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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 6
T. F. SILVA | J. C. DELLA BELLA
concreto em estruturas laminares submetidas a
solicitações de chapa e placa. In: Simpósio EPUSP
sobre estruturas de concreto, 4, São Paulo, 2000.
Anais. São Paulo, 2000.
[16] GUPTA, AJAYA K. Membrane reinforcement in shells:
a review. Nuclear Engineering and Design, v.82,
January,1984. p. 63-75.
[17] PEREIRA, F.A.C. Dimensionamento de estruturas de
betão sujeitas a esforços de membrana associados
com esforços de flexão de acordo com o Eurocódigo
2 – Faculdade de Engenharia da Universidade do
Porto, Porto, 2010
[18] SILVA, T.F. Contribuição das armaduras de
compressão em chapas de concreto armado. 2012.
115 p. Dissertação (Mestrado) – Escola Politécnica
da Universidade de São Paulo, São Paulo, 2012.
10. Symbols
a
sx
reinforcement area in x-direction
a
sy
reinforcement area in the y-direction
E
CS
modulus of elasticity of concrete
f
c’
characteristic compressive strength of concrete according
to ACI
f
c2
principal compressive concrete stress in concrete
f
cd
design compressive strength of concrete
f
ck
characteristic compressive strength of concrete
f
cd1
design compressive strength of uncracked concrete
f
cd2
design compressive strength of cracked concrete
f
c2max
maximum compressive strength of concrete
f
yd
design yield stress of reinforcement
f
yk
characteristic yield stress of reinforcement
h
thickness of membrane
n
c
maximum compressive force in concrete
n
’c
minimum compressive force in concrete
n
x
normal force in the x-direction
n
y
normal force in the y-direction
n
xy
shear force in membrane
n
sx
reinforcement force in the x-direction
n
sy
reinforcement force in the y-direction
ε
1
strain in direction 1
ε
2
strain in direction 2
ε
x
strain in direction x
ε
y
strain in direction y
ε
sx
reinforcement strain in the x-direction
ε
sy
reinforcement strain in the y-direction
ε
c
maximum compressive strain in concrete
ε
c’
minimum compressive strain in concrete
ε
yd
design yield strain of reinforcement
θ
angle between y-axis and direction of principal compression
in concrete
θ
1
limit angle between curves fcd1 and fc2max
θ
2
limit angle between curves fc2max e fcd2
θ*
limit angle that define εy sign
θ
max
limit angle to design of compression reinforcement in case II
and III
θ
xy
angle that corresponds to maximum shear stress
θ
c1
limit angle to membrane remains in biaxial compressive
state in case IV
θ
c2
limit angle to membrane remains in biaxial compressive
state in case IV
θ
x
limit angle to reinforcement force in y-direction to be of com-
pression in case IV
θ
y
limit angle to reinforcement force in y-direction to be of com-
pression in case IV
σ
c
maximum compressive stress
σ
c’
minimum compressive stress
σ
cd
design compressive stress