Lista Prova 1 e 2 Resmat

5kN 3(w) 1,2kN 400.g(1,2) W2=400.9,8.1,2=6,7kN WI=30.981.3=8,829kN -5-W1-6-W2-NA=0 -5-4,7-6-8,82-NA=0 NA=5,4,7+8,82 NA=24,52kN w=200.9,8.1.3=5,89kN NA-8-6,6-4,5-4,5-w=0 NA-8-6-4,5-4,5-5,89=0 -NA=+8+6+4,5+4,5+5,89 NA=34,89kN ΣTc=0 Tc-250=0 TC=250N.m ΣTD=0 -TD-250+400=0 TD=150N.m ΣTc=0 500-Tc=0 TC=500N.m ΣTB=0 TB-500+350=0 TB=150N.m a b c d e f 1590N NA=0KN VA=2,7KN MA=-1,654kN.m WB=0KN ΣFx=0 ↑ΣFy=0 VB-p2-1,5=0 VB=3,98KN VB=3,98KN ΣMB=0 MB+5,3-9,68-1,65 MB=-9,034KN ΣMe=0 Mc+p3-1,5=0 Mc=-11,554KN.m Nc=0KN ↑ΣFy=0 -Nc-1,125-2,925-1,5=0 Nc=5,55KN F1=4,5,6 F1=2,7kN R1a+rB-f1-f2=0 RA+RB-27-8,1=0 RA+RB-35,1=0 ΣMA=0 -(8,1-6,9)+RB-6-(27,3)=0 RB=-22,82KN 9,5kN/m 15kN/m A B 6 m 9 m C D RA RB ↰ 0,5.9.45 P1 RA + 45 - 4,5 - 9 Rb = 0 P2: (15.0,5) x 9 = 4,5kN RB = 5,25 kN RA = 5,25 - 45 - 4,5 RA = 3,75 kN 4: RA + 22,82 - 35,1 = 0 RA = 12,28 kN Ponto CPE → AM V e f3: 4,5.3,6 = 16,2 RA - f3 + Vc = 0 - Vc = 3,92 kN - (RA) + (f3.1) - (12,28.3,6) + (16,2.1,8) - Mc = 0 -Mc = - 15,05 kN.m Ponto E ME + 2,03.1,35 = 0 ↰ΣFy=0 VE = 2,03 kN - ME = 0,91 ME = - 0,91 kNm 5: Ponto D B1 kN 12,28 ↰ΣFy=0 260 VD - 8,1 + 12,28 = 0 -*ΣFx=0 ND=0 260 M_ - ND = 0 MD = 14,81 kN/m 3600 F3= 7,20 kN/m ↰ΣFY=0 1300 VB=1440kN VB=1440 kN Ponto D B1 kN ↰ΣFy=0 RA 12,32.13 RAP ↰ΣFy=0 VD - 8,1 + 12,28 = 0 -*ΣFx=0 ND=0 -M0 = - 14,81 MD = 14,81 kN/m - FB + 900 = FB.5 1800 /*ΣFx=0 А 478.94 VB=1440kN MB=19,200 kN/m _14,81 MD = 14,81 kN/m ND = 0 Ponto D B1kN RA 12,28 ↰ΣFy=0 - VD - 8,1 + 12,28 = 0 *ΣFx=0 ASNode=0 - M0 + 1,09 - 12,28.1,8 =0 -1400 MB=19,20 → + Σ Fx = 0 \underline{Nc = 0 kN} ↑ + Σ Fy = 0 -Vc - P1 - P2 + 3,75 = 0 -Vc - 0,5 - 1,5 + 3,75 = 0 \underline{Vc = 1,75 kN} ΣMA = 0 \underline{Mc - 3,75.3 - 0,5.1 - 1,5.1,5 = 0} \underline{Mc = 8,5 kN.m} 1.19 ------------------ | \ | / | / | | -- ← 0,9 kN/m -- | / | / | / | |------------------ / | 1,5 N/m ↓ B A ---------------------- | 0,5.9 = 4,5 kN | ---------------------- | P2 = (1,5-0,5).9 | = 4,5 kN | --------------------------- | | 2 | ---------------------- ΣMA = 0 -P1.D1 - P2.D2 + D3.RB = 0 -4,5.4,5 - 4,5.6 + 9.RB = 0 \underline{RB = 5,25 kN} ↑ + Σ Fy = 0 RA + RB - P1 - P2 = 0 RA + 5,25 - 4,5 - 4,5 = 0 \underline{RA = 3,75 kN} Ponto D → + Σ Fx = 0 VD - P1 - P2 + RB = 0 VD - 0,5 - 3,5 + 5,25 = 0 \underline{VD = 1,25 kN} ΣMD = 0 MD + 3.1,5 + 0,5.2 - 5,25.3 = 0 \underline{MD = 9,5 kN.m} Lista 2 1.34 ---------------- | | | 8kN | | | | | | ---------------- | | ---------------- | 70 70mm 70mm -------------------- A = ( 0,150.2 + 0,140 ) = 4.400 mm² σ = \frac{N}{A} σ = \frac{8}{4.400} = 1,82 MPa 1.35 dmin = 0,006 cm ---------------- | | ← 6N + 3kN a b 3kN A = \frac{ \pi.d^2 }{4} A = \frac{ \pi \ .0,006^2}{4} A = 28.10^{-8} [\tau_{md} = \frac{P}{A} \ \tau_{md}:3 \ 4:3,75 \ 2:6,25 \ \rightarrow \ \tau_{md} = 53,03 MPa] 1.37 500 N B: 65 mm 140 mm 15 mm 100 mm 500 N Qmed)B = FB / AB B < 65 mm 500 N Qmed)B = 500 / (π * 65 * 10^-3 / 4) Qmed)B = 150.7 KPa Qmed)c = Fc / Ac -> 500 / (π * (140 * 10^-3)^2) Qmed)c = 32.5 KPa Qmed)d = FD / AD -> 200 / (π * (100 * 10^-3)^2 / 4) Qmed)d = 25.5 KPa 0.060003783