Strength Evaluation of Socket Joints

https://ntrs.nasa.gov/search.jsp?R=19940032751 2017-11-26T13:10:55+00:00Z

NASA

Strength Larry Calspan

National Langley

C.

Evaluation

of Socket

Contractor

Report

4608

Joints

Rash Corporation

° Tullahoma,

Tennessee

Aeronautics and Space Administration Research Center • Hampton, Virginia

Prepared 23681-0001

for Langley Research Center under Contract NAS1-19385

June

1994

STRENGTH

EVALUATION Table

INTRODUCTION

ANALYSIS

Forward Load

Forward

Member

Bending

Aft Bending

Moment

Forward

Joint

Bending

................................................................................

..................................................................................................

..........................................................................................................

Contact

Moment

for Aft Joint

Member

with Continuous

Intermediate

Contact

Relief .....................................................................

Equation

Moment

Equation

Equation

Equations

Shear

Stress

........................................

Stress

5 7

8

9 9

................................................................................................

12

.................................................................................................

13

........................................................................................................

for Aft Joint

Member

with

Internw(tiatc

Contact

Relief .........................

..................................................................................................................

...................................................................................................................

.....................................................................................................................................

Pressure

3 3

Stress .................................................................................................................................

Stress

Contact

with

Relationships

Transverse IIoop

Contact

3

............................................................................................................................

Moment

Moment

Bending

Equation

Equation

Member

Aft Bending

Continuous

Equations

Bending

Stress

with

Moment

Development

Forward

Joint

1

............................................................................................................................

Moment

Bending

Bending

of Contents

..........................................................................................................................................

Development

Central

JOINTS

...............................................................................................................................

Joint

Load

OF SOCKET

...................................................................................................................

14

16

17 17 18 19 19

CONCLUSION

..................................................................................................................................

21

APPENDICES

...................................................................................................................................

23

Appendix

A:

IBM BASIC

A1)pendix

B:

Validation

Appendix

C:

List of Symbols

REFERENCES

Program of Loading

................................................................................................

23

with

28

Finite

Elements

...............................................................

..........................................................................................................

..................................................................................................................................

31 32

Ill

FIGURES

iv

..........................................................................................................................................

33

Figure

1.

Typical

Figure

2.

Figure

Socket

Type

Joints

...........................................................................................

33

Illustration

of Socket

Joint

with

Continuous

34

3.

Illustration

of Socket

Joint

with

Intermediate

Figure

4.

Typical

Figure

5.

Finite

Figure

6.

Load

Socket Element Distributions

Joint

Loadings

Model

and

of Socket

Resulting

Results

Contact Contact

.................................................... Relief ........................................

....................................................................

Joint .............................................................................

from

FEA ........................................................................

35 36 37 38

INTRODUCTION

The

results

included

this

report

is intended

was performed of the the

parallel loads

determining support

systems.

overlapping includes

engages

lamppost

with

is supported

determine support

if the the

be

require

some

by

of a unit

results

joint

and

in this can

joints

and

and

for a joint

between

the joint

a gap

be used during was

joints

was

is applicable members

can

system,

which

and

the

analytical

is sufficient conditions. joint

for

The strength

that

The

determine

to what

the

is included

of new

provide

a method

in wind

tunnel

be

model

applicable

to

are illustrated

in Figure

be considered

to be

basically support

of this

report.

A

herein

can

be used

to

of the

soil

to

included pressure

any 1 and

end of a model

is the subject

of

laterally

round

bar assembly

and

to external

forces

and

can

tongue

and

proper here

the design

of a clamped

are subjected

technique. to

bearing

to

forward

technique the

to

found

found

by an aft support

analytical

are

in the

during

for most

the joint

other

joint

at the

the

groove

stress by

joint

relationships

using

strip

theory

moments

would,

however,

which

could

to evaluate

be the

of the joint.

report

for both

the method

a plane

Transonic

The

development

width

method

over

National

objective type

reacted

about

systems

easily

socket

reacted

define

member.

type

analysis

original

in the joints

to better

support could

were

that

was developed

joint

ground

groove

this

a similar

provided

the

high wind

and

using

be used

from

penetration

during

additional

accomplished

The

of

of a tongue

evaluated

strength

depth

the

that

was

1, and

study

the stresses

moment

tapered,

of the

analysis,

of this

technique

analytical

one

to that

of a validation

in the joint

tool that

for which

the results

see Reference

moment

a design

the

report,

the

in the model

the

is supported by

lamppost

the strength

socket

and

Prior

new analytical

precise,

where

pressure

B.

the result

in concentric,

Some joints

to document

found

more

completed,

contact

and

as a company

by assuming

were

joints

be

configurations

by the

resolved

The

and stresses Once

general

system

To

released

as Appendix

and to provide

type joint.

supported

both

loads

were

sting

systems. the

analysis

here

centerline.

LaRC

support

that

the stresses

in typical

at NASA

model

and

horizontal

stresses

were previously

included

systems

of the joint

and

Facility

and

support

to the

report

to formalize

later

model

center

in this

a joint

the

form

design

applications where

with

members

of new model the

the joint

intermediate along

of equations

need of more members contact

about

that

are for a concentric,

support

systems

lengthy

relief.

one-third

The joint

to determine

analyses

are in continuous

of the midsection

socket

the

can be avoided.

contact with

tapered

along

intermediate of the joint,

the

type

strength

of

Results

are

full length

contact typical

relief of

of has

NASALaRCstingjoints,andthejoint members arein full contactforeandaft of thismidsection gap. Illustrationsof bothjoint typesaregivenin Figures2 and3. Analytically,the approach for bothwas to useStrengthof Materialsprinciplesto analyzethe joint members by idealizingthe joint as two rigid, parallelbeamsthat arejoinedby an infinite numberof springsalongthe contactingsurfaces. The contactloadscanbepicturedasbeingequivalentto theloadsdeveloped in the springsalongthe lengthof thejoint attributedto thedifferentialslopebetween two rigidjoint members.The contact loadsbetweenthe joint members arerepresented as externallyapplied,linearlyvarying,distributed loadsandareasshownon thefreebodydiagrams in Figure2 and3. Eachjoint memberis treatedlike a simplebeamandthe contactloadsbetween the beamsaretakento act likeexternalloadsthat are independently appliedto eachof the two beams.Forthefirst joint member, depictedin Figures2b and3b, theexternallyapplied loadsarebalanced by theapplicationof thecontacttypeloadsandfor the secondjoint member, depictedin Figures2cand3c,thecontactloadsarethe onlyloadsthat act on theendof thecantilevered beams.Thesecontactloads,in conjunction with theexternallyapplied loadsfor the forwardjoint members are usedto developindependent expressions for the bending momentalongthelengthof thejoint for thetwojoint members.Thejoint stressrelationships for the joint membersare determinedfrom the bendingmomentequationsby includingthe effectsof appropriatesectionproperties for a givengeometry.The geometry of the contactingsurfaces for the joint in this reportis in theshapeof a frustumof a coneandis representative of the taperedsocket typejointsfoundin modelsupportsystems in NASALaRCwindtunnels. The resultsin this report joints have

directly been

from

programed

report.

A copy

tapered,

socket

joint

can

be used

dimensions

for a personal

of an IBM BASIC type

joint

is included

to determine and

externally

computer program

the

that

as Appendix

distributed

applied

loads.

to automatically was developed A.

contact

loads

As a design compute

to evaluate

all

and aid,

the

stresses

the key equations

results

the results

in sting

given

in this

for a concentric

ANALYSIS

FORWARD

Load

To

JOINT

WITH

CONTINUOUS

joint,

the

CONTACT

Development

identify

moments

the and

members loads

applied

required

mating

surface

the

that

unique that loads forward

F0

the

similar

for this

joint

+

W 1

linear

load

=

L

the

- b

+

variation

triangles

(the

Wl

(l_a-c)

be used

location,

consider

distributed

linear refer

and

at

and

three

moments

provides to Figure

2b.

that

upper

there

each

end

two

for a third Summing

some surface

variable

of the

joint,

equations

equation.

distributed intermediate to

lower

unknowns

which

concentrated

be required and

vertical

the

other

for a

an assumption

For an illustration

in the

of

to simplify

or the

will therefore

of the

forces

at

mating

in terms

of the

are two other

equations

provide

the basis

the

reverses

bending

axis of the beam

magnitudes

as a dependent

loads

loads,

the longitudinal

loading

from

distributed

can be developed

for maximum

can

distributed

loads along

of the

shift

to evaluate

direction

of the for the

0

about

[

of the

solving

loads

reversal

be used

for distributed

direction

location

can

yields

W 2

moments

+

are

dimensions

member

- W 1

reversal

loads

load variation

and

The

of forces

loads

relevant

pressure

tile contact

to the

Summation

distributed

Summing

M0

load

are equivalent

and

a linear

magnitudes

solution. the

by assuming

where

this

To solve

Expressions

equilibrium.

is literally and

contact

stresses.

contact

achieve

maximum

loads

the

to the

to

which

expressions.

in the

loads

attributed

location

are

stresses

ultimately

the externally

For

MEMBER

load center

w2

c

of the externally

(b c)l E 3

assumption,

ratio

_

(X)

-

W2

the

of all corresponding

L - a

loads

can

applied

M0, provides

:°

-

be

F 0 and

loads,

related

sides of similar

(2)

by using triangles

the

geometric

properties

of

are equal)

(3)

To

equate

the

determined

preceding

in terms

load

for a linearly

load

times

equations,

of concentrated

varying

the distance

for the distributed

in terms

using

load the

that

load

distributed

a basic

loads

definition

that

goes to zero is half the

acts.

The

of the concentrated

following

given

in equation

an equivalent

product

relationships

(3) can

of the peak distributed are rearranged

to solve

loads.

(4)

c

(5)

(4)

concentrated

and

loads

(5)

after

into

equation

(3)

gives

the

following

relationship

between

the

grouping

[(b-a)2 - 2c(b-a) + c2] W2 - c2W1 : 0

Three

linearly

independent

simultaneously and

for the

M0) and

the joint

3(b-a)

[M 0

equations,

three

(1),

unknowns

dimensions

+

be

concentrated

2W 2

equations

equivalent

which

for the

2W 1 b-a-c

-

w2 substituting

loads,

distributed over

loads

Wl

expressions

F0(L-a)]

(2),

(3a)

and

(c, W 1 and

as shown

- 2(b-a)2F

in Figure

(3a)

W2) 2.

are

in terms The

now

available

of the externally

load reversal

location

that

can

be

applied would

solved

loads

(F 0

be

0 (6)

6[M 0

To simplify in terms

the

+

F0(L-a)]

following

of the load

3[M 0

+

F0(L-a)]

location,

0

for the equivalent c, which

is defined

-'-

+

concentrated

loads,

in the preceeding

the equations

are expressed

equation

- cF 0

(7)

2(b-a)

3[M 0 W2

expressions

reversal

W 1

- 3(b-a)F

F0(L-a)][c + 2(b-a)

2(b-a)]

F0

(8)

The

dimension

the

varying

The

identifying contact

dimension

surfaces

the load

load

identifies

to the

lower

acting

Forward

Moment

Bending

Expressions

along

downward

contact

acting

considering

the forward as a function

the beam, using

magnitude load

the external

The

variable

would

location and

following

where

the

distinguishes

and for the upward

development contact

where

acting

be used

loads

separate

loads,

to simplify

expression

as an independent shift

governing

see Figure

the

from

the

variable.

upper

equations

for

mating

are required

2.

moment

Wx

at

w1

of the joint

loads

by

load of the x-distance

similar

figure.

triangles,

general

_L-b

the

x-L+b

distributed

distance

would

"x"

from

be

L-o-c

for L-

concentrated

__

load

b.00001

470 480 490

E=O# F=0# PRINT

500 510

INPUT GOTO

520

PRINT

530 540

INPUT PRINT

550 560

INPUT PRINT

570 580 590

INPUT DI2,DM2,DO2 IF DMI.0001) ABS(LAF-X)