An area is defined by two curves y = x and y = x2 as shown...
An area is defined by two curves y = x and y = x2 as
shown below. (a) (2 pt) Define vertical and horizontal
infinitesimal elements. (b) (1 pt) Find the total area. (c) (2 pts)
Calculate the x- and y-coordinates of the centroid C. (d) (2 pts)
Calculate area moments of inertia about x and y axes (Ix and Iy)
first. (e) (2 pts) Apply the parallel axis theorem to find area
moments of inertia about the centroidal axis x and y( x I and y I )
. (f) (1 pts) Calculate the polar moment of inertia about C.
Homework Answers
Determine the Moment of Inertia Ix and Iy of the composite cross section about the centroidal x and y axes. Parallel Axis Theorem I = I + Ad2
Determine the Moment of Inertia Ix and Iy of the composite cross section about the centroidal x and y axes. Parallel Axis Theorem I = I + Ad2 HINT: 1st find the composite centroidal x and y axes, 2nd find the distance from the centroids of each section to the new composite centroidal axis, 3rd calculate the centroidal Ix and ly and areas using formulas for common shapes, 4th use the parallel axis theorem to calculate the moment of inertia. Also find...
Parallel-Axis Theorem for an Area 2 of 8 Learning Goal: I, Iy = ft To be...
Parallel-Axis Theorem for an Area 2 of 8 Learning Goal: I, Iy = ft To be able to use the parallel-axis theorem to calculate the moment of inertia for an area. The parallel-axis theorem can be used to find an area's Submit axis that passes through the centroid and whose moment of inertia is known. If ar and y' are the axes that pass through an area's centroid, the parallel-axis theorem for the moment about the x axis, moment about...
plz help show all work For the area shown, determine the following a. Find the rectangular...
plz help show all work
For the area shown, determine the following a. Find the rectangular moments of inertia I, and ly, 2. the polar moment of inertia Jo, and the radii of gyration Kx, Ky, and ko (3, 3) b. Find the centroid of the area (x, y) c. Using the theorem of Pappus and Guldinus determine the volume obtained by rotating the area about the y-axis Coordinates are in units of inches
The shaded area is equal to 5000 mm^2. Determine its centroidal moments of inertia Ix and...
The shaded area is equal to 5000 mm^2. Determine its centroidal
moments of inertia Ix and Iy, knowing that 2Ix =Iy and that the
polar moment of inertia of the area about point A is Ja=22.5x10^6
mm^4
ded area is equal to 5000 mm2. Determine its centroidal The sha of inertia I, and Iy, knowing that 2, T, and that the polar moments of inertia / and 1 , moment of inertia of the area about point A isJ. 60...
Compute the area moments of inertia (Iz and Iy) about the horizontal and vertical centroidal (x...
Compute the area moments of inertia (Iz and Iy) about the horizontal and vertical centroidal (x and y) axes, respectively, and the centroidal polar area moment of inertia (J-Iz -Iz +Iy) of the cross section of Problem P8.12. Answer: 1x-25.803 in. Ц-167.167 in. and J-192.97 in P8.12 The cross-sectional dimensions of the beam shown in Figure P8.12 are a 5.o in., b moment about the z centroidal axis is Mz--4.25 kip ft. Determine 6.o in., d -4.0 in., and t-...
d. For the area shown below (dimensions in ft), determine the centroid location (ū and y)...
d. For the area shown below (dimensions in ft), determine the centroid location (ū and y) and calculate the moments of inertia (Iz' and Iy about the centroid axes). y 3 ft 3 ft + 1 ft 1.5 ft X
Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.
Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.
(10 points) Determine the moment of inertia of the composite beam about the centroidal x and...
(10 points) Determine the moment of inertia of the composite beam about the centroidal x and y axis. Hint: You need to locate the centroid of the composite area. You can use the tables in Appendix B and C. Then, using the same tables and parallel axis theorem you can calculate the moment of inertia about the centroidal axes. 20 in Ism 5 in W10x54 Note: The drawing is not to scale. is the centerline symbol Problem 1
Please answer the following,and please note that 0.00130,0.00608,-0.000558 does not work. Mohr's circle is a graphical method used to determine an area's principal moments of inertia and to f...
Please answer the following,and please note that
0.00130,0.00608,-0.000558 does not work.
Mohr's circle is a graphical method used to determine an area's principal moments of inertia and to find the orientation of the principal axes. Another advantage of using Mohr's circle is that it does not require that long equations be memorized. The method is as follows: 1. To construct Mohr's circle, begin by constructing a coordinate system with the moment of inertia, I, as the abscissa (x axis) and...
Parallel-Axis Theorem for an Area 2 of 8 Learning Goal: I, Iy = ft To be able to use the parallel-axis theorem to calculate the moment of inertia for an area. The parallel-axis theorem can be used to find an area's Submit axis that passes through the centroid and whose moment of inertia is known. If ar and y' are the axes that pass through an area's centroid, the parallel-axis theorem for the moment about the x axis, moment about...
plz help show all work
For the area shown, determine the following a. Find the rectangular moments of inertia I, and ly, 2. the polar moment of inertia Jo, and the radii of gyration Kx, Ky, and ko (3, 3) b. Find the centroid of the area (x, y) c. Using the theorem of Pappus and Guldinus determine the volume obtained by rotating the area about the y-axis Coordinates are in units of inches
The shaded area is equal to 5000 mm^2. Determine its centroidal
moments of inertia Ix and Iy, knowing that 2Ix =Iy and that the
polar moment of inertia of the area about point A is Ja=22.5x10^6
mm^4
ded area is equal to 5000 mm2. Determine its centroidal The sha of inertia I, and Iy, knowing that 2, T, and that the polar moments of inertia / and 1 , moment of inertia of the area about point A isJ. 60...
Compute the area moments of inertia (Iz and Iy) about the horizontal and vertical centroidal (x and y) axes, respectively, and the centroidal polar area moment of inertia (J-Iz -Iz +Iy) of the cross section of Problem P8.12. Answer: 1x-25.803 in. Ц-167.167 in. and J-192.97 in P8.12 The cross-sectional dimensions of the beam shown in Figure P8.12 are a 5.o in., b moment about the z centroidal axis is Mz--4.25 kip ft. Determine 6.o in., d -4.0 in., and t-...
d. For the area shown below (dimensions in ft), determine the centroid location (ū and y) and calculate the moments of inertia (Iz' and Iy about the centroid axes). y 3 ft 3 ft + 1 ft 1.5 ft X
(10 points) Determine the moment of inertia of the composite beam about the centroidal x and y axis. Hint: You need to locate the centroid of the composite area. You can use the tables in Appendix B and C. Then, using the same tables and parallel axis theorem you can calculate the moment of inertia about the centroidal axes. 20 in Ism 5 in W10x54 Note: The drawing is not to scale. is the centerline symbol Problem 1
Please answer the following,and please note that
0.00130,0.00608,-0.000558 does not work.
Mohr's circle is a graphical method used to determine an area's principal moments of inertia and to find the orientation of the principal axes. Another advantage of using Mohr's circle is that it does not require that long equations be memorized. The method is as follows: 1. To construct Mohr's circle, begin by constructing a coordinate system with the moment of inertia, I, as the abscissa (x axis) and...
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