Determine the moments of inertia of the compound shape cross-sectional area shownabout the y and z centroidal axes.200 mm25 mm25 mm150 mm25 mmly= 1.9x107 mm4Iz=6.06x107 mm4'100 mmAly= 2.2x107 mm4Iz=4.5x107 mm4Bly= 4.7x107 mm4Iz=2.11x107 mm4ly= 1.7x107 mm4Iz=3.06x107 mm4Dly= 4.5x107 mm4Iz=6.78x107 mm4E

Given: To determine: Moment of inertia about y and z axis

Answered: Determine the moments of inertia of the…

Engineering

Mechanical Engineering

Determine the moments of inertia of the compound shape cross-sectional area shown about the y and z centroidal axes.

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 9.8P: Using integration, compute the polar moment of inertia about point O for the circular sector. Check...

See similar textbooks

Related questions

Q: Determine the percent reductions in both area and area moment of inertia about the y-axis caused by…

Q: Determine the moments of inertia Ix and Iy with respect to parallel centroidal axes and…

Q: Determine the moment of inertia about the x-axis of each of the areas shown

Q: Determine the moment of inertia for shaded area about x and y axis.

Q: termine the moment of inertia for the shaded area about x axis

A: given:

Q: Determine the moments of inertia of the Z-section about its centroidal xo- and yo-axes.

Q: Locate the centroid of the beam’s cross sectional area, and then determine the moment of inertia of…

Q: Determine the moment of inertia of the shaded areas with respect to the its centroidal x axis.

A: given:

Q: Determine the moment of inertia about the x-axis of the rectangular area without and with the…

A: Moment of inertia: It is a measure of the rotational inertia of a body which oppose the rotational…

Q: Determine the moments of inertia of the Z-section about its centroidal x0- and y0-axes.

Q: Determine the moments of inertia of the shaded area shown with respect to the x and y axes.

A: Determine the moment of inertia of the shaded portion: The expression to calculate the moment of…

Q: Determine the moment of inertia of the shaded area about the x and y axis shown below a horizontal…

A: SolutionGiven Data.y=0.25x3and x=(y0.25)13

Q: Determine by direct integration the moment of inertia of the shaded area with respect to the y axis…

Q: Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.

A: Given , Consider an elementary strip of width ''dx'' at a distance of 'x' fromy-axis .Area of…

Q: Locate the centroid (x,y) of the coposite area; then find the moment of inertia of the…

Q: Locate the centroid x of the beam's cross- sectional area, and then determine the moment of inertia…

Q: Determine the radii of gyration and centroidal moments of inertia.

A: GIVEN:

Q: Determine the moment of inertia of the area about the y axis

A: Consider a small element dx at a distance x from the origin. The height of the elemental area will…

Q: Determine the moments of inertia with respect to centroidal axis for the cross-sectional area of the…

Q: Determine the moment of inertia of a square cross section of side 3 m about a parallel axis 0.5 m…

A: "C" is the position of centroid of the square area which is at the mid position of the area.

Q: Determine the moment of inertia of the shaded area about the x-axis.

A: Given data: Parabola equation, y=14-0.083 x2

Q: Determine the orientation of the principal axes of inertia through the centroid of the shaded area…

A: Formula for centroid of cut section is given below, y=a1y1+a2y2a1 +a2…

Q: Determine the moment of inertia of the shaded area about the y axis.

A: Consider a vertical element of thickness dx and height y'.

Q: Determine the moment of inertia of the area about the y axis.

Q: Determine the moments of inertia of the Z-section about its centroidal Xo- and yo-axes.

Q: Find the Area Moment of Inertia about an x axis passing through the centroid (Ix) of the composite…

Q: Determine the moment of inertia of the area about the y axis:

Q: Determine the percent reductions in both area and area moment of inertia about the y-axis caused by…

A: Consider a rectangular plate having dimensions b and h. Then the rectangle of dimensions 0.57b and…

Q: Determine the moments of inertia T, and Ty of the area shown about vertical and horizontal axes…

Q: Locate the centroid C (x,y) of the shaded area Determine the area moment of inertia of the shaded…

Q: Determine the moment of inertia of the shaded area about the x-axis and y-axis.

Q: Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.

A: The elementary diagram for the shaded area is as follows:

Q: 3) Determine the moments of inertia of the Z -section about its centroidal xo - and Уо —ахes.

A: Consider the diagram shown below for the given Z-section.

Q: Determine the moment of inertia of the shaded area about x-axis. Set h= 5.7 cm.

A: h=5.7 cm

Q: Find the Area Moment of Inertia about an x axis passing through the centroid (Ix) of the composite…

Q: Determine the percent reductions in both area and area moment of inertia about the y-axis caused by…

A: Consider the diagram shown below for the given section.

Q: Determine the moment of inertia of a square cross section of side 4 m about a parallel axis 0.6 m…

A: The area moment of inertia, also known as the second area moment or 2nd moment of area, is a feature…

Q: Find the moment of inertia of the shaded area shown about a. centroidal axes b. y-axis

A: The schematic diagram of the given area is The area is divided into five parts:- Part 1:- A…

Q: Determine the moment of inertia about the x- and y-axes both passes through the centroid the section…

Q: Determine the moments of inertia Ix and Iy of the shaded area, with respect to an axis passing…

A: Given data as per question Height of bigger rectangle =160 mm considering part 1x1=18+40+422=50…

Q: Determine the moments of inertia Ix and ly of the shaded area, with respect to an axis passing…

A: To calculate the moment of inertia we have to de3vide the fig. in two parts as shown in fig.…

Q: y 13" OK

Q: Determine the moment of inertia about the centroidal x and y axes for the composite area show.

A: To find: The moment of inertia about the centroidal x and y axes for the composite area shown:…

Q: For the shaded area, detemine the moments of inertia with respect to the given x and y axes. 1" 6"…

A: The provided shaded area is given below.

Q: Determine the moment of inertia for the shaded area about the x axis. site

Q: Determine the moments of inertia of the shaded area shown with respect to the x and y axes

A: Given: a = 20 mm To determine: Moment of inertia about x and y axes

Q: Determine the moment of inertia components of the following composite shape wrt x, x’ and y axes.

A: Write the expression of the area of the hollow rectangle. Write the expression of the area of the…

Q: Problems: Determine the centroid and moment of inertia about the centroidal axis of the shaded area…

Q: Determine the area moment of inertia about the centroidal axis X'

A: Giveny=x-x24find intersection oint 0=x-x24x=0,4

Q: Determine the moment of inertia with respect to A-A axis Tor the shaded area shown

Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.

Question

Determine the moments of inertia of the compound shape cross-sectional area shown
about the y and z centroidal axes.
200 mm
25 mm
25 mm
150 mm
25 mm
ly= 1.9x107 mm4
Iz=6.06x107 mm4
'100 mm
A
ly= 2.2x107 mm4
Iz=4.5x107 mm4
B
ly= 4.7x107 mm4
Iz=2.11x107 mm4
ly= 1.7x107 mm4
Iz=3.06x107 mm4
D
ly= 4.5x107 mm4
Iz=6.78x107 mm4
E

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Determine the moment of inertia about the x-axis of the rectangular area without and with the central rectangular hole. without hole: 0.1125 b4; with hole:0.110183 b4 without hole: 0.1152 b4; with hole:0.111038 b4 without hole: 0.1215 b4; with hole:0.111083 b4 without hole: 0.1125 b4; with hole:0.110138 b4
Find the Moment of Inertia of the plate as shown in figure, passing through its centroid with reference to Y -Y axis. Where b1 = 55 mm, d1=110 mm, b2=160 mm, d2=30 mm, b3=65mm, d3=24mm. The value of is (unit in mm) = ______________ Answer for part 1 The value of is (unit in mm) = ______________ Answer for part 2 The value of total for the given plate is (unit in mm4) =________________ Answer for part 3
The shaded area has the following properties: Ix=1.26x10^6 mm^4, Iy=6.55x10^5 mm^4, Pxy=-1.02x10^5 mm^4 Determine the moment of inertia about the x' axis if theta =30 degrees and the moments of inertia about the y' axis if theta=30 degrees
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=55 mm, h=22 mm The triangle: hT=12 mm, lT=19 mm and the 2 circles: diameter=8 mm, hC=6 mm, dC=8 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? Enter the y position of the center of gravity of the bar in mm with one decimal.
Check the alternative that presents the moment of inertia of the hatched figure in relation to the y axis. a = 2cm b = 4.8cm Alternatives: a) 75,52 b) 6,28 c) 5,41 d) 52,19 e) 49,92
Answer Above: Ix = 0.32210 m4 (Unrounded) Answer Above: Ix = 0.322102 m4 (Rounded) Answer Above: Ix = 0.322102 m4 Answer Above is incorrect. Please resolve. Suppose that a = 1.21 m and b = 1.1 m . (Figure 1) Determine the moment of inertia for the shaded area about the x axis. Express your answer to three significant figures and include the appropriate units.
Determine the moments of inertia and the product of inertia of the L3 x 2 x 1/4-14 angle cross section of Prob. 9.74 with respect to new centroidal axes obtained by rotating the x and y axes 30° clockwise.(Reference to Problem 9.75):Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.
Determine the moments of inertia about the y-axis of the circular area without and with the central square hole. 0.785 R4, 0.613 R4 0.875 R4, 0.702 R4 0.578 R4, 0.316 R4 0.758 R4, 0.720 R4
Find the moment of inertia of a triangular section having 50 mm base and 60 mm height about an axis through its centre of gravity and base. Answer :IG = 300 x 103 mm4; IBase = 900 x 103 mm4
1) Sketch the cross-sectional picture of a W8x67 sitting on top of a W16x26 (the vertical centerlines are colinear). a)The magnitude of the Area Moment of Inertia about the horizontal centroidal axis of the built-up member is _____in4. b)The magnitude of the Area Moment of Inertia about the vertical centroidal axis of the built-up member is _____in4. c)The magnitude of the Area Moment of Inertia about the centroidal z-axis (aka Polar Moment of Inertia about the centroidal origin) of the built-up member is _____in4. d)The magnitude of the Radius of Gyration about the horizontal centroidal axis of the built-up member is _____in. e)The magnitude of the Radius of Gyration about the vertical centroidal axis of the built-up member is _____in. f)The magnitude of the Radius of Gyration about the centroidal z-axis (aka Polar Radius of Gyration about the centroidal origin) of the built-up member is _____in.
A 100×100 paper was punched from its left lower corner. A 25×25 square hole was created there. The 25×25 scrap was subsequently glued onto right upper corner of the paper. By neglecting the thickness of the paper,a) Determine the centroid of this composite area,b) Calculate the moments of inertia Ix, Iy and product of inertia, Ixy.c) Determine the principal moments of inertia and the orientation of the principal axes.(a=3 b=1)
A tee section is made up of a 30 mm *150 mm flange and a 30 mm * 160 mm web. 6. Which of the following most nearly gives the moment of inertia with respect to the centroidal x-axis in million (1 x 10⁶).a. 21.84 mm⁴ b. 27.45 mm⁴ c. 54.21 mm⁴ d. 31.54 mm⁴