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moment of area(tut)

moment of area(tut) - THE UNIVERSITY OF HONG KONG Faculty...

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Unformatted text preview: THE UNIVERSITY OF HONG KONG Faculty of Engineering Foundations of engineering mechanics (ENGGIOIO) Tutorial 2: Moments of Mass and Area 1. Determine the second moment of area under the parabola about the x-axis. Solve by using (a) a horizontal strip of area, and (b) a vertical strip of area. Ans: 14.40 (units)4 Figure l 2. Calculate the second moment of area of the X-axis of the area enclosed between the y- axis and the circular arc of radius 3 whose centres are at O and A. Ans: 0.096%“ :41 r-edx T Figure 2 1 i \ ___l l O a/2 3. Determine the second moment of the shaded area shown in Figure 3 with respect to (a) the x-axis, and (b) the y-axis. Ans: (3)230x106mm4 _ | (b) 267x106 m4 T 100 mm i _ _ Figure 3 i 30 mm , it} rnm lUOlmm ' 60mm :0 +‘ i 50 mm 'x'—— 150 mm —>’L W‘- 50 mm 4. Determine the second moments of the shaded area shown in Figure 4 with respect to the x- and y-axes. Ans: 127.4x106 mm4; r 343x106 mm4 T [20 mm 60 mm ‘ Flgure 4 0 —% W .1' {#80 mm +90 mm *80 mm—> 5. Determine the second moments of the shaded area shown in Figure 3 with respect to (a) the x- and y—axes shown in the figure; and (b) the x- and y-axes through the centroid of the area. Ans: (a) 37.7><106 mm“; 246x106 mm4 (b) 13.02x106 mm4; 34.5)(106 mm4 Figure 5 f— 160 mm 4— ‘ 60 mini—)1 ...
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