## 067 032

Notes:

1. bf and tf are the width and thickness of an I-shaped section and hc is the depth of that section and iw is the thickness of its web.

TABLE 20.11 Recommended LRFD Guidelines — Limiting Slenderness Ratio [37]

Description of members

Limiting slenderness ratio Kl/r

Limiting length, L (m)

Unsupported distance for potential plastic hinge zone of columns Ductile compression bracing members

Nominally ductile bracing members

2600 TFy

VFy members designed as tension-only bracing

17250ry y y

### 20.8.1.4.2 Limiting Slenderness Ratio

In SDRs 2 to 6, Table 20.11 summarizes the limiting slenderness ratio (KL/r) for various steel members. Recent studies found that more stringent requirement for slenderness ratios may be unnecessary, provided that connections are capable of conveying at least the member's tension capacity. The ratios shown in Table 20.11 reflect those relaxed limits.

20.8.1.4.3 Limiting Axial Load Ratio

High axial load in a column usually results in the early deterioration of strength and ductility.

The ratio of factored axial compression due to seismic load and permanent loads to yield strength (AgEy) for columns in ductile MRFs and single-column structures shall not exceed 0.4 for SDR 2 and SDRs 3 to 6, respectively.

### 20.8.1.4.4 Plastic Rotation Capacities

In SDRs 3 to 6, the plastic rotational capacity shall be based on the appropriate performance level and may be determined from tests and a rational analysis. The maximum plastic rotational capacity 0p should be conservatively limited to 0.035, 0.005, and 0.01 radians for life safety, operational performance, and in ground hinges and piles, respectively.

20.8.1.5 Concrete Design Requirements 20.8.1.5.1 Limiting Longitudinal Reinforcement Ratios

The ratio of longitudinal reinforcement to the gross cross-section shall not be less than 0.008 and not more than 0.04.

### 20.8.1.5.2 Shear Reinforcement

The shear strength shall be determined by either an implicit approach or an explicit approach. In the end regions, the explicit approach assumes that the shear-resisting mechanism is provided by the strut-tie model (explicit approach) such that fVs > Vu -(Vp + Vc) (20.44)

[0.05a [f[ bw d for plastic hinge zone Vc = i y ffi (20.46)

0.17yf0bwd for outside plastic hinge zone

——fhD' cot y for circular section Vs ={ A s (20.47)

—fyhD" cot y for rectangular section where

Pe = compressive axial force including seismic effects

D' = pitch circle diameter of the longitudinal reinforcement in a circular column, or the distance between the outermost layers of bars in a rectangular column L = column length

A = fixity factor defined in Section 20.6.1.5 bw = web width of the section d = effective depth of the section Abh = area of one circular hoop/spiral rebar

Ash = total area of transverse reinforcement in one layer in the direction of the shear force D'' = centerline section diameter/width of the perimeter spiral/hoops 0 = principal crack angle defined in Section 20.6.1.5

Spiral reinforcement

Spiral reinforcement

FIGURE 20.23 Column single spiral details [37].

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