Anotações e Exercício Aula 5-2022 2

ΣMz^1 = 0 M + \frac{200 \cdot x^2}{3} - 316,67\cdot (x - 1) = 0 M = - \frac{200 \cdot x^3}{9} + 316,67 + x - 316,67 x = 1 \rightarrow M = -22,22 x = 3 \rightarrow M = 33,33 M_{max}^x = 2,18 \approx 144 4 > x > 3 ΣFy = 0 λ + 600 - 316,67 = 0 λ = -283,33 \text{ kgf} ΣMz^11 = 0 M + 600 \cdot (x - 2) - 316,67(x - 1) = 0 M = -283,33x + 883,33 x = 3 \rightarrow M = 33,33 x = 4 \rightarrow M = -250 \sum^\pi Fy = 0 \sum^\pi Mz^III = 0 M + 500x \cdot \frac{x^1}{2} = 0 x^1 = 0 \rightarrow M = 0 x^1 = 1 \rightarrow M = -250 Q (kgf) 250 2,18 3 -60,67 -283,33 x (m) 5 580 500 -250 -22,22 33,33 144 M (kgf m) 400 \frac{kgf}{m} 500 \frac{kgf}{m} 316,67 k ΣMz^5 = 0 1 > x > 0 - \frac{200x^3}{9} x = 0 \rightarrow M = 0 x = 4 \rightarrow M = -22,22 3 > x > 1 400\frac{x}{3} = \frac{200}{3}x^2 Q = - \frac{200x^2}{3} + 316,67 xQ = 2,18 x_λ=0 = \sqrt{\frac{3\cdot316,67}{200}} = 2,18 30 kN/m 60 kN/m 30 kN/m A B C D 6 m 4 m 2 m 26,67 kN 353,33 kN 33,33 kN p(x') 6 > x' > 0 (x')/x = 30/6 p(x') = 5x 5x + x'/2 + 2,5x'^2 30x' 5 x' 33,33 kN ΣFy = 0 α - 2,5x'^2 - 30x' + 33,33 = 0 α = 2,5x'^2 + 30x' - 33,33 x'=0 → α = -33,33 x'=6 → α = 236,67 x'α=0 = -30 + √30^2 + 4*2,5*33,33 ------------------------------------ 2*2,5 1,02 ΣMz = 0 M + 2,5x'^2 * x'/3 + 30x'*x'/2 - 33,33x' = 0 M = -2,5x'^3/3 - 15x'^2 + 33,33x' x'=0 → M=0 x'=2 → M=0 x'=6 → M=-520 M max x'=1,02 = 17,51 p(x'')=30/x'' p(x'') = 5x'' 6 > x'' > 0 ΣFy = 0 α - 2,5x''^2 + 353,33 - 80 - 180 + 33,33 = 0 α = 2,5x''^2 - 116,67 x''=0 → α = -116,67 x''=6 → α = -26,67 ΣMz = 0 M + 2,5x''^2 * x''/3 - 353,33x'' + 90(x''+2) + 180(x''+3) - 33,33(x''+6) = 0 M = -2,5x''^3/3 + 116,67x'' - 520 x''=0 → M=-520 x''=6 → M=0 48 x (cm) -20 0 x1 = 5.0 x2 = 0.2 20.2 18.5 0 -507 -116.67 -26.67 232 x (m) M (kN/m) 48 x (cm) q (kN) 0 -5 5 10 M (kN/m) q = 5 kN 1 x 2 G A B C 10 kN 5 kN 5 kN G G A A C 1 x 2 x 2 M M = / 5 x x q = 5 kN q = 5 kN M = 5 x M = / 5 x 2