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
...
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