End-Plate Strength Predictions

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To design moment end-plate connections for this study, four components of the connection were considered: the beam, the end-plate, the bolts, and the column. First a beam section was chosen with an appropriate flexural strength. Once the flexural strength of the beam was determined, the end-plate was designed for the required strength using yield-line theory. After determining the thickness of the end-plate, the bolt sizes were chosen using bolt force equations derived from the modified Kennedy split-tee model. Finally, the column was checked for strength using guidelines presented by AISC (Manual 1994).
In this chapter, yield-line theory is presented in general terms, followed by its direct application to the four bolt extended stiffened end-plate, the multi-row 1/3 extended end-plate, and the four bolt extended unstiffened end-plate. The method for calculating bolt forces using the “Split-Tee Analogy” of Kennedy et al. (1981) is then presented, followed by its direct application to the same end-plate configurations. The flexural strength prediction of the beam is beyond the scope of this research, and is therefore not presented. The column flanges were detailed such that the strength was greater than that of the connected end-plate.


General Yield-Line Theory

Yield-line theory was first introduced to analyze reinforced concrete slabs, and has more recently been adopted for use in the strength analysis and design of moment end-plates. A yield-line is a continuous formation of plastic hinges along a straight or curved line. An end-plate is assumed to reach failure when the yield-lines form a kinematically valid collapse mechanism. The elastic deformations of an end-plate are assumed to be negligible in comparison to its plastic deformations. Therefore the yield-line development is assumed to divide the end-plate into plane regions.
Derivations of both curved and straight yield lines have been introduced. However, straight yield-lines have been shown to be more accurate for the end-plates tested in this research. To establish the locations of the straight yield lines, the following guidelines must be followed:

  1. Axes of rotation generally lie along lines of support.
  2. Yield lines pass through the intersection of the axes of rotation of adjacent plate segments.
  3. Along every yield line , the bending moment is assumed to be constant and is as the plastic moment of the plate.

The analysis of a yield-line mechanism can be performed by either the equilibrium method or the virtual work method. The virtual work method is simpler than the equilibrium method, and is therefore preferred. In the virtual work method, the end-plate is assumed to rotate about the center of the compression flange of the beam section. Small angle rotation is assumed. The external work, done by rotating the plate through a small arbitrary rotation, is set equal to the internal work, done at the plastic hinges formed over the yield lines, which accommodates the total rotation of the plate. For a specified yield-line pattern and loading, a certain plastic moment will be required along the hinge lines. For the same loading, other patterns may result in a larger required plastic moment capacity. Hence, the controlling pattern is the one which requires the largest required plastic moment. Or conversely, for a given plastic moment capacity, the controlling mechanism is the one which produces the lowest failure load. This implies that the yield-line theory is an upper bound procedure and the least upper bound solution must be found.
To determine an end-plate plastic moment capacity, or failure load, yield line mechanisms are arbitrarily chosen in accordance with the three guidelines presented above. Next, the external work of a unit rotation of the end-plate is found and set equal to the internal work of the relative rotation of the plane sections divided by yield lines. This equation can either be solved for the unknown load acting through the unit rotation or the resisting moment of the end-plate. The results of this procedure for reasonable yield-line mechanisms are compared. The controlling yield line mechanism is that which corresponds to the greatest plastic moment capacity or the smallest failure load.
The following formulation of yield-line analysis is taken from Hendrick et al. (1985). The internal energy stored in a particular yield-line mechanism is the sum of the internal energy stored in each yield line forming the mechanism. The internal energy stored in any given yield line is obtained by multiplying the normal moment on the yield line with the normal rotation of the yield line.Thus the energy stored, Win  , in the nth yield line of length Ln is:
Win  = ò Lnm pq n ds
where qn  is the relative rotation of line n and ds is the elemental length of line n.

Four Bolt Extended Stiffened Moment End-Plates

The yield-line analysis presented here for the four bolt extended stiffened moment end-plates is taken from a study done by Srouji (1983).
One of two yield-line patterns can control the strength of the four bolt extended stiffened moment connection depending on the distance which the end-plate extends beyond the outside bolt line, de, and the dimension s. The two mechanisms are shown in Figure 2.1. The first mechanism, in which a hinge forms near the outside edge of the end-plate, is shown as Case 1. The second mechanism, in which a hinge does not form near the outside edge of the end plate, is shown as Case 2. The dimension, s, is found by differentiating the internal work expression with respect to s and equating it to zero.

1.1 Introduction
1.2 Rotational Requirements for Moment Connections
1.3 Literature Review
1.4 Objective and Scope of Research
2.1 Overview
2.2 End-Plate Strength Predictions
2.3 Prediction of Bolt Forces Including Prying Forces
3.1 Extended End-Plate Testing Program
3.2 Testing Frames
3.3 Instrumentation
3.4 Loading Protocol
3.5 End Plate Tensile Coupon Testing
3.6 Preliminary Analysis of Strength Results
4.1 Overview
4.2 Finite Element Model
4.3 Comparison of FEM to Experimental Bolt Strain Results
4.4 Adjustment of Experimental Results Using Finite Element Model
5.1 Introduction
5.2 Four Bolt Extended Stiffened Moment End-Plate Connections
5.3 Multiple Row 1/3 Extended Moment End-Plate Connections
5.4 Four Bolt Extended Unstiffened Moment End-Plate Connection.
5.5 Seismic Frame Classification
6.1 Summary
6.2 Conclusions.
Evaluation of Extended End-Plate Moment Connections Under Seismic Loading

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