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7.38 Calculate the second moment of area for a

2x6 piece of lumber about the x-x and y-y

axes, as shown. Visit a hardware store and

measure the actual dimensions of a typical

2 x 6 piece of lumber.

h

1

X

V

y

W

X

7 38 Calculate the second moment of area for a 2x6 piece of lumber about the x x and y y axes as shown Visit

Answer :

The second moment of area characterizes a shape's resistance to rotational motion. For a 2x6 lumber (actually 1.5" x 5.5"), we use the formula (1/12)*b*h^3 and (1/12)*b^3*h for x-x and y-y axes.

The second moment of area, also known as the area moment of inertia, characterizes the shape of a body concerning its resistance to rotational motion. In the case of a 2x6 piece of lumber (in reality, 1.5" x 5.5"), the second moment of area about the x-x and y-y axis can be calculated using the formula (1/12)*b*h^3 for x-x axis and (1/12)*b^3*h for the y-y axis, where b is the breadth (or width), and h is the height (or depth). For this lumbar, the second moment of area is (1/12)*1.5*(5.5^3) w.r.t x-x axis and (1/12)*(1.5^3)*5.5 w.r.t y-y axis.

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