Structural Concrete - Hassoun

590 Chapter 16 Continuous Beams and Frames
3. The depth of the compressive block c in concrete at failure at the section of the plastic hinge.
Baker [7] estimated the angle of rotation, θ, of a tensile plastic hinge as follows:
θ = ε pI p
(16.17)
c
where ε p is the increase in the strain in the concrete measured from the initial yielding of steel
reinforcement in the section (see Fig. 16.29c):
If l p = d and the ratio c/d equals λ ≤ 0.5,
ε p = ε ′ c − ε c1
= 0.0035 − ε c1
θ = (0.0035 − ε c 1
)d
= 0.0035 − ε c 1
λd
λ
From strain triangles (Fig. 16.29),
( ) c
ε c1
= ε y = f ( )
y λd
= f ( )
y λ
d − c E s d − λd E s 1 − λ
Figure 16.29 Plastic hinge and typical stress and strain distribution [2].