Question

3. Determine the centroid locations 7 and y (relative to the given coordinate origin) for the cross section shown below. To receive full points, the results must be graphically shown in the sketch. all values in [m] b 4b

Answer 1

solution 디있다 k c* for calculating centroid location of this section, first ble need to convert some basic structures which he com know centroid of that structure ble have divide this structure in to four different types. since he know that 5o = 9,0 + 9202 + 931124 99 na 9, 492493499 - ①, ②, ③ and of controid Where a,, 92, az and qq core the area of © respectively, and do M2, N3 and re are the gl-Cordinate of 0,® , and respectively · from figure 9,2 cl6+b) = C(26) = 206 92= Ź (9+c)(6) = b[9+c) Az = c/c+a+&+) = cla+20) qq = 6xc = b and dozo H2=+226 Hz=bt and Hq = btet 6 74536 te Hence from equation o g

5 = (246)(0) + $ 40+2)+36) + cla+20)(6++ bc/34 +) 206+ b4a74) + c(0+2c) + bc she (9+8) + (at2c)(2672) + bę (36+ 2C) - 3 bc + bat be + cat 2 c2 = ab + b c + (0 c + c4}(26+c) + 369€ + be? Zbc + ab + ca +222 = 96? + b2c + 96c+ 262 +962 +63 + 35°C +be ab +36C+ ac + 2c2 +46°C + 36c++ 962 +962 +23 ab + 7 bet act2c2 21 and ý = 9,48 +4242 +41343 + 99449 - 9+92 +93 + ac alhere Ye , Y2 ,Yz and yq are the Yo coordinate of centroid of 0.0.♡ avd @ respectinely. 4,=0 Y2 = 1 helate) •13= + 0 = ato and 4e = a + z from equation ® - (2cb)() + (a+9x (+)+ c(a+ 2x)(atc)+ bc{a+ 206+ $4974) + (a+20) + bc 02 b + b + abc + are + 3.9c2+e3 + 96C+ be? ab + 2 bc tact 2c² 17 = a b + 2 bę? + 496c+qe + 392€+03 ab + bc + ac + 2c²