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Fig. 1-Three types of lug-pin combinations loaded under tension.

Analysis of Lugs And Shear Pins

Made of Aluminum Or Steel Alloys Method of analysis and procedure for the design of lug-pin combinations made of aluminum or steel alloys. Constructions analyzed include lugs of irregular section and lug-pin combination assemblies having multiple shear connections.

F. P. COZZONE, M. A. MELCON, F. M. HOBLIT Lockheed Atlaaft Corporation

fuc.ufiNATION OF MANY TEST R1!SULTS on lugs of different materials and geometries led to the conclusion that existing conventional methods of stress analysis of lug-pin combinations were conservative in some respects and rather seriously unconservative in others. It seemed desirable, therefore, to thoroughly overhaul the existing methods of lug analysis.

The procedure for lug analysis that resulted from this investigation is presented in the following discussion. It is based largely upon theory, but the

PRODUCT ENCINEERINC- MAY, 1950

validity of the methods has been veri· .fied by comparison with many tests.

This procedure is applicable only to steel or aluminum alloy lugs of uniform thickness, Fig. 1, under tension.

OUTLINE OF METHOD. In analyzing any lug-pin combination, all possible ways in which failure can occur, some of which are shown in Fig. 2, must be considered. These are:

1. Tension across the net section. Because of stress concentration, the full P /A stress cannot be carried. Failure

',,, "'"',,,

\ \

'Jisonsion fi:rilu~·' '· \ She-ar b~aring f'ai/u!Y/ l

Hoop t~nsion fi:lilu~'

Fig: 2-Three .types of lug failure.

to take account of this stress concentration can result in seriously unconservative d~sign.

2. Shear tear-out or bearing. These two types of failure are closely related and are covered by a single calculation based upon empirical curves. Previous methods based upon an arbitrary shear stress calculation have been excessively conservative.

3. Hoop tension at tip of lug. No separate calculation need be made, as the shear-bearing allowables also ac· count for the possibility of hoop tension failure.

4. Shearing of the pin. Conventional methods are satisfactory.

5. Bending of the pin. The load on the pin is assumed to be uniformly distributed along the pin and the ultJmate strength of the pin is based on modulus of rupture. This assumption may be somewhat conservative, but to ignore pin bending completely can be very unconservative. Pin bending is easy to overlook as a cause of failure because pins seldom break; instead, bending of the pin concentrates load at the edges of the lug and causes the actual fracture to occur in the lug.

6. Excessive yielding of the bushing, if a bushing is used. Yielding of the lug is considered to be excessive at a permanent set 0.02 times the pin diameter. Yielding of the lug must always be checked, as it frequently occurs at a lower load than would be anticipated from the ratio of tensile yield stress F,, to ultimate tensile strength F,. of the lug material.

Yielding of the pin, and ultimate strength of the bushmg are never criti· cal in aircraft practice where applied yield loads are between 0.67 (1/ 1.50) and 0.77 (1.15/1.50) of the applied ultimate loads.

FACTORS OF SAFETY. The proper choice of factors of safety is beyond the scope of this discussion. It is suggested, however, that lugs be designed conservatively, as their weight is usu·

113

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1. 0 ~~ 1--.: r-

0. ~ ....... ~ r-..... ....._

1-1--9

'" r": f' to... r-.

\ "" :-....... 1--....

\ ....... I'-.. --\ "' 0.7 '\

06 \

~ 0.5 ""'

0.2

I "' 1--I- ' J-' ! 1-1-- I

R~~ 1-1-- ~ Q -; I

1-f- I 1 I

1-- •-a-.. 0.1

I . . f- -

~)' ~ (i to-.. :-........

~r-t-~ ~ r::::. :----.. f.... ~ --r-~ I'

i' :-........

r\.

~ " r-.... ~ I'-Load

' I 1". ___J_

i>

t

'\ .......

-1""--

"

P',. = K, F,. A, LEGEND. L, T, and N indicate grain in direction F

in sketch: L = longitudinal T = long transverse N = short transverse (normal}

MATERIALS CUilVE 1:

4130 and 8630 11eel 14ST and 75ST pine~ 0.5 (L, T) 7SST bar and extrusion ( L) HST hand for~ted billet~ 144 sq in. (L) HST and 75ST die forgings (L)

Cua.vE 2: 14ST and 75 ST plate> 0.5 in., L 1 in. 75ST extrusion (T, N) 75ST hand forged billet L 36 sq in. (L) 14ST hand forged billet> 144 sq an. (L) 14ST hand forged billet L 36 sq in. (T) HST ~nd 75ST die forgings (T)

CUIIYE 3: 24ST80 plate (L, T) 24ST extrusion (L, T, N)

CURVE 4: 24STO plate (L, T) 24STI plate (L, T) HST and 75ST plate> I in. <L. T) 24ST bar (L. T) 75ST hand forged billet >. 36 sq in. (L) 75ST hand forged billet ~ 16 sq in. (T)

CURVE 5: 195T6, 220T4, and 356T6 aluminum alloy caning 75ST hand forged billet > 16 sq in. (T) l4ST hand forged billet > 36 sq in. (T) OJ>

1.0 1.5 2.0 2.5 3.0 35 4 0 4.5 5.0 CuaVE 6: w/0 Aluminum alloy plate, bar, hand forged billet, and

die forging (N)

Fig. 3-Values of tension efficiency factors of lugs. NoTE: for die forging, N direction exisu only at paning plane.

' -4.<. •

ally smaU relative to their importance, and inaccuracies in manufacture ace difficult to controL .An additional factor of safety (over and above whatever fitting or casbng factor is required by applicable specifications) of about 1.20 is considered appropriate. In addition, it is good practice to provide sufficient material to permit drilling out the hole for a bushing, if such is not already included in the original design.

Notation and Nomenclature

In addition to the letter symbols indicated in Fig. 1, the following notation is used:

t - thickneSJ or lue F,. - ultimate tensile strength of lue

material F,_ - ultimate tensile strength of lue

material with grain F,.. - ultimate tensile strength of lug

material c:ross grain F,. - tensile yield stress of lue material F,.,. - tensile yield stress of lue material

with grain F,.. - tensile yield stress or lug material

c:J'OSI crain F,.. - compressive yield stress of bush inc

material Pr - applied limit load P. - applied ultimate load, this value

is usually 1.5 Pr

114

7SST bar (T)

P. - applied yield load: Air Force and CAA equals Pr, Nayy equals 1.15 Pr

M = applied bendine moment on pin P' • - allowable ultimate load P',. - allowable ultimate load as deter

mined by tension P' t.• - allowable ultimate load as deter

mined by shear-bearing P' • .., allowable yield load on lug P' ~ - allowable yield bearing load on

bushing At. • projected bearine area A, ... minimum net section area for ten-

sion K, - ef!icienc:y fac:tor for tension Kt. = efficiency factor for shear-bearinc C - yield factor

Analysis Procedure

The following outlined procedure gives the allowable load for each possible way in which the lug-pin combination may faiL .Adequacy of the part is then determined by comparing each of these allowable loads (yield or ultimate) with the corresponding ll)>plied load by means of the conventional margin of safety calculation.

Grv~N. Applied ultimate l?ad P. ~d applred yield load P,; requJCed fittmg and casting factors; pin and lug material; and as designated in Fig. 1, the dimensions a, w, D, D,., and thickness J of Jug.

l. Preliminary Calculations. Compute tuj D, ajD, DjJ,

Aw- Dt, and A,- (w - D)t

2. Tension Across the Net Section. Enter Fig. 3 with wjD and obtain K, for the proper material. Obtain allowable ultimate load P' ,. for tension failure:

P'c.- Kc F,. A, The efficiency factor K, given by Fig. 3 is simply the reciprocal of an effective plastic stress concentration factor at ultimate load. Values of K, were obtained using typical stress-strain curves for the various materials, together with the appropriate elastic stress concentration factors to which a semi-rational correction factor had been applied.

3. Shear-Bearing. Enter Fig. 4 with ajD and D/ J and obtain K.,. Obtain allowable ultimate load P' ..... for shearbearing failure:

P't..- Kt. At. F, ..

4. Lug Yield . Take the smaller of P' ,. and P' ... as P' ...... Enter Fig. 5 with P' ••••/ A., F,,. and obtain C. Obtain the aJiowable yield load for the lug.

P'.- c.!tr• ~"-• F, ••

PRODUCT ENGINEERING-MAY, 1950





3. 0

I I I 8 2. I I I I ~

v ~2

3 .......- v r--Fig. -4 - Values of shear·bearing efficiency factors of lugs. / ~ 6

P'bru"' Kbr Abr Ftu,. (min in pion• of lug) v .......- ~ ~ ~ --2. 4

I I I ~ v I- -l I ~ _..... :..,.......-f.--2.4

5

>.l ~ u--, ~ ~ -~ --~ 0 <) ( I f-+-£ ;::J

~ v I--!---' T!' ../ r- ~

2.2

2. 6

/ ...-~-- r ~ ~ ~ 1-- Curve "A" is a cutoff tO be used for all I ' ~ ~

A - aluminum alloy hand forged billet when 1-

b. ~ the long transverse grain direction has = 9

~ ~ ~ r- the general direction "C" in the slcetch.

~ Curve "B" is a cutoff to be used for all 1- 1 -

1.8

1.4

8

0 aluminum allo~ plate, bar, and hand

~~ ~ r- -@ f--- -- forged billet w en the short transverse

grain direction has the general direction f-

1.2

1.0

~ I 1--v .....

v v ..--J v

lu ~ ~ ~ ~ )

o.a

o.e

0.4

0.2

o.o

"C" in the sketch; and for die forgings when the lug contains the parting plane

,..... in a direction ap,proximately normal to the direction "C' Non: In addition to the limi tations pro-vided by curvet "A" and ''B", in nol event shall a X •• greater than 2.00 be used for lugs made from 0.5 in. thiclc or thicker aluminum alloy plate, bar, or hand forged billet.

f- 1 1-

5

1::: 2 0

5 0

t-2 1= 3

r--

0 0.2 ()A. 06 0.8 1.0 1.2 1.4 us 1.8 2.0 2.2 2.4 2.6 2.8 3.0 32 3 .4 3.6 3.6 4.0 o/0

5. Bushing Yield. Take A,,, as the smaUer of the bearing areas of bushing on pin or bushing on lug. (The latter may be smaller as a result of external chamfer of the bushing.) Obtain allowable yield bearing load on bushing P' .,,.:

P'w.- 1.85 F .. A.,. 6. Pin Shear. Check pin shear in

the usual manner. 7. Pin Bending. For the construc

tion shown in Fig. 6, calculate bending stress in the pin resulting from the applied ultimate load P., assuming Afyj I bending stress distribution and maximum bending moment as given by:

AI - ~· (21, +it)

This formula for bending moment foUows from the assumr,tion of uniform bearing stress distnbution across each of the three lugs. This assumption may be conservative in some designs and constructions by as much as 30 percent.

Obtain modulus of rupture of ein from ANC5a or other authoritative source. For a solid round pin of any material having a tensile yield stress

PRODUCT ENCINEERINC- MAY, 1950

P,, at least 75 percent of the ultimate tensile strength P,. and an ultimate elongation of at least 10 percent, the modulus of rupture will be between 1.6o and 1.68 times the ultimate tensile strength.

If there is a gap between mating lugs, as shown in Fig. 7, the pin bending analysis is the same except for the equation giving pin bending moment. In this event, the moment arm b is measured as indicated in Fig. 7, the loads P.j2 being assumed uniformly distributed, and the moment is then given by:

M- P,J 2

If either of the foregoing analyses should show inadequate pin bending strength but an excess of strength in the lug, it may be possible to take advantage of the excess lug strength to show adequate strength of pin, by the following procedure:

A. Consider the pin loads to be uniformly distributed over a reduced lug thickness as shown in Fig. 8, where the cross·s«tion area becomes inactive. This redistribution takes place because as the pin begins to bend, the bearing

load on the lugs tends to concentrate nea.r the shear planes leaving some of the Jug material inactive. The distribution over the reduced thickness tends to remain uniform, however, because of the plastic behavior of the lug. The value of effective thickness to be used in the analysis may have any desired value and should be chosen by trial and error to give approximately equal margins of safety for pin and lugs.

B. Recalculate all lug margins of safety with allowable loads reduced in

1. 1

1.0 !\

" 008

0.7

05oo a.s 1.0 15 2.0 25 30 p~ '"'"~br fi ..

Fig. 5--Values of yield factors for lugs.

115





I X

~ ,. ..... ~ P., 2

:.--,----

~ ~ il ~ - If, 2 ...:t__ ;e {: ,. ~- 2 ... Pu

2

Fig. 6-Lug-pin combination showing d.i.meosions used in cala:J· lacing bending mess in pin caused by applied ultimate load.

Fig. 7-Lug-pin combination witb a gap between mating lugs. Sketch indicates tbe method o( measuring tbe moment arm.

Fig. 8-Method of approximating effective lug tbkkness when recalculating the pin bending moment and margin of sa.fety.

Fig. 9-Design where the resulting eccentricity of load on lug introduces excessive bending stresses in adjacent structure.

the ratio of the effective thickness to the actual thickness of the lugs.

C. Recalculate pin bending moment, .M equals P.b/2, and margin of safety using a reduced value of b as indicated in Fig. 8. Care should be taken not to reduce b as described in Paragraph (A) if the resulting eccentricity of load on the lu$ introduces excessive bending stresses m the adjacent structure, as shown in Fig. 9. In such designs, the pin must be strong enough to distribute the load uniformly across the entire lug.

LUGS OF IRREGULAR SECTION. For lugs of irregular section having the bearing load distributed over the entire thickness, Fig. 10, an analysis should be made based upon an equivalent lug with rectangular sections having areas equal to the actual sections.

For lugs in which the bearing load is not distributed over the entire thickness, Fig. 11, no de.finite rules can be given; however, the general methods given in this article may be adapted to such designs.

MULTIPLE SHEAR AND SINGLE SHEAR CONNECllONS. Lug-pin combinations having the geometry indicated in Fig. 12 should be analyzed according to the following criteria:

A. The load carried by each lug shall be determined by distributing the total applied load p among the lugs as indi· cated in Fig. 12, p being obtained from Table I .

This distribution is based on the assumption of plastic behavior (at ultimate load) of the lugs and elastic bending o£ the pin, and gives aptroximately zero bending deflection o pin.

Table I - Coefficients for Multiple Shear Connections

Total number of Pin lurc indudina {J Shear, h·

otb sides lb

5 0.35 0.50 p' .. ,. r +'1/2 7 0.40 0.53 p' .. , f+(r 9 0.43 o.5• ,. 0.37 t +' /2 11 0.« o.5• ,. 0.39 '+ (' / 2 01> 0.50 0.50 p' 0.50 t + (' /2

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B. The maximum shear load on the pin is then given in T able I.

C. The maximum bending moment in the pin is given by the formula: where b is given in Table I,

M- -p' b/ 2

Single shear connections, Fig. 13, should be avoided wherever possible because of the high degree of uncertainty in their analysis, which results chiefly from the unknown clamping effect of the bolt head and nut and relative stiffness of the attaching members.

Allowable Bearing Stress

The concef.t that shear-tearout and bearing fadures are essentially the same phenomenon can be used to advantage to determine allowable bearing stresses for alloys for which no published bearing allowables are available or for ranges of aj D andDjl for which available values do not apply.

The allowable load for shear-bearing failure of a lug was given pr~ viously as :

P'...,.- K., A.,F, ..

Dividing both sides of this equa· tioo by A •• gives the allowable bearing stress:

F.,..- K.,F, ..

The allowable bearing stress can be

PRODUCT ENGINEERING- MAY, 1950





A

A

!.-- 't - _J OottPd lmes slow ..,uti'CIIt'nf lug fOr CCT lculution

Seefion A-A or B·B

Fig. to-lcrrgular log section with the ~ing load distributed over entire thickneu. This analysis should be based on a lug of equal a.rea having a rectangular section.

Fig. 11-lrrrgular Jug sections with bearing load not distributed over entire thickness. No definite analysis rules apply for such designs but general methods can be adapted.

obtained from this formula for any aluminum or steel alloy and for any value of aj D and Djt, using the values of K •• given by the curves of Fig. 4. The bearing allowables thus obtained apply to holes near the edge of Bat sheet, Fig. 1 (C), as well as to lugs, Figs. 1 (A) and (B).

In ANC-:>a allowable bearing stress is g iven only for aj D equal to 1.5 and 2.0, and only for Djt less than 5.5. The ANC-:>a bearing allowabJes for ajD equal to 1.5 and 2.0 are in dose agreement with Fig. 4. For values of ajD between 15 and 2.0, ANC-:>a specifies linear interpolation, which likewise is in good agreement with Fig. 4. For ajD greater than 2.0,

ANC-5a calls for the use of the value for ajD equal to 2.0, which is seen from Fig. 4 to be conservative. The wide variation in K •• to be seen in Fig. 4 emphasi:zes the fact that allowable bearing stress depends upon the geometry of the appflcation and therefore is not a .fixe(! property of the material like ultimate tensile strength or tensile yield stress.

Yield allowable bearing stress likewise can readily be determined, in the following manner:

1. Obtain K b from Fig. 4. 2. Enter Fig. 5 with

P',..,,. K d b . C --;;--F- .. ,. an o tam n. rw ,.,.

Thrsr lugs of' .quo/ thickn••• r--- -1 r -- -Two out111' l<1,9s of' #quul rhiclrnrss nof lr!!IS

ifum Pr' (IJ i s glvrn in frlble) Pp·-~--+--1

p ~--

'-----These lugsCJF' t'qval thiclrnrs!!l f"

Fig. 12-M~thod of distributing the total applied load among lugs in a multiple shear CQCJ.DeCtion oo the aJSumption of plastic behavior of lugs and ela.stic bending of pin.

PllODUCf ENCINEEiliNC- M,\Y, 1950

3. Obtain yield allowable beanng stress:

Frw~ - C K,. F,~,

Values of F •• , thus obtained agree closely with values given in ANC-:>a for ajD equal to 1.5 and 2.0.

Bearings and Bearing Factors

A bearing may be defined as a Jugpin combination--or, more generally, any pin-jointed fitting-that permits relative movement between the parts joined other than that which results from the deformation of the parts under load.

Allowable bearing pressures for bearings as thus defined are usually much lower than the aJ!owable bearing pressures obtained by the methods previously discussed, which consider only static strength.

Allowable bearing pressures for bearings depend upon such service conditions as frequency and extent of the relative motion, whether the relative motion occurs under maximum load, and whether shock or vibration are present. It is believed that the lug geometry has little effect upon this allowable, but that for unlubricated bearings it should be proportional to the hardness, and hence to the ultimate tensile strength, of the lug or bushing material.

Therefore if such an allowable is obtained by means of "bearing factors" such as given in ANC-5a, the basic allowable to which the factors are applied should not be the bearing allowable used in the static-strength analysis, but should instead be obtained from Fig. 4 or some particular ajD, say ajD equal to UO, which would be used for all lugs regardless of the actual ajD.

This check of the lug as a bearing should be made in addition to, rather than in place of, the static-strength analysis, smce if ajD is very small the static strength may be more critical.

Fig. 13-Single shear connection. This design should be avoided wbeo possible.

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