
0
23235.91
53808.15
TABLE 6. REPRESENTS THE RFRH FAIL LOAD CASE.
Description
Case name
Fittings
Node No
Fx
Fy
Fz
Case 5
FailSafe Condition
RF RH Failed
FF
10001
12832.9
0
90834.3
MFLH
10002
0
147264
589238
MFRH
10003
0
24057.49
759059.2
RFLH
10004
0
23235.91
74067.1
RFRH
10005
0
0
0
The vertical tail is oriented in z axis and force is applied in the direction of y axis. In the Table.1, the first is represented which consist of the intact case. The reaction forces are generated in the three directions Fx, Fy and Fz. In the first case which is an intact case, none of fittings fail and the load acting in the Fx and Fz directions are 19249.3N and 44139.997N. The intact load case is solved for the design loads, and if the fitting is designed for these loads then it would give us an overdesigned result. The aircraft never experiences the design loads in its lifetime; hence the limit loads are considered for the calculations. The negative sign of the loads is ignored and the positive values considered. Table.2, represents the front fitting fail load case, where the front fitting fails and it will not transfer any loads, but instead the other fittings will accommodate for this and share the load which was diffused by the shear fitting to the fuselage. We cannot design the lug for the second case since there is no load representation as it is failing. If we design for the second case
by keeping other loads as a reference then the lug design will be over designed which can lead to overweight. Table.3, represents the third case where middle fitting LH fail which is a bending fitting, the load acting in Fx direction on the front fitting is 12832.86N and 137840.47N in Fz direction. Table.4, represents the fourth case which is a MFRH fail, where the load acting on the front fitting in the Fx direction is 12832.86N and 96154.77N in the Fz direction. Table.5, represents the fifth case which is a rear fitting LH fail (bending fitting) where the load acting on the front fitting in the Fx direction is 12832.863N and in Fz direction 34308.27N. Table.6, represents the sixth case which is an RFRH fail where the load acting on the front fitting is 12832.863N in the Fx direction and in the Fz direction load acting is 90834.26N. From all the load cases maximum limit loads acting on the fittings is considered for the design of lug which is as show in the below table.
TABLE 7. REPRESENTS THE MAXIMUM LOAD ACTING ON THE FITTINGS IN THE DIFFERENT CASES.
Fittings
Fx
Fy
Fz
Failure cases
FF
12833
137840
MFLH
MF
24057
759059
RFRH
RF
54415
728892
MFRH
In the Table.7, the maximum loads acting on the fittings in different load cases are tabulated, where the maximum limit load for front fitting (shear fitting) is 12833N in the Fx direction and 137840N in the Fy direction. Keeping these values as a limit load, further calculations are made. For the design of the bending fitting, other two load cases must be considered.
Material used for the design of the shear fitting is Al 2024 T351 with a thickness of 40 < t < 62 and A grade material. Required parameters from the MIL HDBK 5H are taken into account which are as mentioned below. (MILITARY HANDBOOK1998).
Ultimate tensile strength L (Long) Fts= 62ksi = 428N/mm2 Ultimate tensile strength LT (Long Transverse) Ftus= 62ksi = 428N/mm2
Yield stress/0.2% of proof stress, cross grain Fyts= 42ksi = 298N/mm2
Ultimate bearing strength in L, Fbs(e/D = 1.5)= 94ksi = 649N/mm2
Ultimate bearing strength in L, Fbs(e/D = 2) = 115ksi = 794N/mm2
Factor of safety = 1.5 Fitting factor = 1.15.
Since the loading for the front fitting is 12833 in Fx direction and 137840 in the Fy direction initia lug dimensions are assumed as
Width (W) = 60mm
Fig 7. Represents the specification of the lug.


CALCULATIONS
The calculations for the lug under tension failure condition is as below.
Ptux = Ktux ftux (W dh) t (1)
Where, Ptus is the allowable ultimate axial tension loading ftux is the allowable tensile ultimate stress in axial direction. dh is the lug hole diameter
t is the thickness of the lug
Ktux is the axial tensile failure factor which is obtained from the material graph with respect to ratio of W and a which has
dh W
the value of 0.96 (for the material Al2024).
Hole diameter (dh) = 24mm
Distance from centre of circle to end of the lug is (a) = 36mm Thickness of the lug = 18mm
Tensile reserve factor RFT Ptux = 266250.24N
= Allowable
Actual
(2)
Factual = Fz. * Fitting factor.
Factual = 58516N RFT = 1.67
The calculation of lug under shear – bearing condition is as below
Pqux = Kqux ftum dh t (3)
Pquxis the allowable ultimate axial shear bearing load
Kqux is the axial shear bearing failure factor which is obtained

RESULTS AND DISCUSSIONS
Initially the model of the lug is created with 2D elements, specifically using 2Dquad elements for meshing, and considering the dimensions calculated the analysis is performed. the model is as shown below.
by the material graph for the ratio of a
dh
and dh which has the
t
value of 1.45
ftum is the minimum allowable ultimate tensile stress with respect to grain direction in plane of lug
dh is the lug hole diameter tis the thickness of the lug
Factual= Fz * Fitting factor
Fig 9. Represents the shear fitting with six fasteners positions with 2D
element mesh.
RFS
= Allowable Actual
(4)
Fig.9, represents the shear fitting with a 2D element mesh, which consists of flange as well as lug with a hole. Flange has
Pqux = 268099.2N RFS = 1.7
The calculation of lug under transverse loading condition is calculated as below
Puy= Kuy ftum dh t (5)
Puy is the allowable load in the transverse direction
Kuy is the transverse failure factor which is a ratio of Ae
dh.t
the dimension of 72mm cross 60mm. Flange consist of six
fasteners positions and they are placed in the zigzag pattern.
When the analysis is carried out, two main components are observed Vonmises stress and maximum principal stress. Von mises stress represents shear critical regions, whereas, maximum principal stress represents bending critical regions. Results of this analysis are as shown in the figure below.
ftum is the minimum allowable ultimate tensile stress dh is the lug hole diameter
t is the thickness of the lug Ae is the effective area
A1 = A4 = (a dh sin45) * t = 495.26mm2 (6)
W dh
W dh
2
A2 = ( )t = 324mm2 (7)
2 2
A3 = (a dh)t = 432mm2 (8)
2
e
e
A = 6
( 3 )+( 1 )+( 1 )+( 1 )
= 445.1mm2 (9)
A1 A2
Kuy = 1.14
A3 A4
Puy = 210.78Ã—103N
RFtran = 14.28
The calculation of lug under oblique loading condition is as calculated below
0.625
Fig 10. Represents the Vonmises stress for the combined loading acting on the shear fitting.
Analysis result for the 2D idealization is as shown in the Fig.10, which represents the Vonmises stress for the combined loading. Combined loading consists of axial load and the
1.6 1.6
1.6 1.6
RFult = [ 1 ]
( 1 ) +( 1 )
= 1.637 (10)
transverse load. The highest stress observed in the combined loading is 535N/mm2 near the flange and lug intersection area.
RFt RFtran
After the calculation of reserve factors for different loading conditions it can be observed that RF of tension failure condition as well as shear bearing failure condition is critical, keeping this in mind shear fitting sizing is carried out with the help of finite element analysis.
Fig 11. Represents the maximum principal stress for the combined load in the fitting.
Fig.11, represents the maximum principal stress in the model under the action of combined loads. The highest maximum principal stress observed in the combined loading is 519N/mm2 near the flange and lug intersection area, since load has to be transferred from vertical tail to the fuselage through shear fitting it is necessary to transfer this stress from flange and lug intersection area to the lug hole which is achieved by adding extra gussets and increasing the flange dimension as well as increasing the number of fasteners.
Fig 12. Represents the shear fitting with 2D mesh model having eight fasteners and two gussets.
After observing the results from the 2D idealization of the shear fitting with initial dimensions, changes are made for the second iteration. Fig.12, shows the meshed model of shear fitting which consist of eight fasteners with 40mm inter fasteners distance in the Ydirection and 18mm in the Xdirection. Flange dimensions are 132mm in Ydirection and 60mm in X – direction, gussets end at a distance of 36mm above centre of the lug hole. Gussets are added to stiffen the flange and to transfer the stress from flange and lug intersection area to lug hole region.
Fig 13. Represents the Vonmises stress for the 2D mesh of shear fitting with eight fasteners and two gussets
From the Fig.13, it can be observed that under combined loading of the shear fitting with eight fasteners and two gussets, the highest Vonmises stress is 547N/mm2 and the stress has shifted from flange and lug intersection area to region above the lug hole and much closer to the lug hole.
Fig 14. Represents the max principal stress for 2D mesh of the shear fitting with eight fasteners and two gussets
In the Fig.14, combined loading acting on the shear fitting after adding the gusset, increasing the flange dimensions and increasing the number of fasteners, the highest value of maximum principal stress observed is 556N/mm2 and stresses are reduced in small quantity near the flange and lug intersection area. The overall stresses are increased compared to previous analysis but the main agenda is to shift the stress from flange to the lug hole and stiffen the flange. After observing the change in stress further more modifications are made and to get more accurate results design is carried out with 3D idealization and the model is meshed using 3Dtetrahedral elements.
Fig 15. Represents the 3D model of shear fitting with eight fasteners hole.
Fig.15, represents the 3D model of the shear fitting, which consist of eight fastener holes with 40mm inter fastener distance. Flange has the thickness of 12mm, lug has the thickness of 18mm, gusset has the thickness of 10mm and an extra thickness of 7mm is given near the lug hole since high stresses were observed near this region in the previous analysis, in this model gussets are placed along the direction of the lug.
Fig 16. Represents the Vonmises stress for the shear fitting with eight fasteners position.
From the Fig.16, it can be observed that Vonmises stress in a combined loading is 564N/mm2 and it is more predominant inside the lug hole but still higher stress can be seen near the flange and lug intersection area.
Fig 17. Represents the max principal stress in the shear fitting with eight fasteners position.
Fig.17, represents the maximum principal stress under combined loading, where, the stress observed is 574N/mm2 and higher stresses are observed near the lug hole and at the flange and lug interface. The mass of the shear fitting represented in Fig 16 is 945gm and the surface are is 60749.66mm2.
In order to reduce the mass and surface area of the fitting, major changes are made to the dimensions. Also, it is necessary to reduce the stress concentration due to the abrupt change in geometry near the flange and lug intersection region. Which is as shown in the ig 17. Though the shear fitting transfers shear loads, and is subjected to combined loading, it is predominantly loaded in the axial direction and its failure is characterised by this load. The stresses due to the transverse loading are within the limits of the chosen aluminium material.
Fig 18. Represents the modified 3D model of shear fitting with six fasteners position.
Fig.18, represents the 3D model of the revised design of the shear fitting consisting of six fasteners, a flange dimensions of 90mm in the Ydirection and 115mm in the Xdirection, and a thickness of 12mm. The thickness of the lug is 16mm and 12 mm near the lug hole region. The inter fastener distance is kept 40mm.
Fig 19. Represents the Vonmises stress for the fitting under axial loading condition.
Vonmises stresses in the fitting subjected to axial loading are plotted in the Fig.19. The highest stress observed is 518N/mm2, which is concentrated inside the lug hole and the intersection region of lug and flange.
Fig 20. Represents the Von mises stress in the shear fitting under transverse loading condition.
Fig.20, represents the Vonmises stresses in the shear fitting when it is subjected to transverse loading. The highest stress observed is 143N/mm2 which lies within the allowable limit of the chosen material (Al2024), by this it can be inferred that stress caused due to transverse loading is within the limit and it can be neglected because shear fitting is not critical due to transverse loading condition, and is critical due to axial loading condition.
Fig 21. Represents the Vonmises stress in the shear fitting under combined loading condition.
Fig.21, represents the vonmises stresses in the shear fitting model when it is under combined loading condition. The highest stress observed is 594N/mm2 which appears near the intersection region of the lug and the flange and inside the lug hole. The major improvement in this design is the reduction in the dimensions which reduces the overall volume and eliminates two fasteners which ultimately causes an appreciable reduction in the overall weight. But, the higher stresses near the flange area has to be reduced. This is achieved by modifying the design and providing additional gussets which is as shown in Fig.21.
Fig 22. Represents the improved design of shear fitting with four gussets and six fasteners position.
Fig.22, represents the improved design of the shear fitting, where the flange dimensions are 120mm in the Ydirection and 91mm in the Xdirection, with a thickness of 12mm. The lug hole radius is 12mm and the lug thickness is 16mm, the distance from the lug centre to the flange is 90mm. additional thickness of 14mm is provided on both sides of the lug near the hole. The distance from the lug hole to the bottom end of the lug is 36mm. The gussets provided are 5mm in thickness and there are six fasteners in this design with a 40mm inter fastener distance. Fillets radius of 7.5mm and 5mm are maintained throughout the model wherever necessary.
Fig 23. Represents the analysis results for the improved design of shear fitting model under axial loading.
Fig.23, represents the analysis results for the improved design of shear fitting under axial loading condition, highest Vonmises stress experienced is 442N/mm2 inside the lug hole. In the previous shear fitting model stress concentration was near the intersection area of lug and flange but, addition of four gussets as shown in the Fig.21, caused a decrease in the stress concentration near this region and a higher concentration of stress is observed inside the lug hole. Though the allowable tensile strength of chosen material is 428N/mm2 the stress
obtained in the model is accepted because, this stress value will come down once the bolt is inserted, thus making the design safe.
Fig 24. Represents the analysis results for improved design of 3D shear fitting model under axial loading.
Fig.24, represents the improved design of 3D shear fitting model under axial loading condition, where the maximum principal stress is 454N/mm2 and is highly concentrated inside the lug hole. The maximum principal stress has dropped down to 454N/mm2 near the intersection area of lug and flange, which is lesser when compared to the previous design iteration, achieved by adding extra gussets and increased the thickness near the required regions.
Fig 25. Represents the analysis results for improved design of 3D shear fitting model under combined loading.
Fig.2,5 represents the analysis result for the improved design of 3D shear fitting model under combined loading where, the highest Vonmises stress is 455N/mm2 and is seen predominantly inside the lug hole. The stresses at the lug and flange interface are 425N/mm2 which are within the allowable limits of the chosen material.
The total mass of the improved design of shear fitting is 910.40gm with a total surface area of 56640.65mm2 and a total volume of 328915.86mm3. When the improved design of shear fitting is compared with the fitting of eight fasteners configuration (first 3D model) there is difference of 45gm in the mass, 10722.62mm2 of surface area and volume difference of 4109.01mm3.
Fig 26. Represents the analysis results for improved design of 3D shear fitting model under combined loading.
The analysis result for the improved design of 3D shear fitting model under the action of combined loading is shown in Fig.26. The highest maximum principal stresses are 459N/mm2 which can be seen predominantly inside the lug hole and the highest stresses observed near the intersection areas are 418N/mm2 which is well within the material chosen allowable limit. By keeping the highest stresses acting inside the lug hole as a reference, the bolt design as well as design of the fork end of the fitting can be carried out.
Fig 27. Represents the constrained bolt forces.
For the fitting, generally bolt fasteners are used since they are easy to handle and easily replaceable. Fig.27, represents the constrained bolt forces for the 3D shear fitting model when it is under combined loading condition. It can be seen from the analysis that the highest force experienced is 34500N by one of
the fasteners at the edge, This value is a reference value for the design of bolt for the shear fitting, this paper is mainly focused on design and analysis of shear fitting for the vertical tail of a small aircraft.
finalized, arriving at a flange dimension of 120mm cross 91mm, flange thickness of 12mm, lug thickness of 16mm with four gussets and six fasteners positions with 40mm inter fastener distance. After the analysis of improved design of shear fitting the stress levels were analysed and were found to be within the material allowable limits, which is 428N/mm2. The material chosen for the analysis is Al2024T351 (Agrade material). Since the higher stresses of the improved design of shear fitting are within the material allowable limit, dimensions obtained for the improved design can be considered as the final dimensions and it is suitable for the vertical tail of a small aircraft. In the future the method followed in this paper can help in the analysis of shear fitting for different material and loading condition, further this paper will also prove useful in analysing the effect of the configuration chosen for the vertical tail to fuselage interface.
ACKNOWLEDGMENT
We would like to express our sincere gratitude and thanks to our guide, teacher and mentor Mr. Ashok Sanmani for his guidance and constant support throughout. We credit all our learnings to our mentor without whom we could not have achieved success in the research.
We would like to take this opportunity to express and extend our gratitude to our parents for their constant support and encouragement.
Fig 28. Orthographic drawing of the improved design of shear fitting with all the dimensions.
Fig.28, represent the orthographic drawing of the final design of the shear fitting, with all the final dimensions.

CONCLUSION
Fittings used to attach the vertical tail of an aircraft to its fuselage are primary structures which form an important part in the empennage assembly. They also perform the task of transferring the loads to the fuselage from the tail. Depending on the configuration used, a shear fitting primarily transfers the shear loads, but its criticality depends on the axial load acting on it, and the effect of the transverse load is not very dominant, which is very evident from the analysis performed in this paper. Analysis of the vertical tail, with shear fitting at the leading edge of the bottom rib followed by two bending fittings was carried out initially, which output reaction forces of 12833N and 137840N in Fx and Fy directions respectively. With these reaction forces as a reference for the initial lug dimensions, calculations were performed, for different loading conditions, Failure criteria comprising tension, shear, bearing under transverse, axial and combined loading was were taken into account. This showed that the fitting was critical due to axial loading condition. Preliminary dimensions of the lug were 60mm in width, 24mm lug diameter, 36mm from lug hole centre to the bottom of the lug, 18mm lug thickness and flange dimension of 72mm cross 60mm with six fasteners placed in a zigzag pattern, and modelling was done with twodimensional idealization. The analysis results showed vonmises stress to be 535N/mm2 for the combined condition whereas maximum principal stress was 519N/mm2. After several iterations, dimensions of the shear fitting were completely modified and
REFERENCES

C.V. Rama Krishna, A MohaboobBasha, Failure modes of lug, Design and analysis of lug joint in an aircraft structure using finite element method, Page No 2282, 2017.

I. S. Raju, E. H. Glaessgen , B. H. Mason, T. Krishnamurthy, and C. G. DÃ¡vila, Structural Analysis of the Right Rear Lug of American Airlines Flight 587, April 2020.

IHS ESDU Design of Lugs, An increasingly pragmatic and costeffective approach to material selection and testing, Oct 2011.

J.K. Bennett, K.R. Obee, M.E. Grayley, ESDU91008, Axial loading, tension, shear, bearing, Page No 4.

Military Handbook, Design mechanical and physical properties of 2024 aluminium alloy, MILHDBK5H Page.No. 370, table 3.2.30, 1998.

Rajshekar H Nagaraj, Vishal H Borkar Weight optimization of vertical tail in board box through stress analysis approach, Overview of vertical tail, Page No 72.
BIOGRAPHIES
Sanmati Vikas T L
M.S Aerospace Engineering Kaunas Technological University Lithuania.
Athrey S Katti
B.E Mechanical Engineering Visvesvaraya Technological University Belagavi, Karnataka, India.