Contents

- 1 1. Introduction
- 2 2. Uniform Axial Load
- 3 3. Single-Shear Joint Strength
- 4 4. Transverse Load
- 5 5. Oblique Load
- 6 6. Multiple Shear and Single Shear Connections
- 7 7. Axially Loaded Lug Design
- 8 8. Analysis of Lugs with Less Than 5% Elongation
- 9 9. Stresses Due to Press Fit Bushings

## 1. Introduction

**Lug**or

**Padeye**is basically a plate with a hole in it where the hole is used to connect a clevis pin, a chain, a hook or a rope, with the objective to

**lift**an equipment. This article will only cover the design of lifting lug according to the

**USA Air Force Method.**It’s highly advised that you read and fully understand this article before using our lifting lug design spreadsheet.The Air Force Method is widely used in the industries all around the world and is described in the Stress Analysis Manual of the Air Force Flight Dynamics Laboratory (FDL), which you can be downloaded by free in the Defense Technical Information Center website. This method is similar to those presented in the Analysis and Design of Flight Vehicle Structures from E. F. Bruhn (this book appears in the reference page) and Analysis of Lugs and Shear Pins from M. A. Melcon and F. M. Hoblit.The method described in the book presents static strength analysis procedures for uniformly loaded lugs and bushings, for double shear joints, and for single shear joints, subject to axial, transverse, or oblique loading. It considers materials having ultimate elongation of at least 5% in any directon in the plane of the lug, but there’s part with modifications which can be used with materials having less than 5% of elongation. In addition, a short section on the stress due to press fit bushing is also presented.The first thing that the designer will notice is that this method heavily relies on curves generated by empirical data (results from tests and interpolation) and the second thing is that it is somewhat more complex compared to other lug analysis methods (ASME BTH for example), as it takes in account the bearing, shear-out and hoop tension (combined in a single failure mode) in the lug. The interaction between the lug and the pin (double shear joint) is also considered.

## 2. Uniform Axial Load

**in tension**must be checked for

*bearing strength*and for

*net-section strength*, which we are considering as failure modes. The bearing strength of the lug shown in the Figure 1, depends largely on the interaction between

*bearing*,

*shear-out*, and

*hoop-tension*stresses in the part of the lug ahead of the pin (right side of the section 1-1). Nomenclature shown in the Figure 1:P = Load w_T = Width of the “lug neck” w = Lug width D = Lug hole diameter D_P = Pin diameter a = Distance from the edge of the hole to the edge of the lug e = Edge distance t = Lug thickness

### 2.1. Lug Bearing Strength

*bearing stresses*and loads for a lug failure involving bearing, shear-out, or hoop tension can be determined using the equations below, with an allowable load coefficient ( K) determined from the charts Figure 2 and 3. For values of {e/D lt 1,5}, lug failures are likely to involve shear-out or hoop-tension, and for values of e/D ge 1,5, the bearing is likely to be critical. Actual lug failures may involve more than one failure mode, but such interaction effects are accounted for in the values of K.The lug ultimate bearing stress (F_{bruL}) can be found using the Equation 1 or 2: normalsize color{black}{F_{bruL} = K { a over D } F_{tux} quad textrm{if} quad {e over D} lt 1,5 tag{1}} normalsize color{black}{F_{bruL} = K F_{tux} quad textrm{if} quad {e over D} ge 1,5 tag{2}}Where:F_{tux} = Cross grain tensile ultimate stress of lug materialThe lug yield bearing stress (F_{bryL}) can be found using Equation 3 or 4: normalsize color{black}{F_{bryL} = K {a over D} F_{tyx} quad textrm{if} quad {e over D} lt 1,5 tag{3}} normalsize color{black}{F_{bryL} = K F_{tyx} quad textrm{if} quad {e over D} ge 1,5 tag{4}}Where:F_{tyx} = Cross grain tensile yield stress of lug materialThe value of K can be found using the chart in the Figure 2, if D/t le 5, or Figure 3 if {D/t gt 5}. The allowable lug ultimate bearing (P_{bruL}) for lug failure in bearing, shear-out, or hoop tension is: normalsize color{black}{P_{bruL} = F_{bruL} D t quad textrm{if} quad F_{tux} le 1,304 F_{tyx} tag{5}} normalsize color{black}{P_{bruL} = 1,304 F_{bryL} D t quad textrm{if} quad F_{tux} gt 1,304 F_{tyx} tag{6}} The Equation 7 and 8 can only be used if the load is uniformly distributed across the lug thickness. If the pin is too flexible and bends excessively, the load on the lug will tend to peak up near the shear faces and possibly cause premature failure of the lug. The bending strength of the pin can be checked using the equations in the section “

**Double Shear Joint Strength Under Uniform Axial Load**“.

### 2.2. Lug Net-Section Strength

### 2.3. Lug Design Strength

### 2.4. Bushing Bearing Strength

### 2.5. Combined Lug-Bushing Design Strength

### 2.6. Double Shear Joint Strength

#### 2.6.1. Lug-Bushing Design Strength

#### 2.6.2. Pin Shear Strength

#### 2.6.3. Pin Bending Strength

#### 2.6.4. Lug Tang Strength

## 3. Single-Shear Joint Strength

### 3.1. Lug Bearing Strength

### 3.2. Net-Section Strength

### 3.3. Bushing Strength

### 3.4. Pin Shear Strength

### 3.5. Pin Bending Strength

## 4. Transverse Load

### 4.1. Lug Strength

### 4.2. Bushing Strength

### 4.3. Double Shear Joints

### 4.4. Single Shear Joints

## 5. Oblique Load

### 5.1. Lug Strength

### 5.2. Bushing Strength

### 5.3. Double Shear Joints

### 5.4. Single Shear Joints

## 6. Multiple Shear and Single Shear Connections

- The load carried by each lug should be determined by distributing the total applied load normalsize color{black}{b} among the lugs as indicated in Figure 16, normalsize color{black}{P} being obtained in Figure 17. This distribution is based on the assumption of plastic behavior (at ultimate load) of the lugs and elastic bending of the pin, and gives approximately zero bending deflection of the pin.
- The maximum shear load on the pin is given in Table XX.
- The maximum bending moment in the pin is given by the formulae:

## 7. Axially Loaded Lug Design

### 7.1. Pin Failure

#### 7.1.1. Failure in the Shearing Mode

__Pin and Bushing Diameter__.The minimum allowable diameter for a pin in double shear is:normalsize color{black}{D_p = 0.798 sqrt{P over F_{sup}} tag{49}} The outside diameter of the bushing is normalsize color{black}{D = D_p + 2 t_B}, where normalsize color{black}{t_B} is the bushing wall thickness.__Edge Distance Ratio (e/D)__. The value of normalsize color{black}{e/D} that will minimize the combined lug and pin wiehgt is obtained from Figure 19 for the case where lug bearing failure and pin shear failure occur simultaneously. The lug is assumed not critical in net tension, and the bushing is assumed not critical in bearing.

__Allowable Loads__. The allowable loads for the different failure modes (lug bearing failure, lug net-tension failure, and bushing failure) are determined from Equations 5, 6, 9, 10 and 13 in terms of the (unknown) lug thickness. The lowest of these loads is critical.__Lug Thicknesses__. The required male and female lug thicknesses are determined by equating the applied load in each lug to the critical failure load for the lug.__Pin Bending__. To prevent bending failure of the pin before lug or bushing failure occurs in a uniformly loaded symmetrical double-shear joint, the required pin diameter is:normalsize color{black}{D_p = sqrt[3]{{{2.55P} over {k_{bp} F_{tup}}} Big({t_1 + {t_2 over 2} + 2g}Big)} tag{50}}Where normalsize color{black}{k_{bp}} is the plastic bending coefficient for the pin. If the value of normalsize color{black}{D_p} from Equation 50 is greater than that from Equation 49, the joint must be redesigned because the pin is critical in bending.__Reduced Edge Distance__. If allowable bushing load (Equation 13) is less than the allowable lug load (Equations 5 and 6), a reduced value of normalsize color{black}{e}, obtained by using the curve shown in Figure 21 for optimum normalsize color{black}{e/D}, will give a ligther joint in which lug bearing failure and bushing bearing failure will occur simultaneously. The previously calculated pin diameter and lug thicknesses are unchanged.__Reduced Lug Width__. If the lug net-tension strength (Equation 9 and 10) exceeds the bearing strength (Equation 5 and 6), the net-section width can be reduced by the ratio of the bearing strength to the net-tension strength.

#### 7.1.2. Failure in the Bending Mode

__Pin and Bushing Diameters (First Approximation)__. A first approximation to the optimum pin diameter is shwon in Equation 51.

__Edge Distance Ratio (e/D)__. The value of normalsize color{black}{e/D} that will minimize the combined lug and pin weight is obtained from Figure 20 for the case of symmetrical double-shear joints in which lug bearing failure and pin bending failure occur simultaneously. The lug is assumed not critical in tension and the bushing is assumed not critical in bearing.The curves apply specifically to concentric lugs (normalsize color{black}{a = e - D/2} and normalsize color{black}{w = 2e}), but can be used for reasonably similar lugs.__Allowable Loads (Frist Approximation)__. The allowable loads for the different failure modes (lug bearing failuyre, lug net-tension failure, and bushing failure) are determined from Equations 5, 6, 9, 10 and 13, in terms of the (unknown) lug thickness. The lowest of these loads is critical.__Lug Thicknesses (First Approximation)__. The frist approximation to the required male and female lug thicknesses are determined by equating the applied load in each lug to the lowest allowable load for the lug.__Pin Diameter (Second Approximation)__. The second approximation to the pin diameter is obtained by substuting the frist approximation lug thicknesses into Equation 50.__Final Pin and Bushing Diameters and Lug Thicknesses__. The final optimum pin diameter is very closely approximated by:normalsize color{black}{D_{popt} = 1/3 D_p + 2/3 D_p tag{52}} An average value, however, is generally sufficient. If the final optimum value is not a standard pin diameter, choose the next larger standard pin and bushing.The final lug thicknesses corresponding to the standard pin and bushing are then determined.__Pin Shear__. The pin is checked for shear strength (Equation 49).__Reduced Edge Distance__. If the bushing bearing strength (Equation 13) is less than the lug bearing strength (Equations 5 and 6), a reduced value of normalsize color{black}{e/D}, obtained from the curve in Figure 21, will give a lighter joint. The pin diameter and lug thicknesses are unchanged.__Reduced Lug Width__. If the lug net-tension strength (Equations 9 and 10) exceeds the lug bearing strength (Equations 5 and 6), the net-section width can be reduced by the ratio of the bearing strength to the net-tension strength.

## 8. Analysis of Lugs with Less Than 5% Elongation

### 8.1. Axially Loaded Lug

#### 8.1.1. Bearing Strength

- Determine normalsize color{black}{F_{ty} F_{tu}} and normalsize color{black}{varepsilon_y varepsilon_u}, using values of normalsize color{black}{F_{ty}}, normalsize color{black}{F_{tu}}, normalsize color{black}{varepsilon_y} and normalsize color{black}{varepsilon_u} that correspond to the minimum value of normalsize color{black}{varepsilon_u} in the plane of the lug.
- Determine the value of normalsize color{black}{B}, the ductility factor, from the graph shown in Figure 22.
- Determine a second value of normalsize color{black}{B} (denoted by normalsize color{black}{B_{0.05}}) for the same values of normalsize color{black}{F_{ty}}, normalsize color{black}{F_{tu}}, and normalsize color{black}{varepsilon_y} as before, but with normalsize color{black}{varepsilon_u = 0.05}.
- Multiply the bearing stress and bearing load allowables given by Equations 1 through 6 by normalsize color{black}{B/B_{0.05}} to obtain the corrected allowables.

#### 8.1.2. Net-Section Strength

#### 8.1.3. Strength of Lug Tangs

#### 8.1.4. Lug-Bushing Strength / Single-Shear Joint

### 8.2. Transversely Loaded Lugs

#### 8.2.1. Bearing Strength

- Determine normalsize color{black}{B} and normalsize color{black}{B_{0.05}} as described for axially loaded lugs, where normalsize color{black}{B} corresponds to the minimum value of normalsize color{black}{varepsilon_u} in the plane of the lug.
- Multiply the bearing stress and bearing load allowables given by Equations 42 through 45 by normalsize color{black}{B/B_{0.05}} to obtain the corrected allowables.

## 9. Stresses Due to Press Fit Bushings

__Stress Corrosion__. The maximum allowable press fit stress in magnesium alloys should not exceed 8000 psi. For all aluminum alloys the maximum press fit stress should not exceed normalsize color{black}{0.50 F_{ty}}.__Static Fatigue__. Static fadigue is the brittle fracture of metals under sustained loading, and in steel may result from several different phenomena, the most familiar of which is hydrogen embrittlement. Steel parts heat treated above 200 ksi, which by nature of their function or other considerations are exposed to hydrogen embrittlement, should be designed to an allowable press fit stress of normalsize color{black}{25% F_{tu}}.__Ultimate Strength__. Ultimate strength cannot be exceeded, but is not usually critical in a press fit application.__Fatigue Life__. The hoop tension stresses resulting from the press fir of a bushing in a lug will reduce the stress range for oscillating loads, thereby improving fatigue life.