Question

Learning Goal: To be able to calculate the moment of inertia of composite areas An object's moment of inertia is calculated analytically via Integration, which involves dividing the object's aren into the elemental strips that are parallel to the axes and then performing the integration of the strip's moment of inertia correct The parallel-axis theorem is used in the calculation of the moment of inertia for composite areas. Here, the reference axis coincides with the rectangle's base and semicircle's diameter. Thus, the moment of inertia is calculated using the formulas bh / 3 and 7/8 for the rectangle and semicircle, respectively. Part C. Moment of inertia of an I-beam with two different flange widths about the beam's centroidal axis In practice, engineers often encounter structural members that have areas composed of the common geometric shapes, such as rectangles, triangles, and is when a rental intime and Figure 2 of 2 As shown, an I-beam (Figure 2) has a bottom flange that is 400 mm x 80.0 mm, a web that is 80.0 mm x 400 mm, and top flange that is 200 mm x 80.0 mm. Determine the moment of inertia of the beam about the horizontal centroidal axis using the parallel-axis theorem. Express your answer to three significant figures and include the appropriate units. View Available Hint(s) HIX= Value Units Submit Provide Feedback Next >

Answer 1

Solution: - To find the centroid of a given I beam from Top, Y ΣΑ9 ΣΑ 80 mm 280 520 Somm 400 mm 80 mm K 400mm Y = 200 x 80 X40 of 400 X 80 x 280 f 400780 X520 200x80 of 400x80 + 400080 Y - 828 mm 328 neutral avis I 232 = 560 - 328 Scanned by TapScanner

According to is given by parallel Axis theorem. Mis of about any axis To - Icu & Ah² Too M.I about centroid h- distance between the Central axis (centroid) to the axis where m.iis determined. 0 288 mm The - 228 mm neutral. axis h =182 mm M.I of Rectangulas body (Eu, bd 12 MI about neutral axis, I= Ipfa, hra of I2 + A2h2² & ff Az hz ² 2008 803 + 200x80 X ( 328-30 2 12 + 600x80 & 40 x 80 x (328 - 2002 12 + 400 X 803 + 400 X 80% ( 232 - 50) 12 Scanned by TapScanner

I = 8.483 x 10 mm4 This is moment of inertia about honorted centroidal axis. Scanned by TapScanner