The plastic rotation is:
Lp = plastic hinge length
Φp = plastic curvature
Φm = maximum curvature
Φy = yield curvature
Alternatively, the maximum curvature, Φm may be calculated as:
εcm= maximum limiting compression strain for the prescribed performance level (Table 31F-7-5)
cu = neutral-axis depth, at ultimate strength of section
LIMITS OF STRAIN
|COMPONENT STRAIN||LEVEL 1||LEVEL 2|
|MCCS Pile/deck hinge||εc ≤ 0.004||εc ≤ 0.025|
|MCCS In-ground hinge||εc ≤ 0.004||εc ≤ 0.008|
|MRSTS Pile/deck hinge||εs ≤ 0.01||εs ≤ 0.05|
|MRSTS In-ground hinge||εs ≤ 0.01||εs ≤ 0.025|
|MPSTS In-ground hinge||εp ≤ 0.005 (incremental)||εp ≤ 0.025 (total strain)|
MCCS = Maximum Concrete Compression Strain, εc
MRSTS = Maximum Reinforcing Steel Tension Strain, εs
MPSTS = Maximum Prestressing Steel Tension Strain, εp
Either Method A or B may be used for idealization of the moment-curvature curve.
For Method A, the yield curvature, Φy is the curvature at the intersection of the secant stiffness, EIc, through first yield and the nominal strength, (εc = 0.004).
For Method B, the elastic portion of the idealized moment-curvature curve is the same as in Method A (see Section 3107F.22.214.171.124). However, the idealized plastic moment capacity, Mp, and the yield curvature, Φy, is obtained by balancing the areas between the actual and the idealized moment-curvature curves beyond the first yield point (see Figure 31F-7-5). Method B applies to moment-curvature curves that do not experience reduction in section moment capacity.