Determine m.i. of i section about 2 centroidal axes, Mechanical Engineering

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Q.  An I section has dimensions Top flange = 8 cm × 2 cm; Bottom flange = 12 cm × 2 cm; Web = 12 cm × 2 cm; Over all the depth of section = 16 cm. Determine M.I. of I section about 2 centroidal axes.

582_MI.png

Figure

Sol.: As diagram is symmetrical about the y axis that is,X = 0, x1  = x2  = 0

A1 = 8 × 2 = 16 cm2

A2 = 12 × 2 = 24 cm2

A3 = 12 × 2 = 24 cm2

y1 = (2 + 12 + 2/2) = 15 cm

y2 = (2 + 12/2) = 8 cm

y2 = 2/2 = 1 cm

Y = (A1y1  + A2y2 + A3y3)/(A1  + A2 + A3)

= (16 × 15 + 24 × 8 + 24 × 1)/(16 + 24 + 24) = 7.125cm

C.G. = (0, 7.125)

Moment of inertia (M.I.) about x-x axis = IXX  = IXX1  + IXX2

291_MI1.png

The moment of inertia about  y-y axis =1873_mi3.png
As

1624_MI2.png


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