Concept explainers
Find the mass moment of inertia with respect to

Answer to Problem 9.137P
The mass moment of inertia with respect to
The mass moment of inertia with respect to
The mass moment of inertia with respect to
Explanation of Solution
Given information:
The thickness (t) of sheet steel is
The density
Calculation:
Divided the section into three geometric portions as shown below:
- Upper Flange
- Lower Flange
- Horizontal base
Find the mass of the upper flange component using the relation as shown below:
Here, V is volume of component of upper flange and A is the area of the section.
Find the area A of upper flange as shown below:
Here, b is the width of section and h is the height of section.
Substitute
Substitute
Find the mass of the lower flange component using the relation as shown below:
Here, V is volume of component of lower flange.
Find the area A of lower flange as shown below:
Here, b is the width of section and h is the height of section.
Substitute
Substitute
Find the moment of inertia about x axis of upper lower flange section as shown below:
Substitute
Find the moment of inertia about y axis of upper lower flange section as shown below:
Substitute
Find the moment of inertia about z axis of upper lower flange section as shown below:
Substitute
Find the mass of the horizontal base using the relation as shown below:
Find the area A of horizontal base as shown below:
Here, b is the width of section and h is the height of section.
Substitute
Substitute
Find the moment of inertia about x axis of horizontal base as shown in below:
Substitute
Find the moment of inertia about y axis of horizontal base as shown in below:
Substitute
Find the moment of inertia about z axis of horizontal base as shown in below:
Substitute
Find the total moment of inertia
Here,
Substitute
Thus, the mass moment of inertia with respect to
Find the total moment of inertia
Here,
Substitute
Thus, the mass moment of inertia with respect to
Find the total moment of inertia
Here,
Substitute
Thus, the mass moment of inertia with respect to
Want to see more full solutions like this?
Chapter 9 Solutions
VECTOR MECHANICS FOR ENGINEERS: STATICS
- (◉ Home - my.uah.edu Homework#5 MasteringEngineering Mastering X + 8 https://session.engineering-mastering.pearson.com/myct/itemView?offset=next&assignmentProblemID=18992146arrow_forward(read image)arrow_forward(◉ Home - my.uah.edu Homework#5 MasteringEngineering Mastering X + 8 https://session.engineering-mastering.pearson.com/myct/itemView?assignmentProblemID=18992147&offset=nextarrow_forward(◉ Home - my.uah.eduarrow_forward(read image)arrow_forward(◉ Home - my.uah.edu Homework#5 MasteringEngineering Mastering X + 8 https://session.engineering-mastering.pearson.com/myct/itemView?assignmentProblemID=18992148&offset=nextarrow_forward(◉ Home - my.uah.edu Homework#5 MasteringEngineering Mastering X + 8 https://session.engineering-mastering.pearson.com/myct/itemView?assignmentProblemID=18992144&offset=nextarrow_forwardCalculate the forces in members BC, BG & FG of the truss shown using the Method of Sections. For your answer, provide atruss diagram of the calculated member forces and indicate whether the member is in Tension (+) or Compression (-)arrow_forwardSelect the speed, feed and depth of the cut to turn wrought, low carbon steel (hardness of 200 BHN) on lathe with AISI tool material of HSS M2 or M3. (Hint: refer to Chapter 21 for recommended parameters).arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill EducationControl Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEYmoment of inertia; Author: NCERT OFFICIAL;https://www.youtube.com/watch?v=A4KhJYrt4-s;License: Standard YouTube License, CC-BY