Lista Prova 1 e 2 Resmat

1.2 ΣTC=0 TC-250=0 TC=250N .m ΣTD=0 -TD-250+400=0 TD=150N .m 1.3 ΣTC=0 500-TC=0 TC=500N.m ΣTB=0 TB=500+350=0 TB=150N.m 1.8 V4=1,5 1500N NA +ΣFx=0 MA=0KN → +ΣFy=0 NA=2,7KN MA=1,654KN.m NA → +ΣFx=0 WB=0KN ↑ +ΣFy=0 VB-P1=0 VB=3,98 KN VB=3,98KN ΣMB=0 MB+5,33+2,5-1,65 MB=-9,034KN.m NC → +ΣFy=0 -NC-1,125-2,925=0 NC=5,55KN ΣMC=0 MC+P3,195+5,5+3,9=0 MC=-11,554KN.m 1.11 45KN/m 6KN/m RA+RB-F1-F2=0 RA+RA-27,8=0 RA+RB-35,1=0 ΔΣMA=0 -(8,1,6,9)+RB(6-2,7,3)=0 RB=-22,82KN 2.1 5KN 3KN W NA (α) W2=400.g.1,2 (α) W2=400.9,81.1,2=6.7 KN W1=30.9,81.3=8,829KN 5-W1-6-W2-NA=0 5-4.7-6-8,82-NA=0 NA=5,47+6,08+8,82 NA=24,52 KN W=200.9,81,3=5,89KN 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=34,89KN Ra + 22,82 - 35,1 = 0 Ra = 12,28 KN Ponto C R a S c 3,6 Ve Mc f3: 4,5, 3,6 = 16,2 Ef = 0 f3 R... a + f3 + Vc = 0 -> 12,28 - 16,2 + Vc = 0 Vc = 3,92 Kn Ef=0 Nc=0 E ME = 0 (Ra * L) + (f3 * L) - (12,28 * 3,6) + (16,2 * 1,8) - Mc = 0 Mc = -15,05 KN nm Ponto E j f 1,35 Ve ME = 0 Ef y=0 ME + 2,03. 1,35 = 0 3 VE = -0,91 K ME = -0,91 KN/m (tilibra) VE=2,03 Kn Ponto D B 8 KN EfY = 0 ND = 0 RAP 12 -VD - 8 + 12,28 = 0 VD = 4,18 Kw 1,8 VD XdMD -MD= - 14,81 MD= 14,81 KN/m Ef x = 0 (mo) f1.7 A B 2m C 900 KN/m2 PB = 900 + FB -> 3600 = Fb . 5 5 4 F3 = 7,20 KN/m 3,0 KN V P f2 720,4 = 1440 KN 2 EfX = 0 Ef Y = 0 VB = 1440 = 0 VB =1440 KN E ME= 0 MB + 1440,1,33 = -MB = -1920 MB= 1920 KJ/m (tilibra) 1.8 15 KN/m 9.5KN/m AB P1 R1 9m 6 m A Ic DI B RA Y: 0,5 9 9 45 -95 45 - 45.6 +9 RB =0 P2: (15.0.5) x9 = 4,5 KN 2 RB = 5,25 KN/ EfY =0 R A+ R B- P-P2 =0 RA+ 5,25 -45= 0 RA= 5,25 -45-4,5 RA = 3,75 KN/ P1 R1 3m Vc M (tilibra) p S q= f2 h. j KN/m →+ΣFx=0 Nc=0KN ↑+ΣFy=0 -Vc-P-P2+3,75=0 -Vc-0,5-1,5+3,75=0 Vc=1,75KN ΣMA=0 Mc-3*5,3-0,5*1,5*1,5=0 Mc=8,5KN*m 15N/m Ra P1 A' P2 A B Rc 9m P2=0,5*9=4,5KN P2=(1,5-0,5)*9/2=4,5KN ΣMA=0 -P1*D1-P2*D2+D3*Rc=0 -4,5*4,5-4,5*6+9*Rc=0 Rc=5,25KN ↑+ΣFy=0 RA+RB-P1-P2=0 RA+5,25-4,5-4,5=0 RA=3,25KN Ponto D. VD2P2 P1 P21 3m RB g=1/3=h 1K g=h N/m P1=0,5KN P2=3,5KN →+ΣFx=0 ND=0KN ↑+ΣFy=0 VD-P1-P2+RB=0 VD-0,5-3,5+5,25=0 VD=1,25KN ΣMD=0 MD+3*3,15+0,5*2-5,25*3=0 MD=9,5KN*m Lista 2 1.34 8KN 2 7cm 2cm A=10*150,2+10*140=4.400mm^2 σ=N/A σ=8/4,400 σ=1,82MPa 1.35 6mm=0,006m A=πd^2/4 A=π*0,006^2/4 A=28*10^-6 τmed=P/A τmed=1,5/28*10^-6 τmed=53,03MPa 1.37 500 N 65 mm 140 mm 150 mm 100 mm 500 N (smed)B = Fn AB B = 65 mm 500 N (smed)B = 500 π.65.10 4 (smed)B = 150,7 KPa (smed)C = Fc -> 500 -> (smed)C = 32,5 Kpa Ac -> π.(140.10³) 4 (smed)D = Fd -> 200 -> (smed)D = 25,5 Kpa AD -> π.(100.10³) 4 100