PROBLEM 2: Compute the location of centroid from the given reference x and y axes. Then, calculate the centroidal moment of inertia about x and y-axes. ANS: x = 25.86 mm, y = 68.54 mm, I¸ = 12.96 × 106 mm², Iy = 2.27 × 106 mm² -60- 30 25 90 -80- 20 20 Dimensions in mm x
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- Figure Q2b shows a solid and homogeneous section, where (31.25 mm, 41.54 mm) are its centroid coordinates (X , ỹ) relative to the axes origin, 0. The dimensions for the section in Figure Q2b are b1 = 15.75 mm , b2 = 15.75 mm, b3 = 62.50 mm, d1 = 75.85 mm and d2 = 20.25 mm. Calculate the second moment of area for the solid and homogeneous section shown in Figure Q2b about its centroidal x-axis. Give your answer to two decimal places. y b1 b2 di d2 b3D 5. Find the centroidal distances from x-axis and y-axis. y 80 30 60 90 -20- 30 Dimensions in mmFigure Q2b shows a solid and homogeneous section, where (31.25 mm, 41.54 mm) are its centroid coordinates (x̄ , ȳ) relative to the axes origin, O. The dimensions for the section in Figure Q2b are b1 = 15.75 mm , b2 = 15.75 mm, b3 = 62.50 mm, d1 = 75.85 mm and d2 = 20.25 mm. Calculate the second moment of area for the solid and homogeneous section shown in Figure Q2b about its centroidal x-axis. Give your answer to two decimal places.
- Find the centroid of the area bounded by the function f(x) = 1+ sin(æ) and the x-axis and the lines x-1 and x=3. Calculate the center of mass for R (round to 2 decimal places) xbar = ybar Find the centroid (E, 9) of the region bounded by: y = 3x2 + 6x, y = 0, = 0, and r = 3A rectangle has: length (parallel to the x - axis) of 120mm and width (parallel to the y - axis) of 10mm has a centroid where the distance x = 50 mm y = 187 mm Calculate the second moment of area relative to the x axis. Give your answer in mm4Calculate ly about the centroid of the following shape. (It should look familiar). Recall that xpar = 2.11 ft. Remember you want to calculate I of each shape about its centroid, then use the parallel axis theorem to relate it to the global centroid. Hint: break into 4 pieces: half circle, square, triangle and open circle. Remember you want to subtract the empty circle! Use Ix'= 0.11r4 for the half- circle. Then just figure out each distance from the centroid of the component to the global centroid and that is your D in the AD? term. Good luck! Enter your answer without units in the space below. Follow correct sig figs! y 3 ft- -3 ft- 1.5 ft 1 ft X-
- Determine the locationof the centroid for the cross-section shown below and draw a scaled sketch of the cross-section, clearly showing the centroid and indicate its distance from the selected origin. (Start your calculations be setting an origin from the bottom, left-most point on the cross-section). 2 Calculate the second moments of areas about the centroidal axes for the beam cross- section. 60 mm |10 mm 10 mm 100 mm 10 mm 40 mmDescribe the Parallel-Axis Theorem for an Area?3) A hemisphere of diameter 60 mm is placed on the top of a cylinder, whose diameter is also 60 mm. The height of the cylinder is 75 mm. Find the common CG of the composite body. Hence CG of the given solid is at (0 mm, 47.6 mm, 0 mm)