Composite Beam DesignUsing A Spreadsheet

By ERNEST R. JONESE. R. Jones Engineering

14 Beacon Drive EastPhoenixville, PA 19460

215/933-0188

LIKE many other readers of SPORTAVIATION, I read with interest the re-cent series of articles by John Roncz onthe use of spreadsheets for aircraft de-sign. Although I use a computer everyday, and was familiar with the spread-sheet concept, I had never had an occa-sion to write one. Using John's articlesas a perfect excuse to learn more aboutspreadsheets, I typed in the programs,and was very pleasantly surprised andsomewhat amazed by the results. Thiswas powerful stuff!

I recently needed to perform a pre-liminary design of a composite wingspar in preparation for a more detailedfinite element analysis of the wing of ahomebuilt aircraft, and after doing onesection by the normal hand calculationmethods, decided that it would bequicker to write a computer program todo the large number of remaining sec-tions. I wrote a small Basic program todo it, but then remembered John's pleain his last article for structural analyststo take up the call for spreadsheets forstructures design and analysis tasks.The resulting spreadsheet is the subjectof this article.

The spreadsheet turned out to be re-latively simple, and very easy to use.With it, a composite spar can be de-signed in just a few minutes. It can alsobe used for the design of a wooden boxspar. Of course, there are a fewsimplifying assumptions inherent in theprogram, and it only calculates stres-ses, not safety margins. Even so, it is aconvenient way to rapidly and accu-rately estimate the sizes of spar capsand shear webs for wood or compositebeams.

In the general spar design process,the loads (bending moments, shearforce, and axial force) will be calculatedfor a large number of sections (wing sta-tions) along the wing. Then, for givenmaterials, the task is to determine howthick the spar caps and shear web

should be. The width of the spar capsis selected by the designer, and canalso be varied as part of the design pro-cess.

The process for composite and woodspars is complicated by different mate-rial allowable stresses in tension andcompression, which results in caps of

FIGURE 1

SPORT AVIATION 61

a

ww/2

FIGURE 2

different thickness for normal loadcategories and a weight efficient de-sign. The caps are also generally tiltedat a small angle in order to conform tothe airfoil. This angle is just largeenough that you don't want to ignore it,but requires a lot of extra computationaleffort to include. Taken together, thesefactors make the design a tedious, errorprone, time consuming task using handanalysis methods - and make it a per-fect candidate for the spreadsheetmethod.

A typical composite spar cross sec-tion is schematically shown in Figure 1,and a typical wood box beam cross sec-tion is shown in Figure 2. Figure 2 alsoshows how the wood beam dimensionscan be approximated to look like a com-posite spar. This approximation will re-sult in only a small error for most spargeometries.

Use of the program is straightforward.Enter a descriptive title in cell A1 asshown in the printout of the spreadsheetin Figure 3. Then enter the input vari-ables in their respective cells as shown.The inputs required are the overallheight of the beam in cell C2, the loadsin cells C3, G2, and G3, the modulusvalues in cells B6-B8, the angles of thespar caps in cells C6 and C8, the widthof the spar caps and shear web in cellsD6-D8, and the height of the spar capsin cells E6 and E8.

Notice that the shear web height isnot input, but is calculated from theoverall height and the thickness of theupper and lower caps. The shear webthickness (width) is the total thickness

12345678910111213141516171819

I A I I B I IExample Beam ProblemOverall Height (in)Bending Moment (inlb)

I I E

7.7396000

Axial Load (Ib) =Shear Load (Ib) =

; I

04700

sectionupper capshear weblower capsum

sectionupper capshear weblower capsum

E8e64e68e6

alpha402

width4

.214

height.54

6.82.34

equiv-w4

.1054

equiv-A2.16.71611.36

4.2361

Ay IsubO d A*d*d stress16.0488 .0662466 2.952916 18.83458 -28150.82.685375 2.775627 .7270839 .3785670 3196.855

.2312 .0152940 4.307084 25.22932 38067.2218.96538 2.857168 44.44247

Height of Neutral Axis = 4.477084(inches from bottom)Moment of Inertia (in~4) = 47.29964

FIGURE 3

62 JULY 1991

of the web material, ignoring any coreor empty spaces. Be sure to use consis-tent units, such as inches and poundsthroughout; the angles should be inputin degrees.

The equations which make thespreadsheet work are listed in Figure 4,and should be copied into the indicatedcells. Different spreadsheets, such asLotus 1-2-3, Excel, etc., may requireslight modification to work properly. Thecontents of row 4 (A4-H4) may be ig-nored since their only purpose is todraw a horizontal line below the loadssection. Of course any cell containingonly text may be changed as desired toimprove the appearance and clarity ofthe spreadsheet, but the cells contain-ing equations should be copied exactly.The example problem shown in Figure3 may be used as a check case to verifythat your spreadsheet is functioningproperly.

The program will calculate the sectionproperties and stresses, and output theresults in their respective locations. Themaximum stresses in the upper andlower spar caps are output in cells F12and F14, and the maximum shearstress is output in cell F13. If the stres-ses are too high or too low, simplychange one or more of the spar capthicknesses or width or shear web thick-ness until the desired stress levels areachieved. The moment of inertia isprinted out in cell D19, and the heightof the neutral axis above the bottom ofthe beam is printed out in cell D17.

After a few iterations, the stresses willconverge quickly on the desired stressvalues. When finished, print out the re-sulting spreadsheet for a permanent re-cord of the design, or give it a uniquefile name and save it to a backup disk.

The program is based on simplebeam theory, as given in any goodstrength of materials or aircraft struc-tures textbook, e.g. Reference 1. Forbeams made of materials having differ-ent moduli, the spreadsheet first con-verts the actual beam into an equivalentbeam of the upper spar cap material.The stresses are calculated based onlinear elastic theory, and are correct forthe actual beam. The spreadsheet doesnot account for many details in struc-tural design and analysis of beams,e.g., the attachment of the shear webto the spar (these angles are ignored inthe spreadsheet). Also, the spar capsand shear webs are assumed to containno holes for fasteners, etc., which willintroduce significant stress concentra-tions, especially in composites.

There are many failure modes in awing spar in addition to the obviousones of exceeding the material ultimate

Audit Contents Report - BLOCK Cells

AlA2C2E2G2A3C3E3G3A4B4C4D4E4F4G4H4A5B5C5D5E5F5G5H5A6B6C6D6E6F6G6H6A7B7C7D7E7F7G7H7A8B8C8D8E8F8G8H8A9G9AllBllCll

Beam ProblemHeight (in)

(lb

(inlb)

RR

"Example"Overall7.7"Axial Load0"Bending Moment396000"Shear Load (lb) =4700-0,100,35,10,55,10-0,100,35,10,55,10-0,100,35,10,55,10-0,100,35,10,55,10-0,100,35,10,55,10-0,100,35,10,55,10-0,100,35,10,55,10-0,100,35,10,55,10

TL = "section= »E= "alpha= "width= "height= "equiv-w= "equiv-A, »y

= "upper cap= 8E6= 4= 4= .54= D6= E6*F6= E8+E7+E6/2= "shear web= 4E6= 0= .21= C2-E6-E8= D7*B7/B6= E7*F7= E8+E7/2= "lower cap= 8E6= 2= 4= .34= D8*B8/B6= E8*F8= E8/2= "sum= G6+G7+G8

TL = "section= "Ay= "ISUbO FIGURE 4

(Continued on following page)

SPORT AVIATION 63

(AUDIT CONTENTS REPORT - BLOCK CELLS - Cont.)

DllEllFllA12B12C12

D12E12F12

A13B13C13D13E13F13

A14B14C14

D14E14F14

A15B15C15E15A17D17A18D18A19D19

RRR

= "d= "A*d*d= "stress= "upper cap

G = G6*H6= (F6*E6/12)*(E6"2*COS

(C6*PI/180)"2+F6~2*SIN(C6*PI/180)~2)= C2-D17-E6/2= G6*D12*D12= (-C3*((C2-D17)+D6/2*SIN

(C6*PI/180))/D19+G2/G9)= "shear web

G = G7*H7= (F7*E7~3)/12= D17-E8-E7/2= G7*D13*D13= (G3/D19/F7)*(((C2-D17-E6/2)

*G6)+((C2-D17-E6)"2*F7/2))*B7/B6= "lower cap

G = G8*H8= (F8*E8/12)*(E8"2*COS

(C8*PI/180)~2+F8~2*SIN(C8*PI/180)~2)= D17-E8/2= G8*D14*D14= (C3*(D17+(D8/2)*SIN

(C8*PI/180))/D19+G2/G9)*(B8/B6)= "sum

G = B12+B13+B14= C12+C134-C14= E12+E13+E14= "Height of Neutral Axis == B15/G9= "(inches from bottom)

G

"MomentC15+E15

of Inertia (in~4) =FIGURE 4 (Continued)

stress in tension, compression, orshear. For example, the wing sparshear web may fail by buckling, sincethe allowable buckling stress may bemuch less than the material shear al-lowable. Also, there are often significantvertical forces in the plane of the shearweb due to kick loads or the attachmentof landing gears, etc. These requirespecial consideration beyond the scopeof this simple program.

This spreadsheet was generatedusing the SuperCalc Ver. 5 software,but can be adapted to any of the avail-able spreadsheet programs with minormodifications. If you have trouble get-ting the program typed in correctly, orjust want to save some typing, I will behappy to make a copy (xxx.cal format)for you on your disk enclosed in astamped self addressed disk mailer(SSADM); or you can download it usingyour modem by giving me a call first on215/933-1088 (evenings and weekendsonly). If you don't have a spreadsheetprogram, I can also provide an execut-able program which will do the samething (again, SSADM please).

The program has been checked invarious ways, and is believed to be cor-rect. However, it is provided free in thepublic domain, and all responsibility forits accuracy is assumed by the user. Ifthere is sufficient interest, I may be ableto come up with other spreadsheetswhich would be of use.

References

1. Timoshenko, S. and Young, D. H.,"Elements of Strength of Materials",Fourth Edition, Van Nostrand Com-pany, Inc., Princeton, NJ 1962.

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PHILLIP J. BELLANCANiagara Falls, NYDALE BERKIHISERHuntington Beach, CAGLENN BOTSFORDCudahy, WlELON H. GARYPark Rapids, MNDANIEL GATHERCOALPalatine, ILKENT GREENToronto, Canada

PHILIP HAMILTONEllensburg, WAJAMES R. HARMANDes Plaines, ILGERARD HUBERMaplewood, WlJERE KIRSTWisconsin Rapids, WlPAUL KURTZFairfield, OHDAVID LAWRENCEWarner Robins, GA

JOHN LUKETwenty Nine Palms, CASERGIO MACHADOPorto Alegre, BrazilPHILIP MAYSGeorgetown, KYAL NARKEWICZPlacerville, CABRIAN PERKINSanta Clara, CABERNARD A. RASCHBenton City, WA

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LOYD VEALBison, SdAL WARRINERSlidell, LABUR ZERATSKYGreen Lake, Wl

64 JULY 1991