## Yps

Projection S 0.2L

U bars

Effective breadth of slab < 6Ds at edge columns

FIGURE 22.46 Moment transfer through reinforcement at perimeter columns: (a) connection details and (b) reinforcement detail.

frame a moment connection to the exterior column will increase the moments in the column, resulting in an increase of column size. Although the moment connections restrain the column from buckling by reducing the effective length, this is generally not adequate to offset the strength required to resist this moment.

### 22.4.7.3 Unbraced Composite Frames

For unbraced frame subjected to gravity and lateral loads, the beam typically bends in double curvature with negative moment at one end of the beam and positive moment on the other end. The concrete is assumed to be ineffective in tension; therefore, only the steel beam stiffness on the negative moment region and the composite stiffness on the positive moment region can be utilized for frame action. The frame analysis can be performed with variable moment of inertia for the beams (see Figure 22.47). Further research is still needed in order to provide tangible guidance for design.

If semirigid composite joints are used in unbraced frames, the flexibility of the connections will contribute to additional drift over that of a fully rigid frame. In general, semirigid connections do not require the column size to be increased significantly over an equivalent rigid frame. This is because the design of frames with semirigid composite joints takes advantage of the additional stiffness in the beams provided by the composite action. The increase in beam stiffness would partially offset the additional flexibility introduced by the semirigid connections.

The moment of inertia of the composite beam Icp maybe estimated using a weighted average of moment of inertia in the positive moment region (Ip) and negative moment regions (In). For interior spans, approximately 60% of the span is experiencing positive moment and it is suggested that (Leon 1990)

where Ip is the lower bound moment of inertia for positive moment and In is the lower bound moment of inertia for negative moment. However, if the connections at both ends of the beam are designed and detailed for simply supported, the beam will bend in single curvature under the action of gravity loads and Ip should be used throughout.

The story shear displacement A in an unbraced frame can be estimated using a modified expression from Equation 22.4 to account for the connection flexibility

where A; is the shear deflection of the i'th story, E is the modulus of elasticity, Ic is the moment of inertia for columns, Ig is the moment of inertial of a composite girder based on the weighted average method, hi is the height of the i'th story, Li is the length of girder in the i'th story, Vi is the total horizontal shear force

Is = Moment of inertia of steel section Ic=Moment of inertia of composite section

FIGURE 22.47 Composite unbraced frames: (a) story loads and idealization, (b) bending moment diagrams, and (c) composite beam stiffness.

Is = Moment of inertia of steel section Ic=Moment of inertia of composite section

FIGURE 22.47 Composite unbraced frames: (a) story loads and idealization, (b) bending moment diagrams, and (c) composite beam stiffness.

in the ¿th story, ^(IcJh) is the sum of the column stiffnesses in the ith story, ^(Ig/L) is the sum of the girder stiffnesses in the ¿th story, and Kcon is the sum of the connection rotational stiffness in the ¿th story.

Further research is required to assess the performance of various types of composite connections used in building construction. Issues related to accurate modeling of effective stiffness of composite members and joints in unbraced frames for the computation of second-order effects and drifts need to be addressed.

### 22.5 Wind Effects on Buildings 22.5.1 Introduction

With the development of lightweight high-strength materials, the recent trend is to build tall and slender buildings. The design of such buildings in nonseismic areas is often governed by the need to limit the wind-induced accelerations and drift to acceptable levels for human comfort and integrity of nonstructural components, respectively. Thus, to check for serviceability of tall buildings, the peak resultant horizontal acceleration and displacement due to the combination of along wind, across wind, and torsional loads are required. As an approximate estimation, the peak effects due to along wind, across wind, and torsional responses may be determined individually and then combined vectorally. A reduction factor of 0.8 may be used on the combined value to account for the fact that in general the individual peaks do not occur simultaneously. If the calculated combined effect is less than any of the individual effects, then the latter should be considered for the design.

The effects of acceleration on human comfort are given in Table 22.3. The factors affecting the human response are

1. Period of building — tolerence to acceleration tends to increase with period.

2. Women are more sensitive than men.

3. Children are more sensitive than adults.

4. Perception increases as you go from sitting on the floor, to sitting on a chair, to standing.

5. Perception threshold level decreases with prior knowledge that motion will occur.

6. Human body is more sensitive to fore-and-aft motion than to side-to-side motion.

7. Perception threshold is higher while walking than standing.

8. Visual cue — very sensitive to rotation of the building relative to fixed landmarks outside.

9. Acoustic cue — Building make sounds while swaying due to rubbing of contact surfaces. These sounds and sounds of the wind whistling focus the attention on building motion even before motion is perceived, and thus lower the perception threshold.

10. The resultant translational acceleration due to the combination of longitudinal, lateral, and torsional motions causes human discomfort. In addition, angular (torsional) motion appears to be more noticeable.

Since the tolerable acceleration levels increase with period of building, the recommended design standard for peak acceleration for 10 year wind in commercial and residential buildings is as depicted in Figure 22.48 (Griffis 1993). Lower acceleration levels are used for residential buildings for the following reasons:

1. Residential buildings are occupied for longer hours of the day and night and are therefore more likely to experience the design wind storm.

2. People are less sensitive to motion when they are occupied with their work than when they relax at home.

3. People are more tolerant of their work environment than of their home environment.

4. Occupancy turnover rates are higher in commercial buildings than in residential buildings.

5. People can be easily evacuated from commercial buildings than residential buildings in the event of a peak storm.

TABLE 22.3 Acceleration Limits for Different Perception Levels

Perception

Acceleration limits

Imperceptible a < 0.005g

Perceptible Annoying

0.005g < a < 0.015g 0.015g < a < 0.05g 0.05g < a < 0.15g

Very annoying Intolerable a > 0.15g

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