Stress Distribution near a Rectangular Cut-out in a Reinforced Circular Cylinder due to Direct Shear Loading and Torque. Part I. Test Results

d Z O Q , LU REPORT No. 51 TECHNISCHE 'HOGESCHOOL VLIEGTUIGIOUWKUNDE Kanaalsuaat 10 — DELFT

17 APR 1952

THE COLLEGE OF AERONAUTICS

CRANFIELD

STRESS DISTRIBUTION NEAR A RECTANGULAR

CUT-OUT IN A REINFORCED CIRCULAR CYLINDER

DUE TO DIRECT SHEAR LOADING AND TORQUE

PART I-TEST RESULTS

by

G. HENSON, D.C.Ae.

T/i/s Report must not be reproduced without the

permission of the Principal of the College of Aeronautics.

KanaalsUaat 10 — DILFT REPORT NO. 5J_ J a n u a r y , 1952

17 APR 1952

T H E C O L L E G E O F A E R O N A U T I C S C R A N P I E L D

Stress Distrihution near a Rectangular Cut-out in a Reinforced Circular Cylinder due to Direct

Shear Loading and Torque part I; Test Results

_ hy

-G. S. Henson, D. C. Ae.

— o o O o o —

S U M M A R Y

A cylindrical reinforced cylinder

187" "by 100.6 outside diameter, with two horizontally opposed rectangular cut-outs was loaded separately "by direct shear and torque.

Electric resistance strain gauges indicated skin shear in the bay with cut-outs, longeron and frame loads, and stringer-longeron weh shear.

The stress distributions found are compared with those of previous tests with this structure, when

fitted vi^ith transverse (floor) "beams and a third (luggage hatch) cut-out.

The ^resent tests are compared with theoretical predictions in Reference 1. Pair agreement is o"btained.

C O N T E N T S I n t r o d u c t i o n A p p a r a t u s D e t a i l s of T e s t s R e s u l t s TECHNISCHE HOGESCHOOL VUEGTUIGIOUWKUNDE Kcmaalsuaat 10 - DEIiT

\ 7 m

1952

P a g e 1 1 1 2 Conclusions References 2

Appendix: Criticism of Cut-out Design

Table I

. 7

Introduction

The specimen available for tests had been modified to contain cut-outs and tested to destruction by the Bristol Aeroplane Co. Ltd. (Reference 2).

It was repaired and simplified by removing floor beams and filling a third cut-out, to leave the structure given in Table I and Figures 2, 3> 6 and 7. This comparatively simple structure was expected to be more amenable to calculation, and by comparison with previous tests, to indicate floor beam effects.

Study of previous work (see references) showed that there existed a need for such investiga-tion, particularly on a structure that could be

considered typical of present (pressurised) aircraft, in having a heav,y angle member at the edge of the cut-out, connecting reinforced frames and longerons.

Apparatus

A simple 'A Frame* was strengthened, and a calibrated hydraulic torque and direct shear loading rig added. Ram bending and friction effects were reduced as far as possible. The specimen was

locally strengthened and bolted to a rigid backplate of steel I beams. Figure 1. 90 ohm strain gauges

(H. Tinsley and Co. Ltd. ) were cemented to the

specimen in shear and tension groups. Compensation for temperature changes was provided, and, where

both sides of the material were accessible, also for buckling. In the few cases where buckling compensa-tion was required but could not be provided, results have been neglected.

Percentage resistance change of these gauges was measured on a 50 vvay R.A.E. type. Savage and Parsons unit.

Deflections of the specimen were measured relative to the floor, and the deflections of the backplate were taken at three points to enable tilt

to be measured and to ensure negligible rig distor-tion and consistency between tests.

Details of Tests

Load was applied in increments and percentage change of resistance noted. These were plotted and show very good linearity.

Typical plots are Figures k and 5» I"t will be seen that for direct shear loading, jack pressure was plotted directly since pressure-load calibration

followed a straight line law. In some cases a change of slope occurred with skin buckling.

Slopes of these plots v/ere recorded giving percentage resistance change due to load increments of direct shear (AW) or torque (/iiT).

Skin shear distribution about the centre line of bay with cutouts was first determined

-Figures 9 and 10. Assuming values of shear modulus, skin thickness (nominally 19G) and gauge sensitivity factor this was converted to values of resistance of skin to load.

Since resistance to A w was 87 per cent while resistance to A T was 98 per cent of applied load, further tests included investigation of stringer and longeron web loads in one quadrant of the cylinder, Figure 8. In fact, 5 per cent of the resistance to A W proved to come from stringer and longeron webs in shear (of course, these could not resist A T ) . Frame and longeron axial strains were also found.

Results

Assuming values for the elastic constants of the materials, and the gauge sensitivity factor, and calculating section constants for the various mem-bers (making allowance for skin tension and compression

cases), the readings of strain were converted to skin stresses, web loads and frame and longeron loads. These results have been presented graphically.

After checking results for linearity of strain across the section of a member, Figure 6, load increments in a member by more than one method etc. (figures 8, 12 and 13)> it is felt that these results give fair indica-tion of the stress distribuindica-tion at the corner of the cut-out investigated.

The most doubtful value plotted is that of maximum frame load where some non-linearity of strain across the section was found. The value plotted is thought to be within 10 per cent of the true value.

Also of doubtful value is the distribution of direct stress near the cut-out (Figure 11). This is due to the poor skin riveting and resultant skin buckling even in unloaded condition. These gauges were compensated for buckling, but rate of acceptance

of load was affected.

Conclusions Tests

The filled in cut-out did not affect the symmetry of stress distribution. Removal of floor beams had little effect on skin shear stress but

completely changed the pattern of frame loads. 'I • Skin Shear

When direct shear'.AW was applied, the maximum shear stress found was 2.6 times that for

uncut cylinder, and occurred in the bay with cut-outs, the stress in other bays being very considerably belov/ this,(Reference 2). Skin provided 87 per cent of the

resistance to this load, and stringer and longeron webs 5 per cent: total 92 per cent. For torque A T applied, the maximum stress was 3-k times that for uncut cylinder, the skin providing 98 per cent of resistance.

Since results are based on over 700 strain gauge readings, and only the calibrated loading

apparatus differed between tests, better agreement had been expected between these resistances.

2. Longeron Loads

Stress due to axial load was small (20 per cent of the stress due to BM). Both BM and axial load were a maximum at the edge of the cut-out and

died away exponentially. BM was of the same magnitude as that in the frame.

3' Frame Loads

Both BM and axial load were a maximum at the edge of the cut-out and thereafter very rapidly became negligible.

k' Skin Hoop Stress reached a high value (Figure 11). 5. Skin Buckling

The load-strain curve became almost linear again after skin buckling, but a given load increment then caused about 18 per cent more stress at some points in frame, and longeron near the cut-out, than before buckling. Maximum skin shear stress increased

similarly about 8 per cent.

Theory

Theoretical prediction of the stresses is compared with these test results in Reference 1.

Design

The structure may be considerably simplified and maxim\Mi stresses decreased by a simple change in layout and a further change in longeron construction

- u

-R E F E -R E N C E S

Author Title, etc.

Henson, G. S , vj. u .

Butler, S.

Gololobov, M. M.

Stress Distribution near a Rectangular Cut-out in a Rein-forced Circular Cylinder due to Direct Shear Loading and Torque. Part II, Theory.

College of Aeronautics Report (to be published^.

Type 167 Shear Tests on Half Scale Fuselage with Door Cut-outs.

Sc. and Tech. Memo. 6/50.

Shear Distribution due to Twist in a Cylindrical Fuselage with Cut-out.

Jour. Aeronautical Sciences Vol.lii, 19I4.7. pp. 253-6. Langhaar, H. L. and Smith, C.R. Podorozhny, A. A. Kay, W. and Micklethwaite, F. Hoff, N.J. and Boley, B.A. Hoff, N.J. , Boley, B.A. and Klein, B.

Hoff, N.J., Boley, B.A. and Klein, B.

Stresses in Cylindrical Semi-Monocoque Open Beams.

Jour. Aeronautical Sciences Vol.li]., 19U7. pp. 211-20.

Investigation of the Behaviour of Thin-vValled Panels with Cut-outs.

NACA Tech. Memo.109U, 19i+6.

The Stressing of Large Rectangular Cut-outs in Fuselages. Strain Ga^ige Analysis of York.

A.R.C. R and M.

2135-Stresses in, and General Instability of, Monocoque Cylinders with Cut-outs. I - Experimental Investiga-tion of Cylinders with a Symmetric Cut-out subjected to Pure Bending. NACA Tech. Note 1013, 1946.

Stresses in, and General Instability of, Monocoque Cylinders with Cut-outs. II - Calculation of the Stresses in a Cylinder with a SyiTimetric Cut-out.

NACA Tech. Note lOlij.» 1914-6.

Stresses in, and General Instability of, Monocoque Cylinders with Cut-outs. Ill - Calculation of the Buckling Load of Cylinders with Symmetric Cut-out subjected to Pure Bending.

References (contd.) NOj_ Author 10. Hoff, N.J.,

Boley, B.A. and Viggiano, L.R. 11. Hoff, N.J.,and Klein, B. 12. 13. 1i|. 15. Hoff, N.J. , Klein, B. and Boley, B.A. Hoff, N.J. , Boley, B.A. and Mele, J.J.

Hoff, N.J. , Boley, B.A. and Mandel, M.W.

Cicala

Title, etc.

Stresses in, and General Instability of, Monocoque Cylinders with Cut-outs. IV - Pure Bending Tests of Cylinders with Side Cut-out.

NACA Tsch. Note 1261)., 191+7.

Stresses in, and General Instability of, Monocoque Cylinders with Cut-outs. V - Calculation of the Stresses in Cylinders with Side Cut-out.

NACA Tech. Note 11+35» 191+8.

Stresses in, and General Instability of, Monocoque Cylinders with Cut-outs. VI - Calculation of the Buckling Load of Cylinders with Side Cut-out subjected to Pure Bending.

NACA Tech. Note 11+36, 191+3.

Stresses in, and General Instability of, Monocoque Cylinders with Cut-outs. VII - Experimental Investi-gation of Cylinders having either Long Bottom Cut-outs or Series of Side Cut-outs.

NACA Tech. Note 1962, 191+9.

Stresses in, and General Instability of, Monocoque Cylinders with Cut-outs.-' VIII - Calculation of the Buckling Load of Cylinders ?/ith Long Symmetric Cut-out subjected to Pure Bending.

NACA Tech. Note 1963» 191+9. Effects of Cut-outs in Semi-Monocoque Structures.

Jour. Aeronautical Sciences Vol.15» 191+8, pp. 171-179.

6

-A P P E N D I X

Criticism of Design

The load carrying ability of the existing structure seems to be open to criticism at two points:

(i) Since the cut-out edge member and longeron are separated, the edge member transmits large axial loads (in a longitudinal direction) which have to be resisted by the frames at the cut-out in sideways bending.

(11) The maximum value of bending (in a normal manner) and axial load in the frames at the cut-out occurs at a point of low second moment of cross sectional area.

Separation of Longeron and Cut-out Edge Member The discontinuity in skin shear stress distribution occurring at the longeron (Figure 10) indicates an axial load increment in the longeron of the order found (Figure 13),

A discontinuity four times as great occurs at the edge of the cut-out. This implies the presence of axial loads of a high order. There is little re-distribution of stress aftei buckling. These loads cannot continue as direct stresses and must load the skin and frame at Y (Figure l6a) in an unconventional manner. This is supported by the skin buckling that occurred. This could be avoided by putting the

longeron at the edge of the cut-out; shaping in section as Figure l6b, which has the distribution of area required.

Lack of Frame Reinforcing

Referring again to Figure l6a, the existing structure has a local reinforcing channel at Vv where the longeron cuts into the skin flange of the frame

(Figure 7). At Y the only reinforcing Is due to a flange from a 21+G doubling plate.

At Z the frame is heavily reinforced by the cut-out edge angle.

Maximum frame loads occur at Y (Figure I5). This leads to frame stresses three times those found in the longeron and twice those elsewhere in the frame.

It is suggested that this could be prevented by continuing the reinforcing from the longeron frame

T A B L E I

DIMENSIONS OF TEST SPECIMEN - See Figure 2

Cylinder of 17 - 11" Bays (187") 100.6 outside diameter

SKIN 19G Uniform

+ 21+G Doubler in Radius of Cut-out Corner.

STRINGERS LONGERON Z Average Spacing 2.1+7" A = 0.185 with 2" skin I = .0359 Inches^ X = 0. 35' from skin. Maximum FRAME at cut-out A = 0.705 Inches I = .305 inches^ X = 0.585" from skin. Maximum 2 A = 0.1+90 inches I = 0.227 (0.20 used as weighed mean for calculation) X = 0.71+"from skin. Mean of skin tension and V Compression ' Values, See Figures

6

and 7* J CUT-OUT 21+. 5° and 25°

From Horizontal Centre Line. LONGERONS 25.5° and 29° )

Door edge 10G Mg angle otherwise D.T.D. 390.

COLLEGE OF AERONAUTICS REPORT No. SI.

I. DIRECT SHEAR: HYDRAULIC LOADING RIG AND JACK.

JACK MOUNTED ON ROLLERS.

2. TOROUE: HYDRAULIC LOADING RIG AND JACK.

3. SAVAGE AND PARSONS TYPE STRAIN RECORDER.

1 o ₅ lO 15 2 0 25 3 0 35 4 q 45 5 0 55 6 0

SEE ALSO FIGS 9. lO.

f 1 2 3 4 \ 5 . 1 ' '' ' ' ^ = —

1

— = = = = = = = « = - V FIR3. 4.5. • — ... • T | < ' ' A 2 S ^ - = ^ ( » A - ^

N=^

- : .1 ^ I * A 1 ^ ' 1 A = ; I El E3 ' 2 4 i A 6 'A7

TWi

2 1 1 2 24.G.DOUBLER

i

j

^m

I I . 17" BAYS i> 7 8 9 lO tl 1GIA3. 1 H8.9.IQ 1 11.12.13,14. E7 E9 1 ^B~6 lO 1 I H 4 5 . 6 1 1 H1.2,3. r ^ ^ = — = Eli 12 _ = 1 / f 1— j » ~ i k A-- ^ '^' ' 1

i

. / . CO L REP O / / / / / / / 5tn z '" o r. w St iü Tl ^ m a j O z > c o ut

rO -^

K °

• * / •?

\/o

/ / / / / / / / / / ^ ,

AS FIG IC- LINE OF SKIN SHEAR GAUGES.

SYMMETRIC ABOUT VERT t ARRANGEMENT OF STRAIN GAUGES.

vFILLED IN CUT OUT THIS SIDE ONLY

JOINT CHANNEL SECTIONS l: 2"x-45" 19 G 2.5:2"»t-70'' 166 3.4: SEE FIG.6. 6 : 2 ' i f 6 0 * 18 G

ALL SECTIONS EXCEPT 3 ; 4 HAVE STRINGER CUT OUTS.

DOOR FRAME SCALE. '/|6

KO-5'i

POR FURTHER DETAILS SEE FIG: 6 . 7

FIG. 3. DETAIL OF STRUCTURE.

^ 2 0 . G .

^ii==.

STANDARD FRAME i-o

f>s\ssssss

:o o n! o -0 r O tH m Ci m O > » O

r

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kWWWNW'

S C A L E : FULL SIZE %r O -r

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REINFORCED FLOOR LONGERON I " T " , ,r •',

SCALE: FULL SIZE L O N G E R O N R E I N F O R C E D WHEN FUDOR BEAMS R E M O V E D . NOT STRAIN G A U G E D .

9

• 1-36"

G/l960st44& 10 - DBLFT J^H4

- O l

I 2 0 0 H 3. 6

FRAME TENSION GROUPS EXAMPLE OF:

JACK PRESSURE >TRAIN GAUGE READING

COLLEGE OF AERONAUTICS REPORT No. 51. - 0 2 SENSITIVITY - 0 1 °/o CHANGE IN

RESISTANCE _{SLOPES PLOTTED}

FIG. 6. '

®

2 0 0 4 0 0 LONGERON 6 0 0 F S . 8 0 0 JACK PRESSURE l b / I N ^ - 0 1 SENSITIVITY M 2 "/o CHANGE IN RESISTANCE SLOPES PLOTTED FIG. 7. DEF'N INS. G.3. , JACK PRESSURE l b / I N ' 14-3

* * "^VyCHECK FROM PREVIOUS TEST

5

13*8

A, 3, ARE POINTS ON THE LOADED END OF THE CYLINDER. 2 0 0 4 0 0 6 0 0 DIRECT SHEARrA.B.ANPq. 8 0 0 JACK PRESSURE lb ƒ I N ' 0-2 SENSITIVITY x 2 O 2 p O O 4 , 0 0 0 6iOOO

FRAME AND LONGERON. DEF'N. INS. 8 . 0 0 0 1 0 , 0 0 0 F JACK LOAD: lb J 22-7 2 0 - 4 A 2 0 - 2 '

!S

r ' • ——— • -'———

E H ^ ^

HECK FROM PRE

P^^::^

^lOUS TJST O 2 . 0 0 0 4 , 0 0 0 TORQUE: D.ANDE. 6,000 22-5 8 . 0 0 0 1 0 , 0 0 0 JACK LOAD: lb p j Q g

LINEARITY OF STRAIN ACROSS SECHON. (TENSON - V E ) - 0 - 2 I - O - l L-O l _o o-l 0-2 I 0 - 3 8 GROUP 2 , 4 , 6 * F 0 - 3 0 ' GROUP 8. 0 - 2 l " GROUP lO: No 2 0 G ,0-l4" GROUP I2-. No 2 0 G + 0 9 " WIDE

UDNGERON

0 0 4 _{A W g 2 0 ; 0 0 O l b DIRECT SHEAR. ATiM-92.10° TORQUE}

• 0 0 4 " 3 6

FOR H 4 S 6 MG. ANGLE PARTED FROM FRAME REPLACED BY 24 G DOUBLER ANGLE: FIG.16.

A W - 2 0 . 0 0 0 l b DIRECT SHEAR. g r = l 9 2 » c l o 6 | b IN TORQUE.

FIG. 6. STRAIN DISTRIBUTION ACROSS FRAME AND LONGERON

p S ÏÏ o -n > m •J} O z o (A

• / o GAUGE RESISTANCE CHANGE F O R - A T A W D A W .

81 + DI

U—i.o"->J ^'

FIG.7 STRAIN DISTRIBUTION ACROSS FRAME.

Bt AW = 2 0 , 0 0 0 lb. DIRECT SHEAR. Ql. QL Bi ATasl-92>tlO'''{blN TOROUE TO m O :o -t z o UI ' o o r-m O m o -»i > m X3 o 2 > C -1 O V

REPORT No. 51.

TORQUE ATa I-98. lO*^ lb IN 3 8 8 1^ :^20 .LONGERON DIftECT SHEAR: A W » 2 0 . 0 0 0 l b . 3 7 0 lb - 3 0 . - 2 0 - l O O lO 2 0 3 0 RADIAL WEB SHEAR LOAD IN STRINGER: lb

CHECKS:

2 H » M O M E N T O F AREA Of- Z STMNGER • 2 " S K I N » 0 0 3 6 i N ^ 1 R A T I O ' f t fi „ LONGERON i i = 0 - 3 I O l N ^ J

COMPARE MEAN EQUIVALENT RADIAL WEB LOADS.! ^ ^ ' ^ ' N ' ^ ^ ' ' - ' * 5 ' b - \ R A T I O ' 8 ' 4 C LONGERON: 3 7 8 IbJ

ALSO FROM FIG. 12, LOCAL SLOPE OF LONGERON BM. C I A G - - 0 1 4 l b / l b . IE. LONGERON SF APPROX 2 8 0 lb C^W = 2 0 , 0 0 0 lb.)

IN SECTION T E S T F D :

TOTAL OF COMPONANTS OF WEB LOADS ASSISTING SKIN To RESIST DIRECT SHEAR LOAD OF 2 O OOO l b : APPROX:s250 l b .

I,E. TOTAL IS 5 °lo OF AW. _ . , _

STRINGER AND LONGERON WEB LOADS AT CENTRE OF BA^ WITH CUT OUTS

i <

c«

0-5 SHEAR STRESS lb/lN^//lbAW O lO 2 0 3 0 4 0 5 0 60

SHEAR STRESS AT <t. OF BAY WITH CUT OUTS: DUE TO AW.

7 0 DEGREES 8 0 90 m •o O •a z o UI o O m O m O "«I > m O •z > c O FROM VERTICAL t p . Q g

SHEAR STRESS Ib/IN^//2R.AT.IfaJM. Ra50-3" f V ï JM. 0-4 0-3 0-2 O'l O PRESENT TESTS "COMPRESSION SIDE "TENSION SIDE" ^''*"*'*'~^.^ ^^'""^«„^^ LHS: +AND RHS:» **^ SUPERIMPOSED. UNCUT CYLINDER BATHO Dl

^ t ; .

-ST'N

\

^ .

-J-\ \ ^ j ^ s

J

_J7

hf

1/

/ M 1^ / /

y

X

+

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k

^ LONGERON % T 64'5*' •fcOMP'N SIDE!' 61" " T E N S I O N SIDE".' 1 1 24.5" 'COMP'N SIDE" 25* "TENSION S D E " 1 O lO 20 30 4 0 so 6 0

SHEAR STRESS AT t OF BAY WITH CUT OUTS: DUE TO AT

O :o z o

7 0 8 0 9 0 DEGREES FROM VERTICAL g F i G . t O .

m O m O > m :o O z > c o o»

COLLEGE OF AEItONAUTICS REPORT No. 51. SECTION XX. TORQUE. 0 - 4 WR6CT STHEgS: t« fr Ik lm' FOB amitm i R=50-3" Q TENSION-V^ DIRECT STRESS: t»;tr Ib n ' FOW AW«I>, TENSION-VE PRESENT 2eTESTS

SHEAR STRESS y y l>/IN^ FOR AHHIIb

SECTION YY DIRECT SHEAR.

O 0.2 0 4 SHEAR tTBESS ^»y ft/IN^

FOP A T e 2 R l b l N P-50.3f

SECTION YY

TORQUE-SECTION XX. DIRECT SHEAR

RG. II.

DISTRIBUTION OF DIRECT AND SHEAR STRESSES

BENDING MOMENT.

Ib.lN. / lb. AW O-l

•CUT OUT- PRESENT TESTS

8.A. C2 TESTS SKIN TENSION + VE / > • — * * i ^

c^'^

>

V

. ^ ^ " -o-l AXIAL LOAD Ib / IbAW O-l TENSION •4-VE - O l FR.3. _FR.4. FR5. FR.6. _FR.7 FR.8.

SLOPES OF OPPOSING SIGN SINCE

TESTS ON OPPOSITE SIDES OF CYLINDER.

< • — _{- + r^} . - — - - ^ ^ ^ ' ^ ^ w

>s^

< . ™ . . ™ ^ . , . • ^ ^ . ^ "^ •

A : AXIAL LOAD IN LONGERON DUE TO BENDING ( T K E O R Y . ) B : EQUIVALENT AXIAL LOAD INCREMENT TO DISCONTINUITY

IN SHEAR STRESS DISFRIBUTiON FIG.9.

NOTE: STRESS DUE TO BM. APPROX S TIMES STRESSES DUE TO A.L.

o-I SKIN TENSION •I'VE - O i BENDING MOMENT Ib IN /2R.AT.IblN CUT OUT » -AT = 2RlblN ( K XI m 13 O X) H Z O UI o O r-m O m O > m 7 j O z > c - 1 O O) FR.3. FR.4. FR.S FR.6. FR.7 FR.8. AXIAL LOAD l b , / 2 R A T I b l N . O-l

A : EQUIVALENT AXIAL LOAD INCREMENT TO DISCONTINUITY IN SHEAR STRESS DISTRIBUTION. FIG. lO.

N O T E : S T R E S S DUE TO B M APPROX. 5 TIMES STRESS DUE TO A.L.

SKIN TENSION -f-VE TENSION + VE 0-I5 O-l O 0 0 5 - 0 ' 0 5 - O - I O -O-IS - O - I O - 0 - 0 5 4 - 0 ' 0 5 +0-I0 o ._ BENDING MOMENT IbIN/lbAW. lO 2 0

1 1

PRESENT TESTS B.A Co. TESTS.

3C 4 0 ^ 1 i

.y

^ . i > ^ 1 ^

y

' so o AXIAL LOAD l b / l b AW 10 2 0 PRESENT TESTS a A. Co. TESTS •—» 3 0 4 0

L'^

, 0 ^

y

so

v

ILONGEROH

y

SO . ^ so *••,» — *^, j T o u r ^ ^

t

7 0 8 0 - ^ ^ • ' ' < 7 0 V \ . — — • • \ ^ BO

DEGREES FROM VERTICAL \ " • * ^ ^ 9C HORIZONTAL < \

Vj^

.1

i 9 0 M m T3 0 :?) —t .^ 0 U l 0 0 r-n i G) m 0 •n > m X) 0 z > c; -« 0 (/>

SKIN TENSION -t-VE TENSION + VE O-IS O I O 0-05 O - 0 - 0 5 O — ^ - r l < w > - 0 - I 5 - O - I O - 0 0 5 O + 0 0 5 j - < ^ . i / - » O BENDING MOMENT lb.lN / 2 R A T l b . l N . lO AXlAL LOAD l b / 2 R AT lb IN lO 1 2 0 3 0 2C — f 3 0 PRESENT TESTS , 4 0 1 1 PRESENT TESTS 4 0

y

^ 1 i / so > /

~y

/ 5 0 y / LONGERON

r—

^ ^ 6 0 ^ ' ^ {.0 — K ^ CUT OUl ^ - v . ^ ^ ^ 7 0 ^

v,^

N.

8 0 ^ - H -_{^ ^}

N

7 0 V

X

V s

8 0

DEGREES FROM VERTICAL <t

4.

— p - t 1

fN

1 ? HOR 2 <t.

N

? :o m u 0 V -» - r 0 C l T" 0 0 r~ r-m 0 m 0 •r\ > m S) 0 z > a -) 0 v>

REPORT No. 51. SKIN BUCKLING. rcx\ EXISTING STRUCTURE NOT TO SCALE. LONGERON. LONGERON SECTION WITH CUT o u r EDGE

/-bN SUGGESTED STRUCTURE

NOT TO SCALE.