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Find the moment of inertia and radius of gyration of the section of this bar about an axis parallel to x-axis going through the center of gravity of the bar. The bar is symmetrical about the axis parallel to y-axis and going through the center of gravity of the bar and about the axis parallel to z-axis and going through the center of gravity of the bar.   The dimensions of the section are: l=51 mm, h=29 mm The triangle: hT=15 mm, lT=18 mm and the 2 circles: diameter=7.4 mm, hC=8 mm, dC=7 mm. A is the origin of the referential axis. Provide an organized table and explain all your steps to find the moment of inertia and radius of gyration about an axis parallel to x-axis and going through the center of gravity of the bar. Does the radius of gyration make sense? In the box below enter the y position of the center of gravity of the bar in mm with one decimal.

Find the moment of inertia and radius of gyration of the section of this bar about an axis parallel to x-axis going through the center of gravity of the bar. The bar is symmetrical about the axis parallel to y-axis and going through the center of gravity of the bar and about the axis parallel to z-axis and going through the center of gravity of the bar.   The dimensions of the section are: l=51 mm, h=29 mm The triangle: hT=15 mm, lT=18 mm and the 2 circles: diameter=7.4 mm, hC=8 mm, dC=7 mm. A is the origin of the referential axis. Provide an organized table and explain all your steps to find the moment of inertia and radius of gyration about an axis parallel to x-axis and going through the center of gravity of the bar. Does the radius of gyration make sense? In the box below enter the y position of the center of gravity of the bar in mm with one decimal.

International Edition---engineering Mechanics: Statics, 4th Edition
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter9: Moments And Products Of Inertia Of Areas
Section: Chapter Questions
Problem 9.46P
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Use the given values in problem to answer the following: 

Find the moment of inertia and radius of gyration of the section of this bar about an axis parallel to x-axis going through the center of gravity of the bar.

The bar is symmetrical about the axis parallel to y-axis and going through the center of gravity of the bar and about the axis parallel to z-axis and going through the center of gravity of the bar.

 

The dimensions of the section are:

  • l=51 mm, h=29 mm
  • The triangle: hT=15 mm, lT=18 mm
  • and the 2 circles: diameter=7.4 mm, hC=8 mm, dC=7 mm.

A is the origin of the referential axis.

Provide an organized table and explain all your steps to find the moment of inertia and radius of gyration about an axis parallel to x-axis and going through the center of gravity of the bar.

Does the radius of gyration make sense?

In the box below enter the y position of the center of gravity of the bar in mm with one decimal. 

Geometric Properties of Line and Area Elements Centroid Location Centroid Location [c b y L-r r sin 0 Circular are segment -L-20r Quarter and semicircle ares aA₂h (a + b) a C Trapezoidal area -b-A-3ab Semiparabolic area AT (++) a- C } L-at Exparabolic area -A-ab 10 b A=4ab Parabolic area T h L h y Circular sector area A-0² sin 1-17² V Quarter circle area y Semicircular area X Circular area z A-²² X A-bh Triangular area -X Rectangular area -A-bh h Area Moment of Inertia 1-¹ (0-sin 20) 1,---r¹(0+ -sin 20) 1 16 4-16 4₂ 274 7774 4 1 1₂--bh³ 12 12 4,--bh³ 36 Formulas Moments of Inertia ¹x = [ y²dA ly ¹y = Sx Theorem of Parallel Axis 1x = 1 +d² A axis going through the centroid x' axis parallel to x going through the point of interest d minimal distance (perpendicular) between and x' lyr=15+d² A axis going through the centroid y' axis parallel to y going through the point of interest d minimal distance (perpendicular) between y and y' Composite Bodies 1-Σ All the moments of inertia should be about the same axis. x²dA Radius of Gyration k =
Transcribed Image Text:Geometric Properties of Line and Area Elements Centroid Location Centroid Location [c b y L-r r sin 0 Circular are segment -L-20r Quarter and semicircle ares aA₂h (a + b) a C Trapezoidal area -b-A-3ab Semiparabolic area AT (++) a- C } L-at Exparabolic area -A-ab 10 b A=4ab Parabolic area T h L h y Circular sector area A-0² sin 1-17² V Quarter circle area y Semicircular area X Circular area z A-²² X A-bh Triangular area -X Rectangular area -A-bh h Area Moment of Inertia 1-¹ (0-sin 20) 1,---r¹(0+ -sin 20) 1 16 4-16 4₂ 274 7774 4 1 1₂--bh³ 12 12 4,--bh³ 36 Formulas Moments of Inertia ¹x = [ y²dA ly ¹y = Sx Theorem of Parallel Axis 1x = 1 +d² A axis going through the centroid x' axis parallel to x going through the point of interest d minimal distance (perpendicular) between and x' lyr=15+d² A axis going through the centroid y' axis parallel to y going through the point of interest d minimal distance (perpendicular) between y and y' Composite Bodies 1-Σ All the moments of inertia should be about the same axis. x²dA Radius of Gyration k =
hy A Ľx .X вт е L
Transcribed Image Text:hy A Ľx .X вт е L
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