Lista Prova 1 e 2 Resmat

1.1 (a) 5kN 3kN W NA 200kN 8kN 6kN 6kN 1,5kN W A 1T NA W2 = 400. g.(1,2) (a) W2 = 400 .9,81. 1,2 = 4,7 kN W1 = 30.9,81.3 = 8,829 kN F = 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 W = 200.9,81.3 = 5,89 kN 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 Ponto D 8 kN RAP =? mo 12 RA=0 L VD=0 VD - 8 + 12,28 = 0 VD = 4,18 kN ΣFy = 0 ΣFX =0 Σ Mo = 0 MD -8 -12,28 1,8=0 -Mo=-14,81 MD = 14,81 KN/m 1.17 900 kN/m A B C 1m 4m PB = 900 = F3,5 5 4 F3 = 720 kN/m -> 720 .4 =1440kN Σ Fx = 0 N=0 ΣFY =0 VB - 1440 =0 VB = 1440 kN C Σ M =0 MB + 1440 . 1,33 = -MB = 19120 MB = 1920 KN/m 1.18 9 kN/m 15 kN/m A D B C 6m 3m A B RA 9m RB Σ MA=0 Y:0,5 .9 .4,5 RA + 5,25 + 4,5 =0 RB = 5,25 kN Σ Fy = 0 RA + RB - P1 - P2 = 0 RA + 5,25 - 4,5 - 4,5 = 0 RA = 5,25 - 4,5 - 4,5 RA = 3,75 KN q = -- kn/m RA + 22,82 - 35,1 = 0 RA =12,28 KN Ponto C RA f3 A mc 12,28-16,2+Vc0=> VC = 3,92 kN Σf = 0 ΣFx =0 ΣMc=0 RA-f3,6 12,28 -3,6 =16,2 - (RA.L) + f3,6 - (-5,05 kNm) MC = -5,05 KNm -> Σ ME = 0 ID Ponto E VE 1,35 ΣF = 0 ME + 2,03 1,35 = 0 2,03 1,35 ME = -0,91 kN/m ME + 2,03 1,35 = 0 →+ΣFx=0 Nc=0KN ↑+ΣFy=0 -Vc-P1-P2+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=0,5.9=4,5KN P2=(1,5-0,5).9/2=4,5KN ΣMA=0 -P1.D1-P2.D2+D3.RB=0 -4,5.4,5-4,5.6+9.RB=0 RB=5,25KN ↑+ΣFy=0 RA+RB-P1-P2=0 RA+5,25-4,5-4,5=0 RA=3,75KN PontoD. ΣFx=0 ND=0KN ↑+ΣFy=0 VD-P1-P2-RB=0 VD-0,5-3+5,25=0 VD=1,75KN ΣMD=0 MD+3.1,5+0,5.2-5,25.3=0 MD=9,5KN.m Lista2 1.34 A=10.150.2+10.140=4,400mm^2 σ=N/A σ=8/4400 σ=1,82MPa 1.35 d=6mm=0,006m A=π.d^2/4 A=π.0,006^2/4 A=28.10^-6 τmed=P/A τmed=15/28.10^-6 τmed=53,03MPa 1.37 500 N B: 65 mm 140 mm 150mm 100mm (σmed)B = FB / AB B < 65mm 500 N (σmed)B = 500 / (π * (65 * 10^-3) / 4) (σmed)B = 150.7 KPa (σmed)c = Fc / Ac -> 500 / (π * (140 * 10^-3)^2 / 4) (σmed)c = 32.5 KPa (σmed)D = FD / AD -> 200 / (π * (100 * 10^-3)^2 / 4) (σmed)D = 25.5 KPa