p3_sol - Problem Set 3 Problem 3.1 Center of Gravity for a...

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Problem Set 3 Problem 3.1 Center of Gravity for a Bent Rod Determine the distance x C and y C to the center of gravity of the bent rod. Figure P9.1: Problem 9.1
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Problem 3.2 Centroid of a Composite Section Determine the location y C of the centroid of the beam’s cross sectional area. Neglect the size of the corner welds at A and B for the calculation. Figure P9.2: Problem 9.2
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Problem 3.3 Centroid of a Tapered Cross Section Locate the centroid y C of the concrete beam with the tapered cross section shown. Figure P9.3: Problem 9.3
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Problem 3.4 Find the x -coordinate of the centroid of the indicated region where A = 2 m and k = π/ 8 m - 1 . x y O y = A cos( kx ) Figure 3.1: Problem 3.1 Solution A = 2; % m k = pi/8; % m^(-1) % y(x) = A*cos(k*x); % intersection of y with x-axis x0 = (pi/2)/k; % x0 = 4 m % Area = int(dx dy) where 0<x<x0 and 0<y<A*cos(k*x) % Ay = int(dy) where 0<y<A*cos(k*x)) Ay = int(1,y,0,A*cos(k*x)); % Ay = 2*cos((pi*x)/8) % Area = int(Ay dx) where 0<x<x0 Area = int(Ay,x,0,x0); % Area = 16/pi (m^2) % first moment of area about y-axis % My = int(x dx dy) where 0<x<x0 and 0<y<A*cos(k*x)
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This note was uploaded on 08/29/2011 for the course MECH 2110 taught by Professor Clark,b during the Spring '08 term at Auburn University.

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p3_sol - Problem Set 3 Problem 3.1 Center of Gravity for a...

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