Environmental Engineering Reference
In-Depth Information
b) Action effects on the concrete
Strains:
e
x
;
cij
¼ e
xk
k
z
y
ij
¼ e
xk
k
z
r
i
cos
a
j
e
x
;
cmj
¼ e
xk
k
z
y
mj
¼ e
xk
k
z
r
m
cos
a
j
e
x
;
caj
¼ e
xk
k
z
y
aj
¼ e
xk
k
z
r
a
cos
a
j
a
j
¼
j
Da ¼
j
p=
n
j
¼
0
n
;
...
Material law for determining internal forces to DIN 1045-1 [33]:
k
h h
2
1
þ
k
2
s
c
f
c
¼
Min
:
0
ð
for details see section 3
:
2
:
1
Þ
;
ð
Þ h
This only takes into account the compressive stresses in the cross-section; tensile stresses in
the concrete are taken into account through the tension stiffening of the reinforcing steel
(
s
s,eff
).
Integration of the stresses over the thickness of the cross-section:
p
n
t
6
;
n
cj
¼
s
x
;
cij
r
i
þ
4
s
x
;
cmj
r
m
þ s
x
;
caj
r
a
j
¼
0
n
...
p
n
t
6
;
m
cj
¼
s
x
;
cij
r
i
y
ij
þ
4
s
x
;
cmj
r
m
y
mj
þ s
x
;
caj
r
a
y
aj
j
¼
0
n
...
c) Action effects on the reinforcement
Strains:
e
x
;
sij
¼ e
x0
k
z
y
ij
¼ e
x0
k
z
r
si
cos
a
j
e
x
;
saj
¼ e
x0
k
z
y
aj
¼ e
x0
k
z
r
sa
cos
a
j
a
j
¼
j
p=
n
Material law for determining internal forces to DIN 1045-1:
;
s
s
¼
Min
:
E
s
e
s
;
s
s
;
eff
;
f
y
f
y
¼
f
ym
=g
S
f
yk
ð
for details see section 3
:
2
:
2
Þ
Note: As the deformations no longer converge once the yield point (f
y
) has been exceeded,
strain hardening is not considered.
Integration of the stresses over the thickness of the cross-section:
n
sj
¼ s
x
;
sij
a
si
þ s
x
;
saj
a
sa
m
sj
¼ s
x
;
sij
a
si
y
sij
þ s
x
;
saj
a
sa
y
saj
¼
0
j
...
n
d) Action effects on the total cross-section
Summary of the “differential” action effects:
n
j
¼
n
cj
þ
n
sj
;
j
¼
0
...
n
m
j
¼
m
cj
þ
m
sj
;
j
¼
0
n
...