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For the shaded shape shown 1. Calculate the area of the shaded shape 2. Calculate the location of the x-centroid of the shaded shape 3. Calculate the location of the y-centroid of the shaded shape 4. Calculate the moment of inertia of the shaded shape about the y centroidal axis 5. Calculate the moment of inertia of the shaded shape about the x centroidal axis 6. Calculate the moment of inertia about the x axis (along the bottom of the...
Problem 3. (25 points total) Determine (a) The area A of the shaded region. (b) The x location of the centroid of the shaded area, which is called x. (Use an integral to confirm the value found by inspection from symmetry.) (C) The y location of the centroid of the shaded area, which is called y. (d) The moment of inertia, Ix, of the shaded area about the x axis. (e) The moment of inertia, ly, of the shaded area...
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...
1. A beam has a max moment of 45 kN-m. The cross section of the beam is shown in the figure below. a. State the distance of the centroid from the 2 axis. b. Calculate the area moment of inertia about the centroid. c. Calculate the maximum stress in the beam 300 mm 20 mm 185 mm 20 mm 35 mm 1. A beam has a max moment of 45 kN-m. The cross section of the beam is shown in...
Please show all work. Correct answer should be H. Will rate! 20) The y-coordinate of the centroid of the shaded area is 5.167 in. above the bottom edge of the section. The area moment of inertia about the horizontal centroidal axis is most nearly: 6 in 4 A. 512 in B. 559 in 2 in. C. 634 in D. 696 in E. 725 in 8 in. in 2 in. F. 779 in G. 819 in 2 in H. 863 in...
just need #6 (5) 12 mm 12 mm Determine the moment of inertia and the radius of gyration of the shaded area at right with respect to the x axis shown. 6 mm [6] Determine the centroid (x & y) of the I-section in Problem (5). Calculate the moment of inertia of the section about its centroidal x & y axes. How or why is this result different from the result of problem (5]? S mm- 21 mm 6 mm...
please show all your work thank you! Problem 2 (25%) 14 in A beam cross-section is shown in the provided figure. 2 in (A)(10%) Determine the distance (y) from the bottom the section to the centroid (C). 16 in 8 in Problem 2 (25% - 14 in- A beam cross-section is shown in the provided figure. 2 in (B) (15%) Determine the moment of inertia of the shape about the X-axis (i.e. the horizontal centroidal axis) 16 in - 2...
1. For the cross section shown in the accompanying illustration, compute the location of the controid (i.e., X, Y), moment of inertias 7, and I, and the radii of gyrations k, and ke about the centroidal axes for combine area shown below. You should first locate the centroid and then transfer your moment of inertia for the individual sub- sections you use to compute the centroid axes using the parallel axis theorem. 1-248-45, +4,8, +4,8, 24 4 + 4 +...
Determine the polar radius of gyration of the area of the equilateral triangle of side b = 16 in. about its centroid C. Answer: kz = By the method of this article, determine the rectangular and polar radii of gyration of the shaded area about the axes shown. Assume r = 0.55a. »-- ------ - - Answers: Calculate the moment of inertia of the shaded area about the x-axis. Assume a = 45 mm, r = 30 mm. a- Answer:...
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...