Lista Prova 1 e 2 Resmat

1.1 (a) 5 kN 3 kN 1.2 kN NA W2 = 400 . g . (1,2) W2 = 400 . 9,81 . 1,2 = 4,7 kN W1 = 30 . 9,81 . 3 = 8,829 kN Σ Fy = 0 -5 - W1 - 6 - W2 - NA = 0 -5 - 4,7 - 6 - 8,82 - NA = 0 NA = 5 + 4,7 + 6 + 8,82 NA = 24,52 kN (b) W = 200 . 9,81 . 3 = 5,89 kN Σ Fy = 0 NA - 8 - 6,6 - 4,5 - 4,5 - W = 0 NA - 8 - 6,6 - 4,5 - 4,5 - 5,89 = 0 -NA = + 8 + 6,6 + 4,5 + 4,5 + 5,89 NA = 34,89 kN 1.2 Σ Tc = 0 w fl 30 kW 25 kW TC = 250 N.m TD = 150 N.m 1.3 Σ Tc = 0 Σ TB = 0 TC = 500 N.m TB = 150 N.m 600N.m 0,50m 1.8 F 1500 NA VA 0 + Σ Fx = 0 b + Σ Fy = 0 NA = 0 kN NA = 27 kN MA = -1,654 kN.m 2 → + Σ Fx = 0 WB = 0 kN ↑ + Σ Fy = 0 VB = 3,98 kN VB = 3,98 kN Σ MB = 0 MB = -9,034 kN 3 Nc = 0 kN Mc = -11,554 kN.m 1.11 45 kN/m F1 = 45,6 F1 = 27 kN F2 = 8 kN ↑ + Σ Fy = 0 RA + RB - F1 - F2 = 0 RA + RB - 27 - 8 = 0 RA + RB - 35 = 0 Σ MA = 0 - (8,1 . 6,9) + RB . 6 . (27,3) = 0 RB = 22,82 kN Ra+22,82-35,1=0 Ra=12,28KN grafo f3 4,5,3,6=16,2 ΣFx=0 Ra-f3+Vc=0 -> 12,28-16,2+Vc=0 -> Vc=3,92KN ΣFy=0 (Nc)=0 ΣMc=0 -(Ra . L)+(f3 . l) - (12,28 . 3,6)+(16,2 . 1,8) -Mc = 0 Mc=-15,05KNm ponte E 1,35 ΣFy=0 ΣMe=0 Ve=2,03=0 VE=2,03KN ME+2,03.1,35=0 3 -me=0,91 ME=-0,91KN/m ponte D ΣFy=0 -VD-8,1+12,28=0 VD=4,18KN ΣFx=0 (ND)=0 ΣMo=0 -Mo=14,81 Mo=14,81KN/m 1.17 grafo 5m 720 ΣMc=0 Pb+900Fb 5 720 KN/m ΣFx=0 ΣFY=0 CΣMc=0 MB=1400 . 1,33 -MB=1920 MB=1920KN/m 1.19 15KN/m 9 AbC ΣFY=0 Ra+Rb-P-P2=0 RA+5,25-4,5-45=0 ra=5,25-45-4,5 Ra=3,75KN Ra=0,5.9=4,5 grafo 9m -> 9m grafo MA=0 -45.45-45.6+9Rb=0 Rb=5,25KN ΣFY=0 graph P ΣMc P graph 3m g KN/m tilibra →+ΣFx=0 Nc=0KN ↑+ΣFy=0 -Vc-P-P+3,75=0 -Vc-0,5-1,5+3,75=0 Vc=1,75KN ΣMA=0 Mc-3,75.3-0,5.1-1,5.1,5=0 Mc=8,5KN.m P1 A B 2 R 15N/m (A) L=B -✓ 6m (D) 9m A 9m B Ra Rb P2=0,5.9=4,5KN P2=(1,5-0,5).9=4,5KN/2 ΣMA=0 -P1.D1-P2.D2+D3Rb=0 -4,5.4,5.4,5.6+9Rb=0 Rb=5,25KN ↑+ΣFy=0 Ra+Rb-P-P2=0 Ra+5,25-4,5-2,5=0 Ra=3,75KN Ponto D. P1 P2 P Rb 1(3m) ↑ 9=1 h, KW/m 3= h P=0,5KN P2=2=3,5KN →+ΣFx=0 No=OKN ↑+ΣFy=0 Vo-P-P2+Rb=0 Vo-0,5-2,5+5,25=0 Vo=1,25KN ΣMo=0 MD+3.1,5+0,5.2-5,25.3=0 MD=9,5KN.m Lista 2 1.34 8KN 70m 05 a A=10.150.2+10.140=4,400mm² σ=NA σ=8 400 σ=1,8 MPa 1.35 6 1 6 3KN 3,5KN A=πd4 A=π0,006 4 3KN A=28.10⁻⁶ Tmd=PA Tmd=53 8.10⁻⁶ Tmed=53,03 MPa 1.37 500 N B 65 mm D 140 mm 15 mm 10 mm 100 mm 500N (cmed)B = Fn AB B 65 mm 500 N (cmed)B = 500 π.65.10 4 (cmed)B = 150,7 KPa (cmed)c = Fc -> 500 -> (cmed)c = 32,5 KPa Ae π.(140.10³) 9 d d 200 D (cmed)D = FD -> D -> 200 -> (cmed)D = 25,5 KPa AD π.(100.10³) 200 4