Environmental Engineering Reference
In-Depth Information
Fig. 3.6 Bending moment-curvature relationship (rectangular reinforced concrete cross-section) to
DIN 1045-1 [33] 8.5.2
From this it follows that a bending moment-curvature relationship for a rectangular
cross-section is approximately trilinear (see Figure 3.6).
In order to be able to use this relationship in the calculations, it is sufficient to
determine the positions of the kinks, that is the transition from the uncracked (I) to
the cracked (II) state, the onset of yield in the flexural tension reinforcement and the
failure condition.
Furthermore, the quantitative progression of the bending moment-curvature curve
(M-
k
curve) depends on the magnitude of the axial force N
Ed
. A change in N
Ed
therefore changes the shape of the M-
k
curve (see Section 3.3.3).
3.3.2 Prestressed concrete cross-sections in general
The character of the bending moment-curvature relationship is different for prestressed
concrete cross-sections. One difference is that the prestressing acts like an external
compressive force. This force generally acts eccentrically in the case of beams
(see Figure 3.7), but concentrically in towers (see Figure 3.9). The cracking moment
(M
I,II
) therefore increases, in the case of eccentric prestressing also helped by the
precambering (
k
0
ΒΌ
(1/r)
0
).
