Bruhn - Analysis And Design Of Flight Vehicles Structures Episode 3 part 4 pdf

ANALYSIS AND DESIGN OF FLIGHT VEHICLE STRUCTURES Table C4.1 Column Formulas for Round Steel Tubes Short columns # Tranal- , Local Material Ptụ; ksi|Fty, ksi|Fco, ksi bị Basic ;a ¡ Hona

ANALYSIS AND DESIGN OF FLIGHT VEHICLE STRUCTURES

Table C4.1 Column Formulas for Round Steel Tubes

Short columns (#) Tranal- , Local

Material Ptụ; ksi|Fty, ksi|Fco, ksi bị Basic ;a ¡ Honal (£) Long columns (9) i

failure Column formula (°) equation Uh

3 Equation C4, 1 may be used in the short column range if E 4 Not necessary to investigate for local instability when

is replaced by Et obtained from the combined stress- D/t 50

strain curves for the material, © This value is applicable when the material is furnished

DLt/o =L/ye: L'/p shall not exceed 150 without specific in condition N (MIL-T-6736) but the yield strength is

authority from the procuring or certificating agency reduced when normalized subsequent to welding to 60

© Transitional L/p is that above which columns are “long” ksi,

and below which they are short." These are approximate

values

smaller, the Fg stress increases Now if the diameter of the tube is relatively large and the wall thickness relatively small or, in other words, if the diameter/thickness (D/t)

Table C4.3 Column Formulas for Magnesium-

Alloy Extruded Open Shapes?

GENERAL FORMULA

° (bạ) ertppling or crushing of the tube wall and

this local failing stress is usually repre~

sented by the symbol Fog The values of Fog

in general have been determined by tests (see

(Stress values are in ksi)

AZ31B, AZ61A, AZ80A | 2,900 | 1/4 | 1.5 Fey,

AZ80A-T6, ZKGOA-TS | 3,300 | 1/4 [1.5 | 0.96 Fey In design, column strength charts are a

great time-saver as compared to substituting

in the various column equations, thus a number

of column charts are presented in this chapter

to facilitate the strength check of columns and the strength design of columns Fig

c4.2 is a chart of L'/p versus Fe for heat treated round alloy steel tubing Fig C4.3

& Formulas given above are for members that do not fail by

Fo = 1.05 Fey 4n is a similar type of chart for aluminum alloy

round tubing Fig, C4.4 gives column charts Max F = F, for magnesium alloy materials A11 three

seen ey charts are taken from (Ref 1) Figs C4.5

the design of steel and aluminum round tubing

C4.7 Short Column Equations for Other Materials

C4.10 Section Properties of Round Tubing

For other metals for which short column equations are not available, the use of Euler’s

equation, using the tangent modulus S¢ can be

used (eq C4.2) Refer to Chapter C2 for

information on how to construct column strength

curves using this equation

4.8 Column Failure Due to Local Failure

The equations as presented give the allowable stress due to failure by bending of

of round tubing A tube 1s designated by giving its outside wall diameter (D) and its

wall thickness (t) Thus a 2-1/4 - 0S8 means

a tube with 2-1/4 inch outside diameter and a wall thickness in inches of 058, Since a tube

is symmetrical about any axis, the polar moment

of inertia, which is needed in torsion problems, equal twice the rectangular moment of inertia

as given in Table C4.3 For weight comparison, the weight of steel and aluminum tubing is

STRENGTH & DESIGN OF ROUND, STREAMLINE, OVAL AND SQUARE TUBING

IN TENSION, COMPRESSION, BENDING, TORSION AND COMBINED LOADINGS,

Table C4.2 Column Formulas for Aluminum Alloys

2014-T3, T4, T451 Sheet and Plate?;

2024-T3, T351, T36, T4, | Rolled Rod, Bar and

Drawn Tube 5052—All Tempers

5083—All Tempers 5086—All Tempers 5454—-All Tempers All Products Fey(1+ ¥ Fey/1000) | Equation | 1.7327 y Z/F,, | Equation

6061-T4, T451, 74510, T4511

All Cast Alloys and | Sand and Permanent

2024-T3510, T3531, T4, | Extrusions T2

2014-T6, T651 2024-T6, T81, T86, T851 | Sheet and Plate*;

7075-T6, T651 Rolled Rod, Bar and Fa(l+ VF 9/1333) | Equation | 1.346" E/? | Equatioa

Tube

201©T6, Tesi, T8510, T6511, Tesz

20274-T6, 181, 18510, 2024-T8, TS, T8510, T8511, T8652

7075-T6, T6510, P8SIt, | Extrusiona, Forgings T082

7079-T6, T8510, T6511, T652

“Tocludes clad ss weil as bare sheet and piste

‘Transitional L’/y ls that above which the columns are “lone” and below which they sre “short”

Equation C4.8 may be used in the short column range If £7 is replaced by £; obtained from the compressive stress-strain curve for the material

ANALYSIS AND DESIGN OF FLIGHT VEHICLE STRUCTURES

given tn the last two columns of the table

C4.11 Some General Facts in Tubing Design

1 For a given area, the larger the tube

diameter, the greater the column strength

if failure due to local crippling is not

critical

The higher the D/t ratio of tube the lower

the crippling or local failure strength

If columns fall within the long colum

category, the use of higher strength alloy

steel or alimminum alloy will not increase

strength of column since £ is practically

* constant for all chrome-moly steel alloys

and likewise for all aluminum alloys

Failure is due to elastic buckling of the

column as a whole and is therefore a

function only of I, L' and E

The column end restraint effects the neces-

sary tube size Consult the design require

ments of the Army, Navy, and C.A.A in this

matter In general with welded steel

tubular trusses a coefficient of C = 2 is

permissible except for engine mount and

Nacelle structures For trusses with

riveted joints a value of not over 1.5 is

generally permissible

The student should realize that practical

limitations such as clearance requirements

may determine the diameter of the tube

instead of strength-welght considerations

Thus design can consist of checking the

tubes available under the given

restrictions

C4 12 Effect of Welding of Steel Tubes Upon the Tension

and Column Strength,

Since welding effects the grain structure

of the tube material adjacent to the weld,

tests show the strength of the material

adjacent to the weld is decreased as compared

to the unwelded material If a tapered weld

is used, the effect of the weld is decreased

Table C4.4 shows the allowable stresses in

tension to use when tension loads are carried

In short columns, the primary column failing stress may be greater than the local

crippling strength of the tube adjacent to

the weld at the end of the tube This local

failing stress Jue to welding 1s referred to

as the weld cut-off stress and the column

compressive stress F, should not exceed this

value This cut-off weld stress is shown by

the horizontal lines in Fig C4.2 and C4.5

C4.5

Tabie C4 4 Tension Allowables Near Welds in Steel Tubing (X-4130)

Normalized | Welded after HT [HT after |’

Type of Weld [Tube Welded |or Norm after Weld| Welding

*Tapered Welds

of 30° or Less( 947 Fry 90, 000 psi +90 Fry All others OAL Fig 80, 000 pst «80 Fry

“Note: Gussets or plate inserts considered 09 “taper'

with @

** For (X-4130) Special, comparable, values to the Fr,

equal to 90,000 and 80, 000, are stresses 94, 500 and

84, 100 psi, respectively

Ret Anc-5

+ C4,13 Dlustrative Problems in Strength Checking

and Design of Round Steel Tubes as Columns

and Tension Members, PROBLEM 1

Tube size 1-1/2 - 058, Length L = 30 in

End fixity coeffictent C = 1

Materlal:— Alloy steel, Fry = 95000

tube is welded at ends

Ultimate design loads are:- P = -14,500

lbs compression, and P = 18500 Ibs tension

Required the Margin of Safety (M.S.)

The

Solution: The compressive (M.S.) will be determined first As the simplest solution,

we can use the column curves in Fig C4.5

Por a length of 20 and C = 1, from the upper right chart we projact upward to the inter- section with the 1-1/2 diameter tube and then horizontally to the left hand scale to read the column strength of 14800 lbs which we will call the allowable failing Pag

The tube strength could also be found by

using Fig C4.2 as follows:

Table C4,.3 as well as the tube area 0.2628

sq in Using 58.7 for L'/p on lower scale

and projecting upward to the Fry = 95000 curve, which is the lower curve, and then horizontally to left hand scale we read

STRENGTH & DESIGN OF ROUND, STREAMLINE, OVAL AND SQUARE TUBING

IN TENSION, COMPRESSION, BENDING, TORSION AND COMBINED LOADINGS

ksi] Reference REF 1

343

COLUMN LENGTH - INCHES (C = 1)

as shown in Table C4.1, the transitional L'/o

1s 91 and the value for our tube is 68.7

Tensile Strength

Since the tube is welded, the tube material adjacent to the weld is weakened

The weld correction values are given in Table

C4.4 We will assume a weld other than

tapered Let P, = allowable or failing tensile

strength of tube

Pg = Fty (weld factor) (area of tube)

= 95000 x 841 x 2628 = 21000 lbs

M.S = (Pg/p)-1 = (21000/18500) - 1 = 0.13, thus compression is critical

PROBLEM 2

Case 1 Tube size 1-1/4 - 049, L = 40 tn

e=l Material: Alloy steel, Ft, = 95000 Find ultimate compressive load 1t will

carry

Solution: From Fig C4.5, Pg = 6000 lbs

Case 2 If tube was heat treated to Fy, =

150,000, what compressive load would

it carry

Solution: Fig C4.5 cannot be used since

Fry = 150,000, thus we will use Fig c4.2

L'=LA © = 40//1T = 4 From Table C4.5,

9 = 425 and area (A) = 1849

L'/p = 40/.425 = 94 From Fig (04.2, using the 150,000 curve, we find F, = 32500

Then Pg = FeA = 32500 x 1849 = 6000 1b Thus

heat treating the tube from 95000 to 150,000

for Fey did not increase the column strength

For a L'/p 2 94, it is a long column and

failure is elastic and E is constant

The strength could also be calculated by Euler’s equation from Table C4.1

Fy = 286,000,000/(L'/p)*

= 286 ,000,000/(94)* = 32500 psi, the

same as previously calculated

Case 3, Same as Case 1, but assume tube 1s

welded to several other tubes at its

end and that the end fixity developed

Pa = 9200 lbs Thus the ¢ = 2 fixity increased the strength of the tube from 6000

to 9200

Case 4 Same as Case 3 but heat treated to

Fry = 150,000 after welding

L'/p = 28.4/.425 = 66.8 From Fig C4.2 using 150,000 curve, we Tead Fy = 63000, whence

Pg = FoA = 63000 x 1849 = 11650 1b

In this case heat treating produced additional strength, whereas in Case 2 it did not The reason for this is that failure

occurs in the inelastic stress range and heat

treating raises the material properties in the inelastic range The end fixity changed the column from a so-called long column to a short

column

The strength could be found also by sub- stituting in the short column equal for 150,000 steel as given in Table C4.1,

Fo = 145000 - 16.36 (L'/p)?

= 145000 ~ 18.36 (66.8)" = 63000 pst

PROBLEM 3 Case l Tube size 2 - 065, L = 24, ¢ = 1.5

Material Fy = 95000 Welded at ends Ultimate design load = 25000 lbs

What is M.S

LỤ “L/€ = 24//1.5 = 19.7 From Fig 04.5 for L = 19.7 one = 1 scale, we project upward to the 2 inch tube and note that it intersects the horizontal weld cut-off line which gives an allowable column load at left scale of Pg = 26700 lb

Failure in this case is local crippling adjacent to welds at the tube ends

Solution:

M.S = Pa/p = 26700/25000 - 1 = 07

Case 2 Assume tube is heat treated to Fry

= 125000 after welding What is tube strength

L'/p = 19.7/.6845 = 28.8 Using Fig C4.2 with L'/p = 28.8 and pro~

jecting up to 125000 curve, we again note that horizontal weld cut-off line is intersected

ANALYSIS AND DESIGN OF FLIGHT VEHICLE STRUCTURES giving Fe = 95000, whence Py = 95000 x 3951

The ultimate design tension and compressive

load in each member as determined from a stress

analysis for the various flying and landing

conditions are shown in ( ) adjacent to each

member The true length L of each member is

also shown Using chrome-moly steel tubes,

Fey = 95000, select tube sizes for the given

loads It is common practice to assume the

column end fixity ¢ = 1 for engine mount

members, since the mount is subjected to

considerable vibration and the true rigidity

given by the engine mount ring is difficult

to accurately determine

e Front View

Side View Fig 4.7

Consider member (3) Ultimate design load =

~ 9250 Referring to the column charts of

Fig C4.5, we find for C = 1 and L = 31.4 the

following tube sizes for a strength near

= 10000/9250) - 1 = 08 1-1/4 ~ 058, Py =

Thus use 1-3/8 - 049 since it is the lightest

as well as the strongest

Consider member (4), Load = - 5470, L = 30,

a minizum tube thickness of 049 will be used, hence the 1-1/8 - 049 tube will be selected

Consider Member (2)

Design Loads 11650 tension and 4250 compression Since the tension load appears eritical, the tube will be designed for the tension load and then checked for the compressive load The Fru of the material equals 95000 psi Since the engine mount ina welded structure, the strength of the tube ad- Jacent to the end welds must be reduced to 841

x 95000 » 80000 psi (see Table C4.4)

Hence tube area required = 11650/80000 = 0.146 sq, in From Table C4.3, which gives the section properties of round tubes, we select the following sizes:

1L-.049, Area = 146, M.S = (.146/,.146) -1 = 0 1- 058, Area = 172, M.S = (.172/.146) -1 3.19 1-1/8 - 049, Area = 166, M.S = 14

tube size for member (1)

C4.14 Dlustrative Problems Using Aluminum Alloy and Magnesium Round Tubes as Columns and Tension Members

In general alloy steel round tubes must

be heat treated to around 180,000 to 200,000 ultimate tension strength before they can com- pare favorably with aluminum round tubes on 4 material weight basis However, aluminum alloy as used for tubes cannot be welded satisfactorily and tims in a truss structure the end connections involving riveted and bolted connections add weight and design difficulties as compared to welded connections

in steel trusses

STRENGTH & DESIGN OF ROUND, STREAMLINE, OVAL AND SQUARE TUBING C4, 12 IN TENSION, COMPRESSION, BENDING, TORSION AND COMBINED LOADINGS, PROBLEM 1 C4.15 Strength of Streamline Tubing

L= 24, ¢ = 1, Material 2024-T3 stream, the air drag is about 15 times greater Find failing compressive load than if it were given a streamlined shape, thus

streamline tubes are used when the member is Solution: The column curves in Fig C4.6 are exposed to the airstream

slightly conservative because the equation used

was Slightly different from the equation now

A column may also fail by local crushing

or crippling of the tube wall, thus the

crushing stress Fee should be determined to

See if it is less than the primary bending

failing stress for the column

For our tube the diameter over thickness ratio D/t = 1.0/.049 = 20.40 Values of D/t

are given in Table C4.3,

MU

Referring to the small chart in the upper right hand corner of Fig C4.3, we find for 4

D/t of 20.4 that Fog = 47500 psi Since this

stress {1s greater than the bending failing ~

column stress of 20,000, 1t 1s not critical

Case 2 Same as Case 1 but use ¢

change material to 6061-TS alloy

Whence Pa = 22500 x 1464 = 3300 1b,

Foc for D/t = 20.4 from Fig C4.3 2 38500 (not

critical)

Case 3 Same as Case 2 but change material to

magnesium alloy, Fey = 10,000

Figs C4.9 and C4.10 give curves for finding the column failing stress F, and the local crushing stress Foc

A streamline tube made from a basic round tube of 2-1/2 - 065 size has a fineness ratio

of 2.5 to l The length L is 30 in Take

¢ #1 Material is alloy steel Fey = 75000

Find the ultimate compressive load the member will carry

Solution: From Table C4.4 for 21/2 ~ 065

size we find the following section properties:-

Area (A) 4972, 9 (major axis) = 5137 in

Then L' = LA/C = 30// T = 30, and L'/p = 30/.5137 = 58.5

D/t value for tube = 2,5/,065 = 38.5

From Fig C4.9 for L'/p = 58.5 and D/t =

38.5, we read Fy = 46500 psi For D/t = 38.5 and reading from small chart in upper right hand corner of Fig C4.9, we read Foo = 66500 Thus Fo is critical and Pg > 46500 x 4972 =

23000 lb

Case 2 Same as Case 1 but change material

to 2024—-T6 aluminum alloy

For this material we use Fig C4.10

For L'/p = 58.5, we read Fe = 26000 psi

For D/t = 38.5, we read Fog = 37500 (not critical) Thus Pa = 26000 x 4972 = 12900 1b

.C4.16 Strength of Oval and Square Shaped Tubes

ANALYSIS AND DESIGN OF FLIGHT VEHICLE STRUCTURES C4.13

Streamline TABLE C4.4 SECTION PROPERTIES OF STREAMLINE TUBING (Fineness Ratio 2.5 to 1)

GD fDec't |Gage | Maior | Minor | ™ per fe Minor | Minar | stnor | {S481 D0 [oage] Maice | Minor | 4° | peri | stor | Mace [Mayr | tiaor | Miaer | Miao

34 |.oxs] 20 [Lotte | 4286| 44786 | 3673 { 0017 | 0| 1446 | 0073 | 0140 | 3046 044 | 18 * “| 1079 | 36684 0032| 0103| 1435 | 0097 | 0187 | 2998 2M| 049) 18 0584 17 14489 | 3773 | 1283 | tors | 145|.5194| 2 4450 | 513 | 1186 { 2660) 3163| 2406| 4343 |1.0377 47644 2747 | LOS t<].0y5| 29 |1-1800| sooo} 094] 3140] 0028} 0122) 4753 | o5 | 0195 | 3572 oe] ie Bor | aie “Tat | 383 | Son So] 33a | Hones 0i9| 18 | 7 | “az | 4333| 0037 | 0149| d7) | 6156 | 0361 | 3323 095 13 T8 | 1440 | 1615| 2941| 3038| 7504| /4333|1.0144

098 | 17 1489 | 506i | 0042 | 01684 167L | 0182 | 030k | 3495 440) ‘agra | 3.090 | 2188| 3063| 4938| : : 4 #424| 3322| Lotst :

1 os 2 1.34834 S74 eed 37 oS a 2020 oe os bi 2% ong 8 3.7088) 1.5714 ae Late 1366 17533 11 sa 7848 | 1.1432

cosa {iz | * "| A716 | [5835 | 006s | 0138| 1939 | 0278 | 0403 | 4033 ‘065 1864 | li6$| 2247| “sore | 2 THỊ 1118 1á |o| ‡o |l4070| «4436| t199 | 4074] 0065 | 616] 2292 | 0257 | 0329 | 4636 3 2364 | nee ams 5609 | Coat | 1241189 oa] ig | | Agee | | | Hới Tây | Gaon | lone | ae “20 3.371 | 2873| 3783| 3476 | 1.2427 | 6525 | 2.1196

065 | 16 2165 | 7359| 0103| 03201 2184 | 049 | 0569| 4923|| 3 | 058 azz | anes | 2493) 236 | đua | 3597 1.2056

1% |.035 | 20 [2.5285 | 1.074] 2033 | 4878 | 0308 | 0973) 3903 | 1227| 0943 | 7789 049 | 18 | 7 A “sai | 9596 | ‘onus | -0779) “sas | 4683 | 1256| 7 || #| 0634 16 [3730| 24081 | Beas 8895 | 2.6784) 5082) 1.7706

063 | 16 3656 | 11257 | 0932 | 0993| 3744 | 2186 | 4683 | 7650 1 Đ| „| „ im 38428 | 1.3055 | Le

“093 | 14 4673 | 11589 | 0680 | 4244| ‘3729 | 2719 | 2093 | 7684 aay - làn | sơn | 106i | 175

> Be 1 | er | Gt? | Sie | ass| “tiga | 2a | 1 ng || ass 084 1€ |40681| 2.5725} 2.ast7 3367 | 4.0156 | 12894 | 1.8696

058 | t7 359 |1203 | o9L | loM| 4088 | 2462| 1793 | 3588 m3) - liêu Pu r1 r1hz

1065 | 16 38 | 1.345 | 0652 | “itary 4062 | 2568 | 3925 | 2217 vel it - |1 Tô | 1 2304| 1.3507 |1 44t

083 | 14 3999 | 1699 | 0793 | 1398| 3996 | 3313 | 1399 | 4136 ay fe Ò [Ea Soot | asso | 27498 | 1832

20 40

Fty= 75000 PSI

STRENGTH & DESIGN OF ROUND, STREAMLINE, OVAL AND SQUARE TUBING

C4 14 IN TENSION, COMPRESSION, BENDING, TORSION AND COMBINED LOADINGS,

TABLE C4.6 SECTION PROPERTIES OF STREAMLINE TUBING