8/2/2019 ATTACCHI

1/8

ARGOMENTO:

Example: Lug Stress Analysis

INDEX

1. Scope ........................................................... ........................................................... ........................................................ 22. References and symbols ........................................................... ............................................................... ....................... 2

Pin section area ............................................................... ..................................................................... ....................... 2Ultimate allowable tension load............................................................... ................................................................ ... 2

3. Assumptions ........................................................... .............................................................. .......................................... 44. Load conditions .................................................... ................................................................ .......................................... 45. Spar fittings............................................... .................................................................. .................................................... 5

5.1 Axial Load: load condition U.L............................................................. ............................................................... ... 55.2 Transversal Load: load condition U.L. ........................................................... .......................................................... 65.3 Oblique Load: load condition U.L. ........................................................... ............................................................. ... 6

8. Pin analysis...................................................... ........................................................... .................................................... 78.1 Spar fitting pin .................................................... ............................................................ .......................................... 78.1.1 Ultimate shear ............................................................... .............................................................. ....................... 78.1.2 Ultimate bending .............................................................. .................................................................... ............. 7

8/2/2019 ATTACCHI

2/8

MEMO DATE

REV. - PAGE 2 of82

1. Scope

The aim of the present report is to give an example of lug stress analysis and to calculate the

margins of safety to failure.

2. References and symbols

The calculation of the margin of safety has been carried out according to the procedures reported in:

[1]E.F. Bruhn,Analysis and Design of Flight Vehicle Structures[2]MIL-HDBK-5, Metallic Materials and Elements for Aerospace Vehicle Structures

Symbol Description Reference

A1 See fig. 2 [1]

A2 See fig. 2 [1]A3 See fig. 2 [1]

A4 See fig. 2 [1]

Abr Bearing area Dt [1]

Abrb Bearing area Dpt [1]

Apin Pin section area

At Net tension area (W-D)t [1]

AXIAL Axial component of load on lug, see fig. 2

b Arm of bending moment on pin (see fig.4)

D Bushing outer diameter [1]

Dp Pin diameter [1]E See fig. 2 [1]

F Resultant of load on lug

fb Bending moment maximum stress on pin

Fbpin Ultimate bending strength (pin)

Fcybush Compressive yield strength (bush) steel [2]

Fsupin Ultimate shear strength (pin)

Ftu Ultimate tensile strength (lug) 7050 T7451 [2]

Ftupin Ultimate tensile strength (pin)

Fy Y component of load on lug, see fig. 1 Finite element analysis

Fz Z component of load on lug, see fig. 1 Finite element analysis

g Gap between frame and spar lugs

Ipin Pin inertia moment

Kbru Shear bearing efficiency factor [1] fig. D1.13

Kbry Shear bearing factor [1] fig. D1.14

Kt Stress concentration factor [1] fig. D1.12

Ktru Efficiency failure coefficient [1] fig. D1.15

Mpin Bending moment on pin

Pbru Ultimate shear bearing failure load

Pbushbry Allowable shear bearing load on bushing

Ptru Ultimate transverse load

Ptu Ultimate allowable tension load

8/2/2019 ATTACCHI

3/8

MEMO DATE

REV. - PAGE 3 of83

t Lug thickness [1]

t1 Lug thickness (fin spar)

t2 Lug thickness (fuselage frame)

TRANSVERSE Transverse component of load on lug, see fig. 2

W Lug width [1]

8/2/2019 ATTACCHI

4/8

MEMO DATE

REV. - PAGE 4 of84

3. Assumptions

Due to the geometrical characteristics of the actual fittings, the procedure has been applied to an

equivalent geometry. As showed in figure 1, the equivalent geometry of the lug used for calculation

purposes is composed by a couple of lugs of the type reported in figure 2, whose axial direction

forms an angle of 45 with the z aircraft axis.

fig. 1fig.2

4. Load conditions

The margin of safety has been calculated on the basis of the following load conditions:

I. Ultimate Load (UL).The Fy and Fz components of the load acting on the lug has been calculated through a finite

element analysis of the structure under investigation. This components have been read in the gridpoint force balance section of the output file of the analysis, in the nodes that represent the

attachment of the fin to the fuselage frames.

The axial and transverse components of load have been obtained by projecting Fy and Fz on the

axial and transverse direction. As each lug works in double shear (figure 3), only one half of the Fy

and Fz components has been considered in calculating axial and transverse load. Furthermore a

fitting factor of 1.15 has been considered.

AXIALufitting = 1.15 AXIALu TRANSVERSEufitting = 1.15 TRANSVERSEu

fig. 3

8/2/2019 ATTACCHI

5/8

MEMO DATE

REV. - PAGE 5 of85

5. Spar fittings

Load condition Fy

[N]

Fz

[N]

AXIALufitting

[N]

TRANSVERSEufitting

[N]

U.L. 12787 267165 98983 89931

D = 33 mm Dp = 29 mm e = 41.9 mm T = 12 mm W = 83.8 mm

A1 = 362.4 mm2 A2 = 304.8 mm

2 A3 = 304.8 mm2 A4 = 362.4 mm

2

W/D = 2.539 e/D = 1.27 D/t = 2.75 t/D = 0.364 Aav/Abr= 0.861

kt = 0.93

[2], fig. D1.12curve 1

kbru = 1.1

[2], fig. D1.13curve A

kbry = 1.2

[2], fig. D1.14

Ktru = 0.67

[2], fig. D1.15curve 8

5.1 Axial Load: load condition U.L.

Tension failure (lug)

P tu..kt F tu A t

MS tuP tu

.1.15 AXIALu

1

MStu = 1.47

Shear - bearing failure (lug)

Pbru..kbru F tu Abr

MSbru

Pbru

.1.15 AXIALu

1

MSbru = 0.90

8/2/2019 ATTACCHI

6/8

MEMO DATE

REV. - PAGE 6 of86

Yield failure-bushing

Pbushbry..1.85 F cybushAbrb

MSbushbry

Pbushbry

.1.15 AXIALu

1

MSbushbry = 3.36

5.2 Transversal Load: load condition U.L.

P tru..ktru AbrF tu

MS tru

P tru

.1.15 TRANSVERSEu

1

MStru = 0.27

5.3 Oblique Load: load condition U.L.

Ru: smaller of Pbru or Ptu

RauAXIALu

Ru

RtruTRANSVERSEu

P tru

MS u1

Rau1.6

Rtru1.6 0.625

1

MSu = 0.12

8/2/2019 ATTACCHI

7/8

MEMO DATE

REV. - PAGE 7 of87

8. Pin analysis

The analysis on the pin is carried out in order to evaluate the margins of safety for shear and

bending load. A gap between frame lug and spar lug will be assumed in the evaluation of the

bending moment arm (fig.4). The procedure for determining the margins of safety is reported in [1],

par. D1.14.The pin is assumed to be an AN steel with Ftu=862 N/mm2, Fsu=517 N/mm2 and Fb=1241 N/mm2.

fig. 4

8.1 Spar fitting pin

8.1.1 Ultimate shear

The ultimate shear load for the pin (in double shear) and the relative safety margins are:

Ppds..2 F supinApin

MSpds

Ppds

.1.15 F

MSpds = 4.44

8.1.2 Ultimate bending

b g t 1 t 2

Mpin...1

21.15 F b

8/2/2019 ATTACCHI

8/8

MEMO DATE

REV. - PAGE 8 of88

fb

.Mpin

dpin

2

Ipin

MSpb

Fbpin

fb

1

MSpb = 2.09