Question

Problem 1 1. Locate the centroid of the shaded plane area shown (x,y) 2. The moment of inertia about the x-axis ** All the dimensions are in mm. 80 30 60 -20- Problem 2 The tower truss is subjected to the loads shown. 1. Using Method of sections, determine the force in members EF, EG, and DG 2. Using the results from (1) and Method of joints, determine the force in member ED Indicate whether the members are in tension or compression 500 lb 1000 ID 1000 lb 500 lb LITT 10 5 12 8 811 8

Answer 1

solutions- y-axis Domm problemi 130mm Gomm Tommt Fromm Bomp gomm 3 G (32-8,79-2) a3 @ Romm Comm of x-axis finding of = 2400 mm? 17 Day 130mm ci) Locate the centroid the shaded area ( J J ) area Area 1 section A = 30x8 o = 2400mm² Area of section A2 = 4 x 30x60 = 900mm? Area of ③ section A3=20x 90 = 180omm? Area of 9 section Ay = 30x8o find y, ,92 1931 Yy ., X3 → Y = 30+90+30 = 135mm, 9 = 185mm → Y₂ = 30 + 60+20= 110mm, [y2 = 110mm Y3 = 30 +90 = 75mm, Ly3 = 75mm yy = 30 = 15mm, 94 = 15m X, = 20 = 40mm, 12= Yomm 20 = 10mm, [x3= 10mm 1 xy = go=yomm] & Di, dzi ixy 1 π [0x2= 204 60 uomm - 1 3 Now, find x 7 20 = AX, TA222 + A ₃X₃ + Ayxy - 2400X40 +900x40+1800X107 Q400X40 Ait Azt Azt Ay 2400 + 9 00 + 1800 +2400 5o = 32.8mm Distance from y-axis

y=aiyit A. Yu+Hayz + Ay 4y = 2400x185+900X10 +18.00% 7542400415 AITA₂+ Azt Ay 2400+ 9oot 1800+2400 y = 79.2 mm distance from 3-axis centroid coordinates (32.8, 7900 mm f Ixxi 12 2 find the moment inertia about the X-axis (base) Ixx=Ixx, + I xx ₂ + Ixx₂ + Ixxy bd² taihi hi = 135mm 8ox (30)3 4 +2400x (135) = - 43 920000 mm Ixx, = 43920000mm" bh? + Azha h2 = 110mm 36 Gox 303 + 900x (110) = 10935 000 mm 36 Ixx₂ = 10935000 mm Ixx z= b 2 t Azha hz = 75mm = 20X @o13 .+ 1800x (75) = 11340000 mm 13 Ixx3 = 11340000mmy IXX₂= y 3 2 2 ५ 2 Ixxy= + Ayhui 15mm hy 12 bd3 = dox (30)² + 2400 x C15} = 720000mm" - 720000mmy ५ put all the Ixx + Ixxy = Ixxit IXX2 + Ixxz- Ixx = 66915000 mm values, we get

sumonary Answers centroi c5c,g)=(32-8, 79-3) Coordinates mo I (Ixx) 66915000 mm a base