AA-SM-219 Tools - Various Mass Balances - Linear and Rotational

ABBOTT AEROSPACE INC. PROPRIETARY INFORMATIONSubject to restrictions on the cover or first page

Author:R. Abbott Document Number:Check: Revision Level :Date:Dec-09 Page:

Two Body - Two Dimensional

Point Masses - (No individual body mass properties)

Mass 1 = Mass 2 =5 lb 15

L = 20.00 in= 1.67 ft

Center of gravity distance from point 'a':= 15 / (5 + 15) 20 = 15.0 in= 1.25 ft

Mass moment of 'a' about centroid: Mass moment of 'b' about centroid:0.243 slugft 0.081

Total Mass moment of inertia about the centroid:= (20 - 15) 15 + 15 5 = 1500 lbin= 0.324 slugft

Applied Load:P = 200 lb

Distance from 'a' = 16 in= 1.33 ft

Moment effect:M = (15 - 16) 200

= -200 inlb= -16.7 ftlb= -0.52 sluglb

Liner accelleration:n = 200 / (5 + 15) = 10 g

Angular Accelleration:= - 0.52 / 0.32 = -1.6 rad/sec

Author:R. Abbott Document Number:

The system is assumed to be held in a quasi steady state, the intertia reaction to the applied moment will be calculated:

ABBOTTAEROSPACE [email protected]

ABBOTT

ba

Moment Convention(Point 'a' up)

Load Convention(Positive up)


Check: Revision Level :Date:Dec-09 Page:

Two Body - Two Dimensional

Reaction load Due to linear accelleration:at 'a' = - 10 5 at 'b' = - 10 15

-50.00 lb -150.00 lb

Reaction Loads due to Angular Accelleration:at 'a' = - - 1.6 0.24 / (1.25) 32.2 at 'b' = - 1.6 0.08 / (1.67 - 1.25) 32.2

9.99 lb -9.99 lb

Total load at 'a': Total load at 'b':= - 50 + 9.99 = - 9.99 + - 150 = -40.01 lb = -159.99 lb

Check on Total Load:Sum of Reactions = -200.0 lb

Applied Load = 200.0 lb 0.0



AA-SM-219A1 of 1

lb

Mass moment of 'b' about centroid:slugft

AA-SM-219

The system is assumed to be held in a quasi steady state, the intertia reaction to the applied moment

b


A2 of 1

- 1.6 0.08 / (1.67 - 1.25) 32.2


Author:R. Abbott Document Number:Check: Revision Level :Date:Sept 2013 Page:Title: LINEAR AND ROTATIONAL MASS BALANCE

LINEAR AND ROTATIONAL MASS BALANCEComponent

Local Distance LocalMass from Mass

Locations Coordinate Mass Moment Coordinate CG Mass Moment(in) (lb) (lbin) (ft) (ft) (slug) (slugft)

1 0.00 10.00 0.0 0.00 -3.79 0.31 0.002 6.00 12.00 0.0 0.50 -3.29 0.37 0.003 10.00 15.00 0.0 0.83 -2.96 0.47 0.004 23.00 5.00 0.0 1.92 -1.87 0.16 0.005 25.00 30.00 0.0 2.08 -1.71 0.93 0.006 30.00 40.00 0.0 2.50 -1.29 1.24 0.007 45.00 65.00 0.0 3.75 -0.04 2.02 0.008 50.00 90.00 0.0 4.17 0.38 2.80 0.009 55.00 50.00 0.0 4.58 0.79 1.55 0.0010 60.00 40.00 0.0 5.00 1.21 1.24 0.0011 65.00 30.00 0.0 5.42 1.63 0.93 0.0012 70.00 20.00 0.0 5.83 2.04 0.62 0.0013 75.00 10.00 0.0 6.25 2.46 0.31 0.0014 0.00 -3.79 0.00 0.0015 0.00 -3.79 0.00 0.0016 0.00 -3.79 0.00 0.0017 0.00 -3.79 0.00 0.00

Mass Moment Moment417.0 0.0 0.0

Mass Moment =Centroid Location = 45.5 in

3.79 ft

Location of Applied LoadP = 200 lb

Distance from Point 1 = 15.0 in

Moment effect:M = (45.47 - 15) 200

= 6094.5 inlb= 507.9 ftlb= 15.77 slug

Liner accelleration:n = 200 / 417 = 0.48 g

Angular Accelleration:= 15.77 / 28.03 = 0.5628 rad/sec

Author:R. Abbott Document Number:


ABBOTT


Check: Revision Level :Date:Sept 2013 Page:Title: LINEAR AND ROTATIONAL MASS BALANCE

LINEAR AND ROTATIONAL MASS BALANCE

Reactions at each mass:(Loads expressed perpendicular to part axis)

Load from Load fromLinear Angular TotalAccell. Accell. Load

Locations (lb) (lb) (lb)

1 0.00 -4.80 -0.66 -5.462 6.00 -5.76 -0.69 -6.453 10.00 -7.19 -0.77 -7.974 23.00 -2.40 -0.16 -2.565 25.00 -14.39 -0.89 -15.286 30.00 -19.18 -0.90 -20.097 45.00 -31.18 -0.04 -31.228 50.00 -43.17 0.59 -42.579 55.00 -23.98 0.69 -23.2910 60.00 -19.18 0.85 -18.3411 65.00 -14.39 0.85 -13.5412 70.00 -9.59 0.71 -8.8813 75.00 -4.80 0.43 -4.3714151617

Lin. Ang. Total-200.00 0.00 -200.00


0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00

-50.0

0.0

50.0

100.0

150.0

200.0

Span (ft)

Shear Load (lb)


AA-SM-219A1 of 1


ComponentTotalMass

Moment(slugft)

4.54.04.10.52.72.10.00.41.01.82.52.61.90.00.00.00.0

28.03 slugft

AA-SM-219


A2 of 1


0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00

-50.0

0.0

50.0

100.0

150.0

200.0

Span (ft)

Shear Load (lb)

Fraction Decimal Metric 1 in = 1/32 0.0313 in 0.79 mm 1.65 mm = 1/16 0.0625 in 1.59 mm 1/ 8 0.1250 in 3.18 mm 1 = 3/16 0.1875 in 4.76 mm 1 = 1/ 4 0.2500 in 6.35 mm 5/16 0.3125 in 7.94 mm 1 Pa = 3/ 8 0.3750 in 9.53 mm 20000 MPa = 7/16 0.4375 in 11.11 mm 1 psi = 1/ 2 0.5000 in 12.70 mm 1 ksi = 9/16 0.5625 in 14.29 mm 5/ 8 0.6250 in 15.88 mm 11/16 0.6875 in 17.46 mm 1,000 N = 3/ 4 0.7500 in 19.05 mm 1 lbs =

13/16 0.8125 in 20.64 mm 7/ 8 0.8750 in 22.23 mm

15/16 0.9375 in 23.81 mm 1 in-lbs =3.74E+05 N mm =

10 lb/in =

Linear Equations:1x-7y = 53x+2y = 7

[A] = 1 -7 [B] = 53 2 7

0.087 0.304 [x y] = [A]-1 [B]-0.130 0.043

x = 2.565y = -0.348

-1x-2y-7z = 51x+3y-5z = 6-2x+6y+2z = -1

-1 -2 -7 5[A] = 1 3 -5 [B] = 6

-2 6 2 -1

-0.265 0.279 -0.228 [x y] = [A]-1 [B]-0.059 0.118 0.088-0.088 -0.074 0.007

x = 0.581y = 0.324z = -0.890

in2in2

[A]-1 =

[A]-1 =

Moment-211 Nmm Torque

LoadForce

21150 N

FixedSupport

PinnedSupport

DirectionArrow

3DCoordSystem

CoordSystem

203.0 mm VerticalDimension

203.0 mm HorizontalDimension

Weld

MY =

FZ =

A/CFWD

X

Z

Y

X

Y

x

y

A/CFWD

TYP.

+ Moment DirectionRH Rule

25.4 mm #NAME?0.0649606 in

0.0006452 #NAME?645.16

0.000145 psi #NAME?2900755 psi6894.7573 Pa6.8947573 MPa

225 lbs #NAME?4.448222 N

113.0 N mm #NAME?3312.8 in-lbs

1.7513 N/mm #NAME?

Load FactorsNx =Ny =Nz =

Rotational Velocities = = =

Rotational Accellerations = = =

m2mm2

Ply # Stack-Up Orient. Material

45 0

1 452 03 454 05 06 7 08 459 0

10 4511 012 45


1 452 03 454 05 456 07 458 09 45

10 011 4512 0


1 452 03 454 05 456 07 458 09 4510 0

11 4512 0

Sort List, high to low Sort List, Low to high Reverse a list

Original Sorted Original Sorted Original Reverse20.0 2000000.0 20 0.1007 1 102.0 2146.0 2 2 2 912.0 874.0 12 4 3 84.0 542.0 4 6 4 7

500.0 257 8 5 63.0 456.0 6 12 6 5

874.0 56.0 20 7 451.0 51.0 8 23 8 356.0 34.0 0.1007 257 9 2

2146.0 20.0 23 - 10 12.0 13.034.0 12.0542.0 11.0500.0 5.0

4.013.0 3.0

2000000.0 3.0456 2.03 2.02 2.011 1.01 1.01 1.01 1.01 -5 -

Randomise list of numbers Array Math to simplify conditional analysis

Original Randomized1 0.7576977 1 East 22 0.0896566 10 West 33 0.5153141 3 East 44 0.3059949 6 West 55 0.4688449 4 East 66 0.253882 8 West 77 0.1218847 9 East 58 0.7150386 2 West 69 0.3250169 5 East 4810 0.2791538 7 West 2

East 4West 45East 64West 4

133#NAME?

This Needs Cntrl+Shift+Enter to work

Rounding to Significant figures

Orig Value No of AnsSig Figs

2563145 4 2563000

20 Situations and How to Solve them using Excel Formulas26.To get the first name of a person,use=left(name,find(,name)-1)27.To calculate mortgage payments,use=PMT(interest-rate,number-of-payments,how-much-loan)28. To get nth largest number in a range, use =large(range,n) Get Full Tip29. To get nth smallest number in a range, use = small(range,n) Get Full Tip30. To generate a random phone number, use =randbetween(1000000000,9999999999), needs analysis toolpak if you are using excel 2003 or earlier Get Full Tip31. To count number of words in a cell, use =len(trim(text))-len(SUBSTITUTE(trim(text), ,")) Get Full Tip32. To count positive values in a range, use =countif(range,>0) Get Full Tip33.To calculate weighted average,useSUMPRODUCT()function34.To remove unnecessary spaces,use=trim(text)35. To format a number as SSN using formulas, use =text(ssn-text,000-00-0000) Get Full Tip36.To find age of a person based on DOB,use=TEXT((NOW()-birth_date)&",yyyears"mmonths"dddays"),outputwillbelike27years7months29days37. To get name from initials from a name, use IF(), FIND(), LEN() and SUBSTITUTE() formulas Get Full Tip38.To get proper fraction from a number (for eg 1/3 from 6/18),use=text(fraction,?/?)39.To get partial matches in vlookup,use*operatorlikethis:=vlookup(abc*,lookup_range,return_column)40.To simulate averageif() in earlier versions of excel,use=sumif(range,criteria)/countif(range,criteria)41. To debug your formulas, select the portions of formula and press F9 to see the result of that portion Get Full Tip42.To get the file extension from a file name,use=right(filename,3)(doesntworkforfilesthathaveweirdextensionslike.docx,.htaccessetc.)43. To quickly insert an in cell micro-chart, use REPT() function Get Full Tip44.COUNT() only counts number of cells with numbers in them,ifyouwanttocountnumberofcellswithanythinginthem,useCOUNTA()45.Using named ranges in formulas saves you a lot of time. To define one,justselectsomecells,andgotomenu>insert>namedranges>define

,use=PMT(interest-rate,number-of-payments,how-much-loan)

30. To generate a random phone number, use =randbetween(1000000000,9999999999), needs analysis toolpak if you are using excel 2003 or earlier Get Full Tip31. To count number of words in a cell, use =len(trim(text))-len(SUBSTITUTE(trim(text), ,")) Get Full Tip

,use=TEXT((NOW()-birth_date)&",yyyears"mmonths"dddays"),outputwillbelike27years7months29days37. To get name from initials from a name, use IF(), FIND(), LEN() and SUBSTITUTE() formulas Get Full Tip

,use*operatorlikethis:=vlookup(abc*,lookup_range,return_column),use=sumif(range,criteria)/countif(range,criteria)

41. To debug your formulas, select the portions of formula and press F9 to see the result of that portion Get Full Tip,use=right(filename,3)(doesntworkforfilesthathaveweirdextensionslike.docx,.htaccessetc.)

,ifyouwanttocountnumberofcellswithanythinginthem,useCOUNTA(),justselectsomecells,andgotomenu>insert>namedranges>define

Subscript & Character Superscript Character Superscript Character SubscriptSuperscript Code Letters Code Letters Code LettersNumbers & Symbols & Symbols & Symbols

H2D9 H1D43 H1D2C H2070 H1D47 H1D2E HB9 H1D9C HB2 H1D48 H1D30 HB3 H1D49 H1D31 H2074 H1DA0 H2075 H1D4D H1D33 H2076 H2B0 H1D34 H2077 H2071 H1D35 H2078 H2B2 H1D36 H2079 H1D4F H1D37

H2E1 H1D38 H1D50 H1D39 H207F H1D3A

H2080 H1D52 H1D3C H2081 H1D56 H1D3E H2082 H2083 H2B3 H1D3F H2084 H2E2 H2085 H1D57 H1D40 H2086 H1DB8 H1D41 H2087 H1D5B H2088 H2B7 H1D42 H2089 H2E3

H2B8 H1DBB H207A H207B H2019 H02D9

H207D H208E

Upper Case Lower Case Math Fractions DrawingGreek Greek Symbols Call-outsLetters Letters

AnalysisAnalysis (2)InfoMethodsHintsChars.

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AA-SM-219 Tools - Various Mass Balances - Linear and Rotational

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