SlideShare ist ein Scribd-Unternehmen logo
1 von 2
Please provide a detailed solution. Thanks!
Density , thickness-t Figure P4.5 4.5 Th Figúre P4.5. Find, by integration: e midpla ne of a
uniform triangular plate is shownin Jy c. 1 xy What would be good approximations were the
plate thin?
Solution
4.5 for the given planar triangle
densoty = rho
thickness = t
hence
a. dIxx = integrate(dm*y^2)
dm = rho*t*dA = rho*t*dy*(B - By/H)
hence
dIxx = integrate(rho*tB(1 - y/H)y^2*dy) = rho*tB(y^3/3 - y^4/4H) from y = 0 to y = H
Ixx = rho*tB(H^3/3 - h^4/4H) = rho*tB*H^3(1/3 - 1/4) = rho*t*B*H^3/12
b. from symmetry we can say
dIyy = integrate(rho*t(Hx/B)x^2*dx)
dIyy = rho*t*H*B^3/4
c. now, Izz = Ixx + Iyy
hence
Izz = rho*t*B*H(B^2/4 + H^2/12)
d. dIxy = integrate(dm*xy)
dIxy = integrate(rho*t*(Hx/B)x(Hx/B)dx) from x = 0 to x = B
hence
Ixy = rho*t*H^2B^2/4
e. dIxz = integrate(dm*xz)
dIxz = integrate(rho*t*(Hx/B)xz*dx)
now, this is an odd fucntion of z hence Ixz = 0
similiarly Iyz = 0
hence
for thin plate
Ixz = Iyz = 0
and
rest equations remain the same

Weitere ähnliche Inhalte

Ähnlich wie Please provide a detailed solution- Thanks! Density - thickness-t Figu.docx

26 triple integrals
26 triple integrals26 triple integrals
26 triple integrals
math267
 
24 double integral over polar coordinate
24 double integral over polar coordinate24 double integral over polar coordinate
24 double integral over polar coordinate
math267
 
3.7 applications of tangent lines
3.7 applications of tangent lines3.7 applications of tangent lines
3.7 applications of tangent lines
math265
 

Ähnlich wie Please provide a detailed solution- Thanks! Density - thickness-t Figu.docx (20)

Lesson 25: Evaluating Definite Integrals (slides)
Lesson 25: Evaluating Definite Integrals (slides)Lesson 25: Evaluating Definite Integrals (slides)
Lesson 25: Evaluating Definite Integrals (slides)
 
26 triple integrals
26 triple integrals26 triple integrals
26 triple integrals
 
24 double integral over polar coordinate
24 double integral over polar coordinate24 double integral over polar coordinate
24 double integral over polar coordinate
 
Application H-matrices for solving PDEs with multi-scale coefficients, jumpin...
Application H-matrices for solving PDEs with multi-scale coefficients, jumpin...Application H-matrices for solving PDEs with multi-scale coefficients, jumpin...
Application H-matrices for solving PDEs with multi-scale coefficients, jumpin...
 
Final Exam Review (Integration)
Final Exam Review (Integration)Final Exam Review (Integration)
Final Exam Review (Integration)
 
Evaluating definite integrals
Evaluating definite integralsEvaluating definite integrals
Evaluating definite integrals
 
Tam 2nd
Tam 2ndTam 2nd
Tam 2nd
 
Murphy: Machine learning A probabilistic perspective: Ch.9
Murphy: Machine learning A probabilistic perspective: Ch.9Murphy: Machine learning A probabilistic perspective: Ch.9
Murphy: Machine learning A probabilistic perspective: Ch.9
 
Darmon Points for fields of mixed signature
Darmon Points for fields of mixed signatureDarmon Points for fields of mixed signature
Darmon Points for fields of mixed signature
 
FMS_MCQ_QUESTION_BANK.pdf
FMS_MCQ_QUESTION_BANK.pdfFMS_MCQ_QUESTION_BANK.pdf
FMS_MCQ_QUESTION_BANK.pdf
 
19 General Double Integrals and Volumes.pptx
19 General Double Integrals and Volumes.pptx19 General Double Integrals and Volumes.pptx
19 General Double Integrals and Volumes.pptx
 
19 General Double Integrals and Volumes.pptx
19 General Double Integrals and Volumes.pptx19 General Double Integrals and Volumes.pptx
19 General Double Integrals and Volumes.pptx
 
My PhD talk "Application of H-matrices for computing partial inverse"
My PhD talk "Application of H-matrices for computing partial inverse"My PhD talk "Application of H-matrices for computing partial inverse"
My PhD talk "Application of H-matrices for computing partial inverse"
 
19 trig substitutions-x
19 trig substitutions-x19 trig substitutions-x
19 trig substitutions-x
 
The integral
The integralThe integral
The integral
 
Dubey
DubeyDubey
Dubey
 
Multiple integrals
Multiple integralsMultiple integrals
Multiple integrals
 
3.7 applications of tangent lines
3.7 applications of tangent lines3.7 applications of tangent lines
3.7 applications of tangent lines
 
Lesson 30: The Definite Integral
Lesson 30: The  Definite  IntegralLesson 30: The  Definite  Integral
Lesson 30: The Definite Integral
 
Puy chosuantai2
Puy chosuantai2Puy chosuantai2
Puy chosuantai2
 

Mehr von kdavid658

The mutual fund industry is beginning to use the Internet to dissemina.docx
The mutual fund industry is beginning to use the Internet to dissemina.docxThe mutual fund industry is beginning to use the Internet to dissemina.docx
The mutual fund industry is beginning to use the Internet to dissemina.docx
kdavid658
 
Please show ALL work- If written please show with neat handwriting- I.docx
Please show ALL work- If written please show with neat handwriting- I.docxPlease show ALL work- If written please show with neat handwriting- I.docx
Please show ALL work- If written please show with neat handwriting- I.docx
kdavid658
 
Please only answer if you know the answer- I have posted this twice an.docx
Please only answer if you know the answer- I have posted this twice an.docxPlease only answer if you know the answer- I have posted this twice an.docx
Please only answer if you know the answer- I have posted this twice an.docx
kdavid658
 
Please make comments of the following discussion in 150-200 words-If y.docx
Please make comments of the following discussion in 150-200 words-If y.docxPlease make comments of the following discussion in 150-200 words-If y.docx
Please make comments of the following discussion in 150-200 words-If y.docx
kdavid658
 

Mehr von kdavid658 (16)

The mutual fund industry is beginning to use the Internet to dissemina.docx
The mutual fund industry is beginning to use the Internet to dissemina.docxThe mutual fund industry is beginning to use the Internet to dissemina.docx
The mutual fund industry is beginning to use the Internet to dissemina.docx
 
The primary tool for hardening symmetric cryptography is public key in.docx
The primary tool for hardening symmetric cryptography is public key in.docxThe primary tool for hardening symmetric cryptography is public key in.docx
The primary tool for hardening symmetric cryptography is public key in.docx
 
the primary function of the skin the primary function of the skin.docx
the primary function of the skin    the primary function of the skin.docxthe primary function of the skin    the primary function of the skin.docx
the primary function of the skin the primary function of the skin.docx
 
The primary difference between seasonality and cycles is- the duration.docx
The primary difference between seasonality and cycles is- the duration.docxThe primary difference between seasonality and cycles is- the duration.docx
The primary difference between seasonality and cycles is- the duration.docx
 
The pointer in a node points to the data part of a node the count part.docx
The pointer in a node points to the data part of a node the count part.docxThe pointer in a node points to the data part of a node the count part.docx
The pointer in a node points to the data part of a node the count part.docx
 
The nucleus of a 15 a distance of 5-4 x 10-11 m- What is the ratio of.docx
The nucleus of a 15 a distance of 5-4 x 10-11 m- What is the ratio of.docxThe nucleus of a 15 a distance of 5-4 x 10-11 m- What is the ratio of.docx
The nucleus of a 15 a distance of 5-4 x 10-11 m- What is the ratio of.docx
 
The main function of a cell membrane is to allow substances to enter a.docx
The main function of a cell membrane is to allow substances to enter a.docxThe main function of a cell membrane is to allow substances to enter a.docx
The main function of a cell membrane is to allow substances to enter a.docx
 
The left subtree of key value 14 has 3 key values and the right subtre.docx
The left subtree of key value 14 has 3 key values and the right subtre.docxThe left subtree of key value 14 has 3 key values and the right subtre.docx
The left subtree of key value 14 has 3 key values and the right subtre.docx
 
Please show ALL work- If written please show with neat handwriting- I.docx
Please show ALL work- If written please show with neat handwriting- I.docxPlease show ALL work- If written please show with neat handwriting- I.docx
Please show ALL work- If written please show with neat handwriting- I.docx
 
Please only answer if you know the answer- I have posted this twice an.docx
Please only answer if you know the answer- I have posted this twice an.docxPlease only answer if you know the answer- I have posted this twice an.docx
Please only answer if you know the answer- I have posted this twice an.docx
 
Please make comments of the following discussion in 150-200 words-If y.docx
Please make comments of the following discussion in 150-200 words-If y.docxPlease make comments of the following discussion in 150-200 words-If y.docx
Please make comments of the following discussion in 150-200 words-If y.docx
 
Please help!! I need to make the instructions for these by manipulatin.docx
Please help!! I need to make the instructions for these by manipulatin.docxPlease help!! I need to make the instructions for these by manipulatin.docx
Please help!! I need to make the instructions for these by manipulatin.docx
 
PLEASE HELP! 1- The integrating power of globalization forces managers.docx
PLEASE HELP! 1- The integrating power of globalization forces managers.docxPLEASE HELP! 1- The integrating power of globalization forces managers.docx
PLEASE HELP! 1- The integrating power of globalization forces managers.docx
 
please help with answer and explain homo and lumo in terms of acid-bas.docx
please help with answer and explain homo and lumo in terms of acid-bas.docxplease help with answer and explain homo and lumo in terms of acid-bas.docx
please help with answer and explain homo and lumo in terms of acid-bas.docx
 
Please help me with this crossword!SolutionAcross- 4-Constitutional Is.docx
Please help me with this crossword!SolutionAcross- 4-Constitutional Is.docxPlease help me with this crossword!SolutionAcross- 4-Constitutional Is.docx
Please help me with this crossword!SolutionAcross- 4-Constitutional Is.docx
 
Please Type Answer! Compare and contrast the properties of acids and b.docx
Please Type Answer! Compare and contrast the properties of acids and b.docxPlease Type Answer! Compare and contrast the properties of acids and b.docx
Please Type Answer! Compare and contrast the properties of acids and b.docx
 

Kürzlich hochgeladen

Beyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactBeyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global Impact
PECB
 
The basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxThe basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptx
heathfieldcps1
 
1029 - Danh muc Sach Giao Khoa 10 . pdf
1029 -  Danh muc Sach Giao Khoa 10 . pdf1029 -  Danh muc Sach Giao Khoa 10 . pdf
1029 - Danh muc Sach Giao Khoa 10 . pdf
QucHHunhnh
 
Making and Justifying Mathematical Decisions.pdf
Making and Justifying Mathematical Decisions.pdfMaking and Justifying Mathematical Decisions.pdf
Making and Justifying Mathematical Decisions.pdf
Chris Hunter
 

Kürzlich hochgeladen (20)

TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
 
Food Chain and Food Web (Ecosystem) EVS, B. Pharmacy 1st Year, Sem-II
Food Chain and Food Web (Ecosystem) EVS, B. Pharmacy 1st Year, Sem-IIFood Chain and Food Web (Ecosystem) EVS, B. Pharmacy 1st Year, Sem-II
Food Chain and Food Web (Ecosystem) EVS, B. Pharmacy 1st Year, Sem-II
 
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
 
Holdier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdfHoldier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdf
 
Mehran University Newsletter Vol-X, Issue-I, 2024
Mehran University Newsletter Vol-X, Issue-I, 2024Mehran University Newsletter Vol-X, Issue-I, 2024
Mehran University Newsletter Vol-X, Issue-I, 2024
 
Key note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdfKey note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdf
 
Measures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and ModeMeasures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and Mode
 
Application orientated numerical on hev.ppt
Application orientated numerical on hev.pptApplication orientated numerical on hev.ppt
Application orientated numerical on hev.ppt
 
ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701
 
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactBeyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global Impact
 
ICT Role in 21st Century Education & its Challenges.pptx
ICT Role in 21st Century Education & its Challenges.pptxICT Role in 21st Century Education & its Challenges.pptx
ICT Role in 21st Century Education & its Challenges.pptx
 
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptxBasic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
 
PROCESS RECORDING FORMAT.docx
PROCESS      RECORDING        FORMAT.docxPROCESS      RECORDING        FORMAT.docx
PROCESS RECORDING FORMAT.docx
 
The basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxThe basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptx
 
1029 - Danh muc Sach Giao Khoa 10 . pdf
1029 -  Danh muc Sach Giao Khoa 10 . pdf1029 -  Danh muc Sach Giao Khoa 10 . pdf
1029 - Danh muc Sach Giao Khoa 10 . pdf
 
Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17  How to Extend Models Using Mixin ClassesMixin Classes in Odoo 17  How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
 
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
 
Making and Justifying Mathematical Decisions.pdf
Making and Justifying Mathematical Decisions.pdfMaking and Justifying Mathematical Decisions.pdf
Making and Justifying Mathematical Decisions.pdf
 
Sociology 101 Demonstration of Learning Exhibit
Sociology 101 Demonstration of Learning ExhibitSociology 101 Demonstration of Learning Exhibit
Sociology 101 Demonstration of Learning Exhibit
 
psychiatric nursing HISTORY COLLECTION .docx
psychiatric  nursing HISTORY  COLLECTION  .docxpsychiatric  nursing HISTORY  COLLECTION  .docx
psychiatric nursing HISTORY COLLECTION .docx
 

Please provide a detailed solution- Thanks! Density - thickness-t Figu.docx

  • 1. Please provide a detailed solution. Thanks! Density , thickness-t Figure P4.5 4.5 Th Figúre P4.5. Find, by integration: e midpla ne of a uniform triangular plate is shownin Jy c. 1 xy What would be good approximations were the plate thin? Solution 4.5 for the given planar triangle densoty = rho thickness = t hence a. dIxx = integrate(dm*y^2) dm = rho*t*dA = rho*t*dy*(B - By/H) hence dIxx = integrate(rho*tB(1 - y/H)y^2*dy) = rho*tB(y^3/3 - y^4/4H) from y = 0 to y = H Ixx = rho*tB(H^3/3 - h^4/4H) = rho*tB*H^3(1/3 - 1/4) = rho*t*B*H^3/12 b. from symmetry we can say dIyy = integrate(rho*t(Hx/B)x^2*dx) dIyy = rho*t*H*B^3/4 c. now, Izz = Ixx + Iyy hence
  • 2. Izz = rho*t*B*H(B^2/4 + H^2/12) d. dIxy = integrate(dm*xy) dIxy = integrate(rho*t*(Hx/B)x(Hx/B)dx) from x = 0 to x = B hence Ixy = rho*t*H^2B^2/4 e. dIxz = integrate(dm*xz) dIxz = integrate(rho*t*(Hx/B)xz*dx) now, this is an odd fucntion of z hence Ixz = 0 similiarly Iyz = 0 hence for thin plate Ixz = Iyz = 0 and rest equations remain the same