Question

Exercise 6.1.14 The L-shaped steel plate shown below is d = 14 mm thick (i.e., the member extends from z = 0 to z = -14 into the page). Determine a. its mass m b. the location of its center of mass (XM, YM, ZM). Assume: H = 760 mm, h = 130 mm, L = 460 mm, 1 = 95 mm. Material is homogeneous (steel = 7830 kg/m3). K1 H h x L

Answer 1

414600 E-9. m3 Givens A 30 homo gerous object Analysis 95 630 (a) mass of a obiect is Dersity a volumu 760 2 Volume of 0 = exbxh B A 130 = 460x 130x742 0(0,0,0) L 460 A vol of 630x 7 x 95+2 Nass= Mit Me 418950 E-9 m² x 2 7650 balmbx (418600 E-9+41898E-9)m] mi= 6.555 kg kg Mess = 6.556 Mass= 13.116 kg m2 = 6.560 Rg using the funciple of superposition of com. Xem = mix, tm2x2 MHM2 from symmetry ele For past cas have o For part ② Xi=u60 2 = 230 mm - X2= as 95 = 47-5mm Y = 130 = 75mm 425 630 +130 445 mm N = 14 = Form Za F 14 5 Imm All dimensioni aze wat diegos (0,00)

Now using superposition funciple Xem = Ximit x2m2 mitoa 230 (6:55) + 47.516.560) 13. 116 X cm = 138 617 mm Homa Yimi + 42m2 = 7866.55) + 445 (6.560) = 260.02 mm mitm2 13-116 Zem=2, mi+z2m2 416.55) + 716-560) mit in 11 7mm 13:116 hocation 4 ( 6 : Xtm, len, XO)=C(39:62 26/02 ) mm Call from augin )

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