aa sm 002 002 torsion irregular sections

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ABBOTT AEROSPACE INC. PROPRIETARY INFORMATION Subject to restrictions on the cover or first page IMPORTANT INFORMATION About us: About the Abbott Aerospace Analysis Spreadsheets: Proprietary information: To find out more about the Xl-Viking Add-in: Find out more about the Design and Analysis services provided by Abbott Aerospace: XL-Viking was created to make working with Microsoft Excel easier and more efficient. XL-Viking started as an internal group at Abbott Aerospace Inc. developing Excel tools to increase productivity, reliability and quality of Established in 2008, Abbott Aerospace helps people develop new aircraft structure and systems and make modifications to existing structure and systems. We do all types of aircraft - Part 23, Part 25, Civil, Military, Prototype, Experimental - and have extensive experience with composite laminate material selection, process control, manufacture, design, substantiation and certification. We have made these spreadheets available through XL-Xiking and have helped in developing the Xl-Viking add-in. Our in-house structural analysis toolbox is our collection of spreadsheets. The sheets that we make freely available are a small proportion of the sheets that we They are intended to be used by engineers. They are not protected software packages and can be changed in every way by the user. All of our spreadsheets are provided 'as is' with no warranty or guarantee explicitly given or implied. You may these spreadsheets at your own risk. The Author will nor be liable for data loss, damages, loss of profits or any other kind of loss while using or misusing these spreadsheets We have made every reasonable effort to remove all errors but some may still exist [email protected] The spreadsheets contain no proprietary information from outside of Abbott Aerospace Inc. If you think that we have used proprietary information Abbott Aerospace Inc. and XL-Viking grants the user the right to use, modify, reproduce and redistribute these spreadsheets. We just ask that if possible you maintain a credit naming Abbott Aerospace Inc./XL-Viking as the source. Our analysis spreadsheets in general do not use Visual Basic routines and the outcome of the analysis in the spreadsheets rely solely on native Excel functions. The display of the math in these sheets rely on the XL-Viking add-in and the spreadsheets will not display correcly if the add-in is not installed. www.XL-Viking.com www.abbottaerospace.com

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Page 1: AA SM 002 002 Torsion Irregular Sections

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

IMPORTANT INFORMATION

About us:

We have made these spreadheets available through XL-Xiking and have helped in developing the Xl-Viking add-in.

About the Abbott Aerospace Analysis Spreadsheets:

Proprietary information:

To find out more about the Xl-Viking Add-in:

Find out more about the Design and Analysis services provided by Abbott Aerospace:

XL-Viking was created to make working with Microsoft Excel easier and more efficient. XL-Viking started as an internal group at Abbott Aerospace Inc. developing Excel tools to increase productivity, reliability and quality of engineering applications. XL-Viking was establised as a seperate company in 2014.

Established in 2008, Abbott Aerospace helps people develop new aircraft structure and systems and make modifications to existing structure and systems. We do all types of aircraft - Part 23, Part 25, Civil, Military, Prototype, Experimental - and have extensive experience with composite laminate material selection, process control, manufacture, design, substantiation and certification.

Our in-house structural analysis toolbox is our collection of spreadsheets. The sheets that we make freely available are a small proportion of the sheets that we have developed for our own use.

They are intended to be used by engineers. They are not protected software packages and can be changed in every way by the user.

All of our spreadsheets are provided 'as is' with no warranty or guarantee explicitly given or implied. You may these spreadsheets at your own risk. The Author will nor be liable for data loss, damages, loss of profits or any other kind of loss while using or misusing these spreadsheetsWe have made every reasonable effort to remove all errors but some may still exist and all analysis work should be thoroughly checked. If you do find errors plese notify us at:

[email protected]

The spreadsheets contain no proprietary information from outside of Abbott Aerospace Inc. If you think that we have used proprietary information inappropriately please let us know.

Abbott Aerospace Inc. and XL-Viking grants the user the right to use, modify, reproduce and redistribute these spreadsheets. We just ask that if possible you maintain a credit naming Abbott Aerospace Inc./XL-Viking as the source.

Our analysis spreadsheets in general do not use Visual Basic routines and the outcome of the analysis in the spreadsheets rely solely on native Excel functions. The display of the math in these sheets rely on the XL-Viking add-in and the spreadsheets will not display correcly if the add-in is not installed.

www.XL-Viking.com

www.abbottaerospace.com

Page 2: AA SM 002 002 Torsion Irregular Sections

Author: R. Abbott Document Number: AA-SM-002-002Check: Revision Level : A

Date: Dec-09 Page: 1 of 6

TORSION CALCULATION FOR IRREGULAR SECTIONSTHICK-WALLED OPEN SECTIONS

References:[1] Stress Analysis Manual, Air Force Flight Dynamics Laboratory, Wright Patterson AFB, OH, Oct 1986

is the peak stress at point 'c' Equation 1

Equation 2

Equation 3

The terms in Equation 3 for the coefficient 'n' are:

f = angle between segments in radians

If you see errors on this spreadsheet it is because you do not have the XL-Viking Plugin, to find out more:

D = diameter of the largest inscribed circler = fillet radius (use a positive value for r)

A = cross sectional area of the segment, not the entire section

Sections with r / t > 2.5 (ratio of the fillet radius to leg thickness) are considered thick-walled sections.

To determine torsional constants of complex shapes, open sections are separated into tee and/or angle segments as shown below. Torsional constant J is a sum of the constants of constituent segments, and it is calculated from Equation 2.

In these sections the stress concentration at the fillet radius is taken into consideration. The maximum torsional shear stress occurs at the fillet radius.

Page 3: AA SM 002 002 Torsion Irregular Sections

www.XL-Viking.com

Page 4: AA SM 002 002 Torsion Irregular Sections

Author: R. Abbott Document Number: AA-SM-002-002Check: Revision Level : A

Date: Dec-09 Page: 2 of 6

TORSION CALCULATION FOR IRREGULAR SECTIONSTHICK-WALLED OPEN SECTIONS (continued)

1. Angle Segment

t₁ = 0.12 mmt₂ = 0.10 mmb₁ = 1.10 mmb₂ = 0.85 mm

r = 0.10 mmΦ = 1.57 radians

Segment AreaA = b₁ × t₁ + b₂ × t₂ + r² × (1 - π / 4)A = 1.1 × 0.12 + 0.85 × 0.1 + 0.1² × (1 - π / 4)A = 0.219

Diameter of the Largest Inscribed CircleD = 2 × (t₁ + t₂ + 3 × r - √[2 × t₁ × t₂ + 4 × r × (t₁ + t₂) + 8 × r²])D = 2 × (0.12 + 0.1 + 3 × 0.1 - √[2 × 0.12 × 0.1 + 4 × 0.1 × (0.12 + 0.1) + 8 × 0.1²])D = 0.164 mm

Coefficienta = (t₂ / t₁) × (0.07 + 0.076 × r / t₁)a = (0.1 / 0.12) × (0.07 + 0.076 × 0.1 / 0.12)a = 0.111

Coefficientn =

n =

n = 0.113Coefficient

K₁ = b₁ × t₁³ × (1 / 3 - 0.21 × (t₁ / b₁) × (1 - t₁⁴ / (12 × b₁⁴)))K₁ = 1.1 × 0.12³ × (1 / 3 - 0.21 × (0.12 / 1.1) × (1 - 0.12⁴ / (12 × 1.1⁴)))K₁ = 0.00059

CoefficientK₂ = b₂ × t₂³ × (1 / 3 - 0.105 × (t₂ / b₂) × (1 - t₂⁴ / (192 × b₂⁴)))K₂ = 0.85 × 0.1³ × (1 / 3 - 0.105 × (0.1 / 0.85) × (1 - 0.1⁴ / (192 × 0.85⁴)))K₂ = 0.00027

Torsional ConstantJ = K₁ + K₂ + a × D⁴J = (5.9E-04) + (2.73E-04) + 0.111 × 0.164⁴J = 0.00094

If you see errors on this spreadsheet it is because you do not have the XL-Viking Plugin, to find out more:

t1 >= t2

mm2

(D / (1 + π² × D⁴ / (16 × A²))) × (1 + (0.118 × LN[1 - 0.5 × D / r] - 0.238 × 0.5 × D / r) × TANH[2 × Φ / π])

(0.164 / (1 + π² × 0.164⁴ / (16 × 0.219²))) × (1 + (0.118 × LN[1 - 0.5 × 0.164 / 0.1] - 0.238 × 0.5 × 0.164 / 0.1) × TANH[2 × 1.57 / π])

mm4

mm4

mm4

www.XL-Viking.com

Page 5: AA SM 002 002 Torsion Irregular Sections

Author: R. Abbott Document Number: AA-SM-002-002Check: Revision Level : A

Date: Dec-09 Page: 3 of 6

TORSION CALCULATION FOR IRREGULAR SECTIONSTHICK-WALLED OPEN SECTIONS (continued)

Tee Segment

0.12 mm0.10 mm1.10 mm

0.85 mmr = 0.10 mmf = 1.57 radians

Segment AreaA = b1 × t1 + b2 × t2 + 2 × r² × (1 - π / 4)A = 1.1 × 0.12 + 0.85 × 0.1 + 2 × 0.1² × (1 - π / 4)A = 0.221

Diameter of the Largest Inscribed CircleD = ((t1 + r)² + (t2 / 2)² + t2 × r) / (t1 + 2 × r)D = ((0.12 + 0.1)² + (0.1 / 2)² + 0.1 × 0.1) / (0.12 + 2 × 0.1)D = 0.190 mm

Coefficienta = IF[t1 > =t2,[t2 / t1] × (0.15 + 0.1 × r / t1),[t1 / t2] × (0.15 + 0.1 × r / t1)]a = IF[0.12>=0.1,[0.1 / 0.12] × (0.15 + 0.1 × 0.1 / 0.12),[0.12 / 0.1] × (0.15 + 0.1 × 0.1 / 0.12)]a = 0.194

Coefficientn =

n =

n = 0.231 mmCoefficient

b1 × t1³ × (1 / 3 - 0.21 × (t1 / b1) × (1 - t1⁴ / (12 × b1⁴)))1.1 × 0.12³ × (1 / 3 - 0.21 × (0.12 / 1.1) × (1 - 0.12⁴ / (12 × 1.1⁴)))

0.00059Coefficient

b2 × t2³ × (1 / 3 - 0.105 × (t2 / b2) × (0.85 × 0.1³ × (1 / 3 - 0.105 × (0.1 / 0.85) × (1 - 0.1⁴ / (192 × 0.85⁴)))

0.00027Torsional Constant

J = K1 + K2 + a × D⁴J = (5.9E-04) + (2.73E-04) + 0.194 × 0.19⁴J = 0.00112

If you see errors on this spreadsheet it is because you do not have the XL-Viking Plugin, to find out more:

t1 =t2 =b1 =b2 =

mm2

(D / (1 + π² × D⁴ / (16 × A²))) × (1 + (0.118 × LN[1 + 0.5 × D / r] + 0.238 × 0.5 × D / r) × TANH[2 × f / π])

(0.19 / (1 + π² × 0.19⁴ / (16 × 0.221²))) × (1 + (0.118 × LN[1 + 0.5 × 0.19 / 0.1] + 0.238 × 0.5 × 0.19 / 0.1) × TANH[2 × 1.57 / π])

K1 =K1 =K1 = mm4

K2 =K2 =K2 = mm4

mm4

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Page 6: AA SM 002 002 Torsion Irregular Sections

Author: R. Abbott Document Number: AA-SM-002-002Check: Revision Level : A

Date: Dec-09 Page: 4 of 6

TORSION CALCULATION FOR IRREGULAR SECTIONSTHICK-WALLED OPEN SECTIONS (continued)

Complex Section - Example

Section 1 - Angle

Section 2 - Tee

Segment 1 Segment 2 Segment 3 Segment 4Angle Tee None None mm0.12 0.12 0.00 0.00 mm0.10 0.10 0.00 0.00 mm

1.10 1.10 0.00 0.00 mm

0.85 0.85 0.00 0.00 mmr = 0.10 0.10 0.00 0.00 radiansf = 1.57 1.57 0.00 0.00

A = 0.219 0.221 0.00 0.00D = 0.164 0.190 0.00 0.00 mma = 0.111 0.194 0.00 0.00n = 0.113 0.104 0.00 0.00 mm

0.00059 0.00059 0.00 0.00

0.00027 0.00027 0.00 0.00

0.00094 0.00112 0.00 0.00

13.7 16.3 0.0 0.0 Nmm

J = 0.0021 Torsional Constant of the Entire Section30 Nmm Applied Torque

Torsional shear stresses are calculated from Equation 1:1649 MPa1514 MPa

If you see errors on this spreadsheet it is because you do not have the XL-Viking Plugin, to find out more:

type =t1 =t2 =b1 =b2 =

mm2

K1 = mm4

K2 = mm4

Ji = mm4

Ti =

T in the table above is the amount of torque on each segment, and it is a direct ratioof the segment J to the total J.

mm4

To =

fSA = Shear Stress at Point AfSB = Shear Stress at Point B

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Page 7: AA SM 002 002 Torsion Irregular Sections

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

Author: R. Abbott Document Number: AA-SM-002-002Check: Revision Level : A

Date: Dec-09 Page: 5 of 6

TORSION CALCULATION FOR IRREGULAR SECTIONSC-Section Analysis

Ref. Structural Analysis, With Application to Aerospace Structures. Bauchau & Craig

Material PropertiesG = 3900000 psi

b = 0.6 inh = 1.2 int₁ = 0.1 int₂ = 0.12 in

Applied Moment =M = 500 inlb

Distance to shear center Torsion Stresses= 3 × t₂ × b² / (h × t₁ + 6 × b × t₂) Stress in Web:= 3 × 0.12 × 0.6² / (1.2 × 0.1 + 6 × 0.6 × 0.12) = G × t₁ × M / H

e = 0.23 in = 3900000 × 0.1 × 500 / 18296= 10658.3 psi

Torsional Stiffness: Stress in Flange:= G / 3 × (h × t₁² + 2 × b × t₂³) = G × t₂ × M / H= 3900000 / 3 × (1.2 × 0.1² + 2 × 0.6 × 0.12³) = 3900000 × 0.12 × 500 / 18296

H = 18295.7 inlb/rad = 12789.9 psi

If you see errors on this spreadsheet it is because you do not have the XL-Viking Plugin, to find out more:

Shear Center

e

b

h

t₁

t₂

A13
Abbott Aerospace: Page title on this line
Page 8: AA SM 002 002 Torsion Irregular Sections

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

www.XL-Viking.com