Question

Part A Locate the centroid of the composite area. Set a = 2 in , b = 4 in .. d = 2 in ., h = 4 in (Figure 1) Express your answer with the appropriate units. THA ? Value Units Figure < 1 of 1 > Submit Request Answer Part B Determine the moment of inertia of this area about the centroidal Taxis. Express your answer with the appropriate units. a a d |С 5 1. - 511.36 10 mm" Submit Previous Answers Request Answer

Answer 1

a" 지 0 네 네 0 젠 CC (②) 12 b 5

(A)

Location of the centroidal axis;

$\bar{y} = \frac{2A_1y_1+A_2y_2}{2A_1+A_2}$

$\Rightarrow \bar{y} = \frac{2(2\times4)(2)+(4\times2)(1)}{2(2\times4)+(4\times2)}$

$\Rightarrow \bar{y} = 1.67\;\;in$

...(Answer)

(B)

Moment of inertia about centroidal x' axis;

$I_{x'} = \sum (I_c+Ad^2)$

$\\\Rightarrow I_{x'} = 2\left [ \frac{2(4)^3}{12}+(2\times4)(2-1.67)^2 \right ]+\left [ \frac{4(2)^3}{12}+(4\times2)(1.67-1)^2 \right ]$

$\\\Rightarrow I_{x'} =29.3\;\;in^4$

...(Answer)