Civil Engineering Reference
In-Depth Information
It should be pointed out that a new sequence of equation numbers, 1 to 6 , has been
introduced. Each of these equation numbers is simply enclosed in a box without the chapter
designation. These fundamental equations will frequently be referred to, especially in the
example problems.
The solution of these six equilibrium and compatibility equations require five stress-strain
relationships of materials: one relating
σ
d
to
ε
d
for the concrete struts, two relating
f
to
ε
and
f
t
to
ε
t
for the mild steel in the longitudinal and transverse directions, and two relating
f
p
to
ε
p
and
f
tp
to
ε
tp
for the prestressed strands in the two directions.
Constitutive law of concrete in compression
Ascending branch
2
ε
d
ζε
o
2
ε
d
ζε
o
f
c
σ
d
=
ζ
−
ε
d
/ζ ε
o
≤
1
(5.100) or
7
a
Descending branch
1
2
(
ε
d
/ζ ε
o
)
−
1
f
c
σ
d
=
ζ
−
ε
d
/ζ ε
o
>
1
(5.101) or
7
b
(2
/ζ
)
−
1
0
.
9
ζ
=
√
1
(5.102) or
8
+
600
ε
r
Constitutive law of mild steel
f
=
E
s
ε
ε
<ε
y
(5.103) or
9
a
f
=
f
y
ε
≥
ε
y
(5.104) or
9
b
f
t
=
E
s
ε
t
ε
t
<ε
ty
(5.105) or
10
a
f
t
=
f
ty
ε
t
≥
ε
ty
(5.106) or
10
b
where
E
s
=
200 000 MPa (29 000 000 psi).
Constitutive law of prestressing steel
f
p
≤
0
.
7
f
pu
f
p
=
E
ps
(
ε
dec
+
ε
s
)
(5.107) or
11
a
12
a
E
ps
(
ε
dec
+
ε
s
)
f
p
>
0
.
7
f
pu
f
p
=
(5.108) or
11
b
12
b
1
m
E
ps
(
1
m
ε
dec
+
ε
s
)
f
pu
+
where
f
p
=
stress in prestressing steel -
f
p
becomes
f
p
or
f
tp
when applied to the longitudinal
and transverse steel, respectively;
ε
s
=
strain in the mild steel -
ε
s
becomes
ε
or
ε
t
, when applied to the longitudinal and
transverse steel, respectively;
