## 20625Seismic Capacity 206251 General

Strength and displacement capacities ofa ductile flexural element shall be evaluated by moment-curvature analysis based on the expected material properties and anticipated damages. The impact the second-order

P-A effect on the strength and displacement capacities of all members subjected to combined bending and compression shall be considered. Components may require redesign if the P-A effect is significant.

### 20.6.2.5.2 Displacement Capacity

The displacement capacity of a bridge system shall be evaluated by an inelastic static analysis (i.e., a static push over analysis). The rotational capacity of all plastic hinges shall be limited to a safe performance level. The plastic hinge regions shall be designed and detailed to perform with minimal strength degradation under cyclic loading.

The displacement capacity of a local member can be evaluated by its rotational capacity. The displacement capacity of a prismatic cantilever member (Figure 20.17) can be calculated as

Curvature

FIGURE 20.18 Idealized moment-curvature curve [35]. where

Curvature

FIGURE 20.18 Idealized moment-curvature curve [35]. where

L = distance from the point of maximum moment to the point of contraflexure

Lp = equivalent analytical plastic hinge length as defined in Section 20.8.2.6

Ap = idealized plastic displacement capacity due to rotation of the plastic hinge

AY°' = idealized yield displacement of the column at the formation of the plastic hinge f Y = idealized yield curvature defined by an elastic-perfectly plastic representation of the cross-section's M-f curve, see Figure 20.18 f p = idealized plastic curvature capacity (assumed constant over Lp)

f u = curvature capacity at the failure limit state, defined as the concrete strain reaching ecu or the main column reinforcing steel reaching the reduced ultimate strain eRu 0p = plastic rotation capacity of an equivalent plastic hinge

However, it should be pointed out that Equation 20.19 might overestimate the displacement capacity for a reinforced concrete column [47]. Column slenderness, high compression axial loads, and a low percentage of reinforcement all may contribute to the overestimating of the displacement capacity. Special attention, therefore, should be paid to the estimation of displacement capacity. It was recommended [47] that the P-A effect should be taken into account in calculating lateral load-carrying capacity and the displacement capacity, especially for medium-long and long columns. The lateral displacement capacity Ac can be chosen as the displacement that corresponds to the condition when lateral load carrying capacity degrades to a certain acceptable level, say a minimum of 80% of the peak resistance (Figure 20.19) or peak load [47-49].

20.6.2.5.3 Shear Capacity

Shear capacity of concrete members shall be calculated using nominal material properties as fVn = f(V + Vs) (20.24)

Concrete shear capacity is influenced by flexural and axial loads and is calculated separately for regions within the plastic hinge zone and regions outside this zone. In the plastic hinge zone, concrete shear capacity is modified based on the level of confinement and the displacement ductility demand (Figure 20.20).

FIGURE 20.20 Shear factors [35].

• Inside the plastic hinge zone vc = Factor 1 x Factor 2 x vf7 < 0.33^ (MPa) (20.27)

• Outside the plastic hinge zone vc = 0.25 x Factor 2 x vf < 0.33^ (MPa) (20.28)

Factor 1 = 0.025 < ^fj + 0.305 - 0.083md < 0.25 (20.29)

13.8 Ag

To ensure reliable capacity in the plastic hinge regions, all column lateral reinforcements are required to be butt welded or spliced hoops capable of resisting the ultimate capacity of the reinforcing steel.

• For confined circular or interlocking core sections:

For pier wall in weak direction p nAbfyhD '

where Ab is the area of an individual interlock spiral or hoop bar, Av is the total area of shear reinforcement perpendicular to flexural tension reinforcement, D. is the cross-section dimension of confined concrete core measured between the centerline of the peripheral hoop or spiral bars, fvh is the specified minimum yield strength of transverse reinforcement, d is the area of shear reinforcement perpendicular to flexural tension reinforcement, n is the number of individual interlock spirals or hoops core section, and s is the spacing of transverse reinforcement.

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