aluminum tube bent diag

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S uare Aluminum Tubes Bent about a Dia onal AxisS uare Aluminum Tubes Bent about a Dia onal Axis

. .

Mr. Dave White

The University of Akron

July 2009



Ob ectivesOb ectives

Review test data for aluminum tubes

ummar ze steps use n ata ana ys s

Aluminum Design Manual – terminology, limit states, allowable

stresses

Results of data analysis

Design Recommendations



Test DataTest Data – – S uare Aluminum TubesS uare Aluminum Tubes

Square tubes with rounded corners; 4 x 0.125 in; 5 x 0.188 in; 6 x

. , . .

Square tubes with sharp corners; 6 x 0.188; 6 x 0.25 in

Alloy 6063-T6, welded with 4043 filler and solution heat treated to

T6 condition

Tubes randomly taken from different lots of material

Test s ecimen len ths varied from 16 – 27 ft

Square tubular members tested in bending about the diagonal and

geometric axis: 36 tests conducted, 6 on each type

,

in HAZ, 4 in casting/weld (3 in sharp corner tube - diagonal), 1

through loading hole



Aluminum Tube Test SetAluminum Tube Test Set--UU



Test ResultsTest Results -- ContinuedContinued

Tube Size Test Average Moment (ft-lbs) Failure

4 x 0.125 Diagonal 5909 Buckle

4 x 0.125 Geometric 6131 Buckle


5 x 0.188 Geometric 13024 Buckle


6 x 0.188 Geometric 24479 Buckle/Hole


.

6.625 x 0.25 Diagonal 31340 Tension

6.625 x 0.25 Geometric 31860 Buckle/Tension

6 x 0.25 S Diagonal 30490 Base/Weld

6 x 0.25 S Geometric 32600 Buckle



Anal sis Procedure and Back roundAnal sis Procedure and Back round

Evaluate interaction equation and reduce to simple form for specifictest conditions

Calculate slenderness of tube elements Evaluate buckling coefficients for 6063-T6 for minimum guaranteed

yield strength and average measured yield strengths

Calculate allowable stress as smallest of tension in element bending inown plane, uniform tension on wall, uniform compression on wall,

compression in element bending in own plane Calculate design moment for geometric axis based on smallest

allowable stress

Use form of interaction equation to calculate a maximum applied

stress on element

Calculate ratio of average test moment to maximum applied momentabout diagonal



Stress Condition for Square TubesStress Condition for Square Tubes

Compressed Element Compressed Elements

Geometric, 1 ComponentDiagonal Bending



Anal sis Assum tionsAnal sis Assum tions

Factor of safety for aluminum components on yielding is 1.65 –

Allowable moments calculated for a geometric axis as for steeltubes

Aluminum Design Manual inelastic buckling coefficients based on

tangent modulus concept

Approach outlined good for square tubes with slenderness lessthan S1 or between S1 and S2

Ranges may be considered as “yielding” and “inelastic buckling”

Slenderness reater than S is elastic bucklin



Inelastic Bucklin of Aluminum ElementsInelastic Bucklin of Aluminum Elements

n g S t r e s s

Bp

t i c

B u c k l i

p - κ p t

Slope = Dp

I n e l a s

Slenderness, b/t

Note:κ depends on specific conditions



Bucklin of Aluminum ElementsBucklin of Aluminum Elements

S t r e s s Fcy/n

B – κD b/t /n

l l o w a b l e

Euler or post buckling strength

Slenderness, b/tS1 S2



Interaction FormulaInteraction Formula

1=⎟⎟ ⎞

⎜⎜⎛

+⎟⎟ ⎞

⎜⎜⎛

α α

Y X M M

allowY allowX

2

==

==

allowallowY allowX

applied Y X

M M M

M M M

, reduceSubstitute

12

2

2 =⎟⎟ ⎞

⎜⎜⎛

α

applied M

⎟

⎠

⎜

⎝

allow



Interaction FormulaInteraction Formula

1SS ≤

6.1=α

091.1

allowapplied M =

21SSS ≤<

allow M =

414.1applied



Stress ConditionStress Condition – – Bucklin Coefficients Plastic BendinBucklin Coefficients Plastic Bendin

Buckling coefficient for uniform vs. gradient;

. t . t = . arp .

Condition more severe for considering uniform compression of

element

Stress – strain curve for aluminum gives rise to 2 shape factors, one

for yielding and one for ultimate

Elastic, erfectl lastic sha e factor = 1.13. For s uare aluminum

tubes, Zy = 1.1, Zu = 1.1



Anal sis ResultsAnal sis Results

4

4.5

Me/Mmxw 25 ksi

3

3.5

m a x w

Me/Mmxw 26.9 ksi

Me/Mmxw 31.3 ksi

1.5

2

2.5

R a t i o M e x p / M

0

0.5

1

4 x 1/8 5 x 3/16 6 x 3/16 6 x 1/4 6 5/8 x 1/4 6 x 1/4

Tube Size



ObservationsObservations

The average ratio of the experimental moment to allowable applied

. .

no case was the ratio less than 1.6. Allowable stresses for 6063-T6 were used and incorporated a

.

A mixture of tubes with slenderness in the yielding and inelastic

buckling range were used Calculations using the interaction equation appear to be

conservative

Square tubes with sharp corners failed by tension in the base or

weld when loaded about the diagonal



Recommended S ecification ProvisionsRecommended S ecification Provisions

Bending of Square Tubes

quare tu es s a meet t e es gn requ rements or en ng a out

the geometric axes. In addition, tubes shall be designed for bendingabout a skewed axis.



Recommended S ecification Provisions ContinuedRecommended S ecification Provisions Continued

For tubes with all elements S ≤ S1 α = 1.6

b

= cy ny

For tubes with elements S1< S ≤ S2 α = 1.0

F b

= Table 6-3

aluminum tube bent diag

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