Question

HOME WORK #IV 1 ON TEST DETERMINE THE SHAPES USING 3 CENTROID THE GIVEN I {4opl} OF FOLLOWING THE ORIGINS ORIGIN x I ORIGI x 4 (SHOW ALL YOUR WORK).

Answer 1

--> 0 k412 417 Origin (Reference axi's) we have four different sections here: (i) For rectangular section 6 A = 8x2 = 16 squar feet x = 2 = 1 ft Y, = 8 + 4 = 8 ft. (2) For rectangular section Az = 10x4 = 40 ft Xq = 2 = 1 et Y2 = 2f+ (3) For triangular section ② Az = 2x4 = 4 ht" 23:4---33 ft Y3 = 4 + 2 = +4.67 ft (4) For triangular section 4 A4 = 2x4 = 4 ft² da = 2+ 4 = 3.33 ft Y4 = 4 + 2 = 4.67 ft X= ARI+ A2x2t Azaz + Adxq = 16x! + 40x! + 4 X(-1.33) A+ A2+ Azt A4 + 4x3.33 16+ 40+ 4 + 4 x = 1 ft 2

} = AY, + A2Y2 + Az Yg + A 4 Y4 A+ A2+ Az+A 1688 + 40x2 + 4x 4.67 + 4 x 4.67 16+ 40+ 4+ 4 7 = 3.83 ft --- - c.G 416 * 417 we have 3 different section hore; (i) for triangular section 6 A1 = 4x4 = 8 ft? x = (6 + 4) = -7.33 ft Y = 4 = 1.33 ft (2) for Rectangular section & A2 = 6x4 = 24 f2 x= -6 = -3 Lt Y = 4 = 2 ft (3) For triangular section a Az = 4x4 = 8 ft 2 x3 = 4 = 1.33 ft 73 = 2x 4 = 2.66 st X = AX,+ A222 +Azaz A+ Azt Az -= 8x (-7-33) + 24*(-3)+ 8X1:33 8 + 24 +8 1 X=-3 ft = left to y axis

J = AY + A2Y2+ A3Y3 AtARTA = 8x1.33 + 24 x 2 + 8 x 2.66 - 1.998 8 + 24 +8 lý 2 st
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