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- Determine Ix for the triangular region shown.The equation of the catenary shown is y = 100 cosh (x/100) where x and y are measured in feet (the catenary is the shape of a cable suspended between two points). Locate the y-coordinate 0f the centroid of the catenary by numerical integration using x=25ft.Figure (a) shows the cross section of a column that uses a structural shape known as W867 (wide-flange beam, nominally 8 in. deep, weighing 67 lb/ft). The American Institute of Steel Construction Structural Steel Handbook lists the following cross-sectional properties: A=19.7in.2,Ix=272in.4, and Iy=88.6in.4. Determine the dimensions of the rectangle in Fig. (b) that has the same Ix and Iy as a W867 section.
- 50 mm 150 mm 150 mm 300 mm find the moment of inertia for this exercise, with the following formulas: Polar Jo= Iox + + Toy Iox - Icx + Adg² Toy = Icg + dobe ² Caculation of centroid attached below. use it to solve the question in red box asap Som Av 3com for Portion A₁ - the figure is symme about y-aris. 2=0. AL 120mm AALD Area of A₁ = 300x50 = 15000 Y₁ = y₁ y = 300 for Pation A2 Area Az = 50x300 = 15000 By Considering Centroid, from the Bottom of the section. 300+ 50 = ₁ + 3/2 = 325 Centroid (ā, y) = = [0₁ SE = 50mm A, Ya+ A₂4 0, A₁+A₂ 15000x150 +15000x325 15000 15000 (0.237.5)For the composite area shown in the image below, if the dimensions are a = 38 mm, b = 240 mm, c = 276 mm, and b = 124 mm, determine its area moment of inertia Ī (in 106 mm²) about the centroidal horizontal X-axis (not shown) that passes through point C. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. 1 aa. find the area and vertical distances from the bottom edge of the cross-section to the centoid of rectangles b. Find Iz, the area moment of inertia about the z centroidal axis for the cross-section. c. Find QH, the first moment of area about the z centroidal axis for the entire area below point H. This area has width 2c2c and height tt. Also, find QK, the first moment of area about the z centroidal axis for the entire area above point K with width b and height t. d. Determine the magnitudes of the shear stress at point H and the shear stress at point K. e. Find Qmax, the maximum first moment of area about the z centroidal axis for any point in the cross section, and τmax, the maximum horizontal shear stress magnitude in the cross section.
- Question 5 Calculate the polar radius of gyration of the shaded area about its centroid C. given t = 105 mm, a = 500 mm, b = 640 mm. r = Blank 1 mm t round your answer to the nearest whole number. Blank 1 Add your answer -at xo bCompute the coordinates of the centroid (î, g) of the area shown. Also compute the area moment of intertia about the r' and y' axes with origin at the centroid. 2013 Michael Swanbom cc BY NC SA a k-d Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 14 mm 111 mm 12 mm d 45 mm h 89 mm w 22 mm The z coordinate of the centroid is a = mm. The y coordinate of the centroid is j mm. The moment of inertia about the z' axis going through the centroid is Iz mm. The moment of inertia about the y' axis going through the centroid is Iy = mm*.1. For the Isosceles triangle shown to the right, find the moments of inertia, Ix and Iy, about the centroidal axes. Hint: break into two right triangles and use parallel axis theorem. Ans: Iy = bh³/36, I, = hb³/48 y 2h/3 h/3 X b/2 b/2
- Compute the coordinates of the centroid (z, 9) of the area shown. Also compute the area moment of intertia about the z' and y' axes with origin at the centroid. 2013 Michael Swanbom BY NC SA a W. k d Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value 6 mm 28 mm 7 mm 13 mm h 33 mm 5 mm w The z coordinate of the centroid is a = mm. The y coordinate of the centroid is j = 26.74 mm. The moment of inertia about the z' axis going through the centroid is I, mm*. The moment of inertia about the y' axis going through the centroid is Iy mmt.For the shaded area shown, find: (a) The location of the centroid (X,Y). (b) The moment of inertia about the centroidal x- axis (horizontal axis going through the centroid) Use the table shown to tabulate all information for the moments of inertia. See the useful equations on the following page. 45° 6 in 9 in 45° 6 in 8 in 10 in xQuestion 2 Calculate the following: i. The centroid ii. Moment of inertia of the channel section about the x'-axis 25mm 25m 100 mm 25 mm 25 mm 75mm 75mm 50mm 50mm' 100mm 25 mm