Moment of inertia of an I-beam with two different flange widths about the beam\'

Question

Moment of inertia of an I-beam with two different flange widths about the beam's centroidal axis As shown, an I-beam (Figure 2) has a bottom flange that is 300mm times 60.0mm. a web that is 60.0mm times 300mm. and top flange that is 150mm times 60.0mm. Determine the moment of inertia of the I-beam about the horizontal censorial axis using the parallel-axis theorem. Express your answer to three significant figures and include the appropriate units. Moment of inertia of an I-beam with two different flange widths about the beam's centroidal axis As shown, an I-beam (Figure 2) has a bottom flange that is 300mm times 60.0mm. a web that is 60.0mm times 300mm. and top flange that is 150mm times 60.0mm. Determine the moment of inertia of the I-beam about the horizontal centroidal axis using the parallel-axis theorem. Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

Moment of inertia of a rectangle I about its own centroid = bh3/12

Moment of inertia of the rectangle 1 is I1 =150x 603/12 = 2700000 mm4

Moment of inertia of the rectangle 2 is I2 = 60 x 3003/12 = 135000000 mm4

Moment of inertia of the rectangle 2 is I3=300 x 603/12 = 5400000 mm4

Area of rectangle 1 A1 = 150 x 60 = 9000 mm2

Area of rectangle 1 A2 = 60 x 300 = 18000 mm2

Area of rectangle 1 A3 = 300 x 60 = 18000 mm2

The distance between datum and the centroid of rectangle 1 y1 = 60 + 300 +(60/2)= 390 mm

The distance between datum and the centroid of rectangle 2 y3 = 60+150 = 210

The distance between datum and the centroid of rectangle 3 y3 = 30

Centroid of the beam = (A1y1+A2y2+A3y3 ) / ( A1+A2+A3) = 174 mm

Vertical distance between neutral axis and centroid of rectangle 1 d1= |y1-|= 243 mm

Vertical distance between neutral axis and centroid of rectangle 2 d2= |y2-|= 36 mm

Vertical distance between neutral axis and centroid of rectangle 3 d3= |y3-| = 144 mm

Itotal = I1+I2+I3 + A1d12+ A2d22+A3d32

= 2700000 + 135225000 +5400000 + (9000x2432) + (18000x362) + (18000x1442)

= 143325000 +928017000

= 1071342000 mm4

= 1.07 x 109mm4

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