Tabela - deflexões

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Inclinações e deslocamentos de vigas simplesmente apoiadas 
VIGAS INCLINAÇÃO DEFLEXÃO CURVA DA LINHA ELÁSTICA 
1 
 
 
𝜃𝑚á𝑥 = −
𝑃𝐿2
16 𝐸𝐼
 
 
𝜐𝑚á𝑥 = −
𝑃𝐿3
48 𝐸𝐼
 
 
𝜐 = −
𝑃𝑥
48 𝐸𝐼
(3𝐿2 − 4𝑥2) 
0 ≤ 𝑥 ≤
𝐿
2
 
2 
 
𝜃1 = −
𝑃𝑎𝑏(𝐿 + 𝑏)
𝐿 6 𝐸𝐼
 
𝜃2 =
𝑃𝑎𝑏(𝐿 + 𝑎)
𝐿 6 𝐸𝐼
 
 
𝜐𝑚á𝑥 = −
𝑃𝑏𝑎
𝐿 6 𝐸𝐼
(𝐿2 − 𝑏2 − 𝑎2) 
𝑥 = 𝑎 
 
𝜐 = −
𝑃𝑏𝑥
𝐿 6 𝐸𝐼
(𝐿2 − 𝑏2 − 𝑥2) 
0 ≤ 𝑥 ≤ 𝑎 
3 
 
𝜃1 = −
𝑀0𝐿
3 𝐸𝐼
 
𝜃2 =
𝑀0𝐿
6 𝐸𝐼
 
 
𝜐𝑚á𝑥 = −
𝑀0𝐿
2
𝐸𝐼 √243
 
 
𝜐 = −
𝑀0𝑥
𝐿 6 𝐸𝐼
(𝑥2 − 3𝐿𝑥 + 2𝐿2) 
4 
𝜃𝑚á𝑥 = −
𝑤𝐿3
24 𝐸𝐼
 
 
𝜐𝑚á𝑥 = −
5𝑤𝐿4
384 𝐸𝐼
 
 
𝜐 = −
𝑤𝑥
24 𝐸𝐼
(𝑥3 − 2𝐿𝑥2 + 𝐿3) 
5 
𝜃1 = −
3𝑤𝐿3
128 𝐸𝐼
 
𝜃2 =
7𝑤𝐿3
384 𝐸𝐼
 
 
𝜐 = −
5𝑤𝐿4
768 𝐸𝐼
 𝑥 =
𝐿
2
 
𝜐𝑚á𝑥 = −0,006563
𝑤𝐿4
𝐸𝐼
 
em 𝑥 = 0,4598 𝐿 
 
𝜐 = −
𝑤𝑥
384 𝐸𝐼
(16𝑥3 − 24𝐿𝑥2 + 9𝐿3) 
0 ≤ 𝑥 ≤
𝐿
2
 
𝜐 = −
𝑤𝐿
384 𝐸𝐼
(8𝑥3 − 24𝐿𝑥2 + 17𝐿2𝑥 − 𝐿3) 
𝐿
2
≤ 𝑥 ≤ 𝐿 
6 
 
𝜃1 = −
7𝑤0𝐿
3
360 𝐸𝐼
 
𝜃2 =
𝑤0𝐿
3
45 𝐸𝐼
 
 
𝜐𝑚á𝑥 = −0,00652
𝑤0𝐿
4
𝐸𝐼
 
em 𝑥 = 0,5193 𝐿 
 
𝜐 = −
𝑤0𝑥
𝐿 360 𝐸𝐼
(3𝑥4 − 10𝐿2𝑥2 + 7𝐿4) 
 
Inclinações e deflexões de vigas em balanço 
VIGAS INCLINAÇÃO DEFLEXÃO CURVA DA LINHA ELÁSTICA 
7 
𝜃𝑚á𝑥 = −
𝑃𝐿2
2 𝐸𝐼
 
 
𝜐𝑚á𝑥 = −
𝑃𝐿3
3 𝐸𝐼
 
 
𝜐 = −
𝑃𝑥2
6 𝐸𝐼
(3𝐿 − 𝑥) 
8 
𝜃𝑚á𝑥 = −
𝑃𝐿2
8 𝐸𝐼
 
 
𝜐𝑚á𝑥 = −
5𝑃𝐿3
48 𝐸𝐼
 
 
𝜐 = −
𝑃𝑥2
6 𝐸𝐼
(
3𝐿
2
− 𝑥) 0 ≤ 𝑥 ≤
𝐿
2
 
𝜐 = −
𝑃𝐿2
24 𝐸𝐼
(3𝑥 −
𝐿
2
) 
𝐿
2
 ≤ 𝑥 ≤ 𝐿 
9 
𝜃𝑚á𝑥 = −
𝑤𝐿3
6 𝐸𝐼
 
 
𝜐𝑚á𝑥 = −
𝑤𝐿4
8 𝐸𝐼
 
 
𝜐 = −
𝑤𝑥2
24 𝐸𝐼
(𝑥2 − 4𝐿𝑥 + 6𝐿2) 
10 
𝜃𝑚á𝑥 =
𝑀0𝐿
𝐸𝐼
 
 
𝜐𝑚á𝑥 =
𝑀0𝐿
2
2 𝐸𝐼
 
 
𝜐 =
𝑀0𝑥
2
2 𝐸𝐼
 
11 
𝜃𝑚á𝑥 = −
𝑤𝐿3
48 𝐸𝐼
 
 
𝜐𝑚á𝑥 = −
7𝑤𝐿4
384 𝐸𝐼
 
 
𝜐 = −
𝑤𝑥2
24 𝐸𝐼
(𝑥2 − 2𝐿𝑥 +
3𝐿2
2
) 0 ≤ 𝑥 ≤
𝐿
2
 
𝜐 = −
𝑤𝐿3
192 𝐸𝐼
(4𝑥 −
𝐿
2
) 
𝐿
2
≤ 𝑥 ≤ 𝐿 
12 
𝜃𝑚á𝑥 = −
𝑤0𝐿
3
24 𝐸𝐼
 
 
𝜐𝑚á𝑥 = −
𝑤0𝐿
4
30 𝐸𝐼
 
 
𝜐 −
𝑤0𝑥
2
𝐿 120 𝐸𝐼
(10𝐿3 − 10𝐿2𝑥 + 5𝐿𝑥2 − 𝑥3)