Question

gure 1 of 1 0.4 m 0.05 m; 0.2 m 0.2 m 0.2 m 0.2 m Roth

Answer 1

It consists of a lower rectangular cross-section (section 1) and an upper trapezoidal cross-section (section 2).

The centroid of the complete cross-section is calculated by using the centroids and areas of the individual trapezoidal and rectangular cross-sections.

Let ¯x1,¯y1x¯1,y¯1 and ¯x2,¯y2x¯2,y¯2 denote the x and y coordinates of the centroid of section 1 and section 2 respectively.

A1A1 and A2A2 be the areas of the cross-section of sections 1 and 2 respectively.

Let G1(¯x1,¯y1), G1(x¯1,y¯1) and G2(¯x2,¯y2)G2(x¯2,y¯2) denote the centroid of the two areas and G(¯x,¯y) denote the centroid of the complete area.
-*- .dsm ot: T - kozm tout 0.3m 0.3m Xo: auton Hene, Xi, Y i ane rectangular crossection , e quase and X2, Jl are trapezoidal crossections, and these are calwlated as, = 0.2 +02 +0.3+0.2 +0.2 -0.55m 2 % = 0.05 -0.025m Al = 0.05X11: 0055 m2 . X2 = 0.55m T h ( 29+b) 2 2 2 2 Catbl 0.3)2+0.71 37017 Tz = 04 0936807) of posted sites ý z = 0.4 (13) 1. Iz = 1.733m Az = (2+b)h = 0,4 (0:340-)=0-2 where, h= height of Ti topizem a = shorder side of porllel sides - b= longer of parllel sides h=0.4, a=0.3, - 6=0.7

We got, Ai = 0.055m² , x1 = 0.55m, Ti = 0.025m Az = 0.2m² , X2=0.55m, J2 = 0.1733m Centroid of complete Gross section is. ğ = Alt + Az Iz i Altar = (0.24 0-1733) + (0.055* 0.025) 0.2 +0.055 3 = 0 -1413 .: The Centroid of crossection is (0-55,0.1413) MOI obout. G = MOI of I about Got Ally,)? +moI of 2 about G+ A2 (9₂)2 I I - Il Gu+ Ally] + [76+ A2 (92)2

than atb (0.3) ² 45 36 X (0-3)*4 460-370.7) +0.732 0.3+0.7 = 2.5244 x 103 my yz = 0.1733 -0.1413 Y₂ = 0.032m Ilgi = wd3 - HlX0.053 125 L- l. 1.14583x10 12 Yi - 0.1413-0.025 y = 0.1163 m IIGI = 1.14583x105m" y, = 0.1163m Iz Gz = 2.52448 10²m", Y ₂ = 0.032m I = Ivan+ Al(9,)? + I7 GR + A2 ( 93 5 1.14583 X10-5 + 0.055(0.1163) +2.5244X1063 + 0.210.032)?| I = 3.4845 X 105 mil

The centroid of the cross-section is G(0.55,0.1413)

The centroid about the y-axis is 0.1413m

The moment of inertia is 0.000034845‬m^4