## 3

Further reduced tangent modulus method

E'

= 0.85E

5.4.8 Load Application

It is necessary, in an advanced analysis, to input proportional increment load (not the total loads) to trace nonlinear load-displacement behavior. The incremental loading process can be achieved by scaling down the combined factored loads by a number between 10 and 50. For a highly redundant structure (such as one greater than six stories), dividing by about 10 is recommended, and for a nearly statically determinate structure (such as a portal frame), the incremental load may be factored down by 50. One may choose a number between 10 and 50 to reflect the redundancy of a particular structure. Since a highly redundant structure has the potential to form many plastic hinges and the applied load increment is automatically reduced as new plastic hinges form, the larger incremental load (i.e., the smaller scaling number) may be used.

### 5.4.9 Analysis

Analysis is important in the proposed design procedures, since the advanced analysis method captures key behaviors including second-order and inelasticity in its analysis program. Advanced analysis does not require separate member capacity checks by the specification equations. On the other hand, the conventional LRFD method accounts for inelastic second-order effects in its design equations (not in analysis). The LRFD method requires tedious separate member capacity checks. Input data used for advanced analysis is easily accessible to users, and the input format is similar to the conventional linear elastic analysis. The format will be described in detail in Section 5.5. Analyses can be simply carried out by executing the program described in Section 5.5. This program continues to analyze with increased loads and stops when a structural system reaches its ultimate state.

### 5.4.10 Load-Carrying Capacity

Because consideration at moment redistribution may not always be desirable, two approaches (including and excluding inelastic moment redistribution) are presented. First, the load-carrying capacity, including the effect of inelastic moment redistribution, is obtained from the final loading step (limit state) given by the computer program. Second, the load-carrying capacity without the inelastic moment redistribution is obtained by extracting the force sustained when the first plastic hinge is formed. Generally, advanced analysis predicts the same member size as the LRFD method when moment redistribution is not considered. Further illustrations on these two choices will be presented in Section 5.6.

### 5.4.11 Serviceability Limits

The serviceability conditions specified by the LRFD consist of five limit states: (1) deflection, vibration, and drift; (2) thermal expansion and contraction; (3) connection slip; (4) camber; and (5) corrosion. The most common parameter affecting the design serviceability of steel frames is the deflections.

Item |
Deflection ratio |

Floor girder deflection for service live load |
L/360 |

Roof girder deflection |
L/240 |

Lateral drift for service wind load |
H/400 |

Interstory drift for service wind load |
H/300 |

Based on the studies by the Ad Hoc Committee [38] and Ellingwood [39], the deflection limits recommended (Table 5.6) were proposed for general use. At service load levels, no plastic hinges are permitted anywhere in the structure to avoid permanent deformation under service loads.

### 5.4.12 Ductility Requirements

Adequate inelastic rotation capacity is required for members in order to develop their full plastic moment capacity. The required rotation capacity may be achieved when members are adequately braced and their cross-sections are compact. The limitations of compact sections and lateral unbraced length in what follows lead to an inelastic rotation capacity of at least three and seven times the elastic rotation corresponding to the onset of the plastic moment for nonseismic and seismic regions, respectively.

Compact sections are capable of developing the full plastic moment capacity, Mp, and sustaining large hinge rotation before the onset of local buckling. The compact section in the LRFD Specification is defined as:

1. Flange

• For nonseismic region

For seismic region bf Es

where Es is the modulus of elasticity, bf is the width of flange, tf is the thickness of flange, and Fy is the yield stress.

• For nonseismic region h Esf 2.75Pu — < 3.76 J— 1 - —-u tw V FA f bPy for fbP

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