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Chapter 9 Solutions
International Edition---engineering Mechanics: Statics, 4th Edition
- Q 1.) Find each of the axis of symmetry and the second moment of area about the X-X axis in the segment T shown in the formarrow_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_forwardFind the moment of inertia of the given lamina about X-X axis passing through its centroid, where b1=110 mm, d1=38 mm, b2= 70 mm & d2=100mm. b2 d2 TP b1 (i) The X value is (unit is in mm) = (i) The Y value is (unit is in mm) = (iii) the Ixx1 value is (unit is in mm4)= (iv) the Ixx2 value is (unit is in mm4)= (v) The Ixx value is (unit is in mm4)=arrow_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_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_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
- Find 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_forwardC 104 in 4 417 in4 1670 in 4 223 in4 b x' h If b = 10 in and h = 5 in, what is Ix'. The x'-y' axes are located at the centroid of the rectangle.arrow_forwardThe corners of a triangle are at (4, 4), (10, 8), and (12, 4). The diameter of a semi-circle ends at (4, 4) and (12, 4) and the semi-circle touches the x-axis. Find the distance of the centroid of the composite figure from the x-axis. 2.3 3.48 4.24 5.33arrow_forward
- 6 - Find the center of gravity M of the three-dimensional homogeneous wire ABCD in the figure using the (x, y, z) coordinate set. The dimensions of the wire are a = 24 cm, b = 36 cm. Which of the following is the correct coordinates of the BC part of the homogeneous wire in the x, y and z axes?A) (36; 12; 24)B) (18; 12; 0)C) (36; 24; 12)D) (36; 12; 0)E) (36; 24; 0)arrow_forwardCalculate the total moment of the system about point A, when P1 = 10 .kN, P2 = 5 kN and 0 = 30° %3D %3D P, 25 kN.m 1.5 m A -1.5 m 1.5 m- P2 اخترأحد الخيارات a. 29.00 kN.m (CW) b. 29.55 kN.m (CCW) c. 4.75 kN.m (CCW) d. 4.00 kN.m (CW)arrow_forwardFind the moment of inertia of the given lamina about X-X axis passing through its centroid, where b1=110 mm, d1=38 mm, b2= 70 mm & d2=100mm. (enter only the values in the boxes by referring the units given in bracket) b2 TP b1 (i) The X value is (unit is in mm) = (i) The Y value is (unit is in mm) = (iii) the Ixx1 value is (unit is in mm4)= (iv) the Ixx2 value is (unit is in mm4) = (v) The Ixx value is (unit is in mm4)=arrow_forward
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