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Chapter 9 Solutions
International Edition---engineering Mechanics: Statics, 4th Edition
- PROBLEM 4: The region is symmetric about the x-axis. Calculate the moment of inertial about the centroidal x and y axes. ANS: 1x = 10.35 × 106 mm², I₁ = 1.74 × 106 mm² 17 mm y 68 mm 17'mm 18 mm 27 mm xarrow_forwardFind the centroid of the region in the first quadrant bounded by the x-axis, the parab y=2x, and the line x +y = 4. Find the moment of inertia about the x-axis of a thin plate bounded by the parabola y and the linex+y =0 if 8(x, y) = x + y.arrow_forwardQ3. Find the moment of inertia about x and y axes for the shaded area shown in the figure below. Y R-6 cm → Xarrow_forward
- 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/2arrow_forwardFind the moment of inertia about centroidal X-axis and centroidal Y-axis of the given geometry Figure: 2a and 2barrow_forwardFind the moment of inertia about centroidal X-axis and centroidal Y-axis of the given geometryarrow_forward
- Find the component of the resultant at the u-axis.arrow_forwarda. 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.arrow_forwarda. 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.arrow_forward
- The weight of the shaded area given in the figure Calculate the y coordinate of the center. a(mm)=95 , b(mm)=65 , c(mm)=35 , d(mm)=190 , e(mm)=55arrow_forwardPlease fast.arrow_forwardFind the moment of inertia (ly) of the given lamina about Y-Y axis passing through its centroid, where b1=108 mm, d1=38 mm, b2= 62 mm & d2=84mm. (enter only the values in the boxes by referring the units given in bracket) b2 TP b1 O The X value is (unit is in mm) = O The Y value is (unit is in mm) (i) the lyyi value is (unit is in mm)= (iv) the lyy2 value is (unit is in mm)= . (V) The lyy value is (unit is in mm4)=arrow_forward
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