878570_Tabelas

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A
B
P
a
yB
θBL
x
−Pa
A
B
M
a
yB
θBL
x
−M
A
B
a
yB
θBL
x
w
−
wa2
2
w
2M = (2ax − a2 − x2)
for 0 ≤ x ≤ a
A
B
a
yB
θBL
x
−
wa2
6
M = −
w
w
6a (a − x)3
for 0 ≤ x ≤ a
A B
P
L
2
L
2
ymax
θA θB
x
PL
4
A B
P
ymax
θA θB
Pab
L
a b
L
x
A B
ymaxθA θB
L
x
M
M
A B
ymax
θA θB
L
x
w
M = wx6L
L
3
wL2
9 3(L2 − x2)
A BθA θB
L
x
w
a
a
x
L(1 − )M = wa22
 a ≤ x ≤ L
(2L − a −
0 ≤ x ≤ a
M = wax2L )Lxa
A B
ymax
θA θB
wL2
8
L
x
w
M = wx2 (L − x)
A B
θA
θB
a
L
x
M
Ma
L
M(1 − )aL
FIXED-END MOMENTS
P
L
2
L
PL
8
PL
8
P
L
a b
Pa b 2
L2
Pa 2b
L2
L
a b
M
Mb
L2 
(b − 2a) Ma
L2 
(2b − a)
L
w
wL2
12
wL2
12
L
w
a
wa3
12 L2
wa2
12 L2 
(6L2 − 8aL + 3a2) (4L − 3a)
L
w
wL2
20
wL2
30
L
w
L
2
5wL2
96
5wL2
96
L
6EI
L2
ΔΔ
6EI
L2
Δ
L
θ4EI
L
θ 2EI
L
θ