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Estruturas de Concreto FORMULÁRIO
βx,lim =
{
0, 450 fck ≤ 50 MPa
0, 350 fck > 50 MPa ζc =
0, 8 fck ≤ 50 MPa
0, 8− fck − 50
400
fck > 50 MPa
W0 =
Aw
3c
(
h2 + 3c2
)
+
Aa
3c
(
h2
f + 3c′2
)
T
Aw = bwh
Aa = (bf − bw)hf
AT = Aw +Aa
c =
Awh
2AT
+
Aa
2AT
(2h− hf )
c′ = h− c
W0 =
bwh
2
6
retangulares
Msd,min = 0, 8W0fctk,sup
fctk,sup =
{
0, 39 3
√
f2
ck fck ≤ 50 MPa
2, 756 ln(1 + 0, 11fck) fck > 50 MPa
ηc = αc
ηc = 0, 9αc
αc =
0, 85 fck ≤ 50 MPa
0, 85
[
1, 0− fck − 50
200
]
fck > 50 MPa
βx =
1
ζc
− 1
ζc
√
1− 2Mrdw
ηcbwd2fcd
βz =
z
d
= 1− 0, 5βy βy = ζcβx
βs =
Es
fyd
(
1− βx
βx
)
εcu ≤ 1, 0
β′
s =
Es
fyd
βx − d′
d
βx
 εcu ≤ 1, 0
βc = ηcζcβxβz =
Mrdw
bwd2fcd
Mrd,lim =
0, 251bwd
2fcd fck ≤ 50 MPa
ζcbwd
2 (0, 298− 0, 052ζc)
[
1, 0− fck − 50
200
]
fcd fck > 50 MPa
As =
[
Mrdw
βzd
+
M ′
rd
(d− d′)
]
1
βsfyd
A′
s =
M ′
rd
(d− d′)β′
sfyd
M ′
rd = Msd −Mrd,lim
nϕℓ
=
⌈
4As
πϕ2
ℓ
⌉
n′
ϕ′
ℓ
=
⌈
4A′
s
πϕ′2
ℓ
⌉
nϕℓ
≤
⌊
bw − 2cnom − 2ϕt + ah
ϕℓ + ah
⌋
n′
ϕ′
ℓ
≤
⌊
bw − 2cnom − 2ϕ′
t + ah
ϕ′
ℓ + ah
⌋
ρmin =
As
Ac
≥ 0, 15%
βx =
fyd
ηcζcbwdfcd
(
As,efβs −A′
s,efβ
′
s
)
ρmax =
As,ef +A′
s,ef
Ac
≤ 4%
Se ρmin 50 MPa
w
R1 R2
M2
L
A
x
AE1-w
MA =
wx (3L − 4x)
8
VA =
w (3L − 8x)
8
R1 =
3Lw
8
R2 =
5Lw
8
M2 = −
L2w
8
F
R1 R2
M2
a
L
A
x
B
AE8-fa
MA =
Fx
(
2L3 − 3L2a + a3
)
2L3
MB =
Fa
(
2L3 − 3L2x + a2x
)
2L3
VA = F −
3Fa
2L
+
Fa3
2L3
VB =
Fa
(
−3L2 + a2
)
2L3
R1 = F −
3Fa
2L
+
Fa3
2L3
R2 =
Fa
(
3L2 − a2
)
2L3
M2 =
Fa
(
−L2 + a2
)
2L2
AE10-m
M
R1 R2
M2
a
L
A
x
B
MA =
3Mx
(
−L2 + a2
)
2L3
MB = M −
3Mx
2L
+
3Ma2x
2L3
VA =
3M
(
−L2 + a2
)
2L3
VB =
3M
(
−L2 + a2
)
2L3
R1 =
3M
(
−L2 + a2
)
2L3
R2 =
3M
(
L2 − a2
)
2L3
M2 =
M
(
−L2 + 3a2
)
2L2
w w
R1 R2
a
L
A
x
B
VB1-w
MA =
wx
(
−L2 + 2La − ax
)
2a
MB =
w
(
−L2 + 2Lx − x2
)
2
VA = −
L2w
2a
+ Lw − wx
VB = w (L − x)
R1 =
Lw (−L + 2a)
2a
R2 =
L2w
2a
Combinações 1