Connections in steel structures III : behaviour, strength, and design : proceedings of the third international workshop held at Hotel Villa Madruzzo, Trento, Italy, 29-31 May 1995

This book publishes the proceedings from the Third International Workshop on Connections in Steel Structures: Behaviour, Strength and Design held in Trento, Italy, 29-31 May 1995. The workshop brought together the world's foremost experts in steel connections research, development, fabrication and design. The scope of the papers reflects state-of-the-art issues in all areas of endeavour, and manages to bring together the needs of researchers as well as designers and fabricators. Topics of particular importance include connections for composite (steel-concrete) structures, evaluation methods and reliability issues for semi-rigid connections and frames, and the impact of extreme loading events such as those imposed by major earthquakes. The book highlights novel methods and applications in the field and ensures that designers and other members of the construction industry gain access to the new results and procedures. Read more...

Chapter One

FINITE ELEMENT MODELING OF PARTIALLY RESTRAINED BEAM-TO-GIRDER CONNECTIONS

Clinton O. Rex

W. Samuel Easterling

Abstract

In recent years the design of steel framed composite floor systems has been controlled more often by serviceability criteria than by strength. It has been suggested that a partially continuous composite floor system would improve serviceability limit states; and that, partially restrained beam-to-girder connections are the key to such a floor system (Rex and Easterling 1994). A research project aimed at developing design methods and criteria for partially restrained beam-to-girder connections and partially continuous floor systems is currently in progress at Virginia Polytechnic Institute and State University (VPI). This paper focuses on a finite element modeling technique that is being used to predict the moment-rotation behavior of various beam-to-girder connections. This method relies heavily on the behavior models of various connection sub-elements (bolts, welds, etc ...). These connection sub-element models are also discussed.

1. INTRODUCTION

In many cases concrete floor systems are chosen over steel framed composite floor systems in design situations where the overall floor depth is limited. Shallow concrete floor systems can be designed to meet both strength and serviceability design criteria while still remaining economical. Shallow steel framed composite floor systems can meet strength design criteria and remain economical thanks to advancements in composite beam design and the availability of low cost high strength steel. However, in many cases these systems are unable to meet serviceability design criteria while still remaining economical.

One possible method to improve both the strength and serviceability design aspects of a steel framed composite floor system is to design the system as partially continuous. The key to designing a partially continuous floor system lies in the design and analysis of the beam-togirder connections. A research project investigating the design and analysis of partially restrained steel and composite beam-to-girder connections is currently in progress at Virginia Polytechnic and State University (VPI).

To date, four full scale composite beam-to-girder connections have been constructed and tested to failure (Rex and Easterling 1994). These four connections are shown schematically in Fig. 1. Connection #1 is a standard single plate shear connection which is commonly used in the United States. To enhance the moment resistance of beam-to-girder connections, both before and after concrete hardens, it was believed that the details of the connections would have to be changed from typical, currently used, details. Connections #2 through #4 represent varying degrees of departure from the typical connections. The results of the tests showed that these simple connections could develop significant rotational restraint and thus justified additional development.

An analytical technique to model the moment-rotation behavior of the connections is needed to develop design methods and recommendations for partially restrained beam-to-girder connections. Currently, non-linear finite element analysis is being used.

2. FINITE ELEMENT MODELING

Finite element analysis is currently being used to model the partially restrained beam-to-girder connections. Certain simplifications have been adopted so that the finite element models do not become excessively complex. First, the three dimensional connection behavior is reduced to a two dimensional problem by ignoring out-of-plane effects. This is a common assumption made in most research involving connections. Second, the two dimensional problem is then further simplified by using only one dimensional finite elements placed in two dimensional space. The elements used are beam, truss, and non-linear spring elements. Beam elements are used to represent the beam and rigid links. Truss elements are used to represent reinforcing steel, concrete, and steel plates. Non-linear springs are used to represent shear studs, bolts, and welds. Schematics of the finite element models of Connections #1 through #4 are shown in Fig. 2.

Clearly these models have many assumptions and simplifications incorporated into them. Aside from ignoring out of plane effects (such as shear lag in the slab and instabilities in the steel) many in plane effects have been ignored as well. First, the flexural contribution of the concrete slab to the overall rotational resistance of the connection is considered negligible. Second, it is assumed that the composite deck remains in contact with the top flange of the beam at all times (i.e. no slab uplift). Third, shear deformations of the beam are ignored and the beam is assumed to remain elastic. Finally, the vertical shear strength of the connection is assumed sufficient to ensure that a shear strength failure at the connection does not occur and that vertical shear deformation at the connection is small. These assumptions are justified as follows.

• Ignoring shear lag in composite slab: The results of the tests so far showed that within a 60-in. design strip that shear lag was not significant.

• Ignoring instabilities in the steel: Connection #1 failed as a result of distortional buckling of the section; but, subsequent connections and connections that are currently being developed all have some restraint on the bottom flange (such as a seat angle) and buckling of this type has been eliminated. Connection #4 ultimately failed in web crippling. Connections similar to Connection #4 are no longer being considered. In general, proper connection design details will ensure that instabilities do not occur.

• Ignoring flexural contribution of slab: The center of rotation for the connections tested to date was near or below the centerline of the bare steel beam. This places the reinforced composite slab in almost pure tension. As a result, the axial stiffness of the slab is far more dominant than the flexural stiffness of the slab when considering the overall connection behavior.

• Neglecting slab uplift: Because the composite slab is attached to the steel beam with welded headed shear studs the slab cannot separate from the beam without first failing one of the shear studs. This will typically only occur after significant rotational deformations have occurred and the connection is near failure. The ability to predict the behavior of the connection beyond failure is not of current interest.

• Ignoring shear deformations of beam: The beams in partially continuous composite floor systems are going to be long and shallow. This is a situation in which shear deformations are known to have little effect.

• Assuming beam remains elastic: Currently it is believed that the beam-to-girder connection will be detailed such that the connection moment capacity will be less than the elastic moment capacity of the beam.

• Assuming connection has sufficient shear strength: Proper design guidelines will ensure that a shear strength failure does not occur prior to a moment strength failure in the connection. • Assuming vertical deformation at the connection is negligible: Proper design of the connection to ensure proper shear strength should also ensure relatively small vertical deformations.

Despite the fact that the connections tested to date violated some of the above assumptions, analytical and experimental results generally compared very favorably, as indicated in Fig. 3, with three notable exceptions.

First, the analytical stiffness for the non-composite connection behavior of Connection #1 is not as stiff as that measured during testing. The authors are currently not sure of the reason for this deviation. Possible reasons include bad load measurement for this stage of the connection loading and stiffening effects of materials not accounted for in the model such as pour stops, steel decking and reinforcing steel in the wet concrete. Because later steel connections were much stiffer than Connection #1 these stiffening effects were probably less noticeable. This is more fully discussed by Rex (1994). Second, the model response was much stiffer than the measured response in the latter stages of the test on Connection #1. This is because Connection #1 failed as a result of distortional buckling of the section. Once the buckling began the connection response softened. Because nothing in the model currently represents such a response it would be expected that the two behaviors would diverge at this point. The third notable difference is the non-composite connection behavior of Connection #4. The model behavior was much stiffer than the measured behavior. It is currently believed that some of this difference may be a result of the method used to measure the experimental rotations. It is believed the accuracy of measurement was insufficient to measure the very small rotations associated with this rather stiff steel connection.

The reader should note that both the data and the models have two stages of behavior. These represent the two stages of connection loading associated with construction loads (loading imposed before the composite slab hardens) and subsequent imposed loading (loading that occurs after the composite slab has hardened). The ability to design and analyze the connection for both stages of behavior is very important.

Another important assumption in the finite element modeling is that we have the ability to predict the behavior of the fundamental elements of the connection (bolts, welds, etc...). These fundamental elements are referred to as "sub-elements". The term "elements" has been reserved for connection parts that are combinations of the sub-elements such as a seat angle connection and a reinforced composite slab. Clearly the ability to predict the behavior of the connection as a whole is directly linked to the ability to predict the behavior of the connection sub-elements. So the question arises, how well can we predict the behavior of the various connection sub-elements?

3. SUB-ELEMENT MODELS

Connection sub-elements are essentially the materials and fasteners used in any non-composite or composite connection. This section summarizes current models used to predict the behavior of sub-elements and points out where some of these may need additional consideration before being used in general modeling of partially restrained beam-to-girder connections. Schematics of the load-deformation behavior and the stress-strain behavior incorporated into the finite element models are presented in Fig. 4.

Usually, the ability to predict the strength of a connection sub-element is the first problem to solve. Then, based on the predicted strength, a method to predict the load-deformation or stress-strain behavior is developed. For brevity, the focus of the following paragraphs is on methods of predicting the load-deformation or stress-strain behavior of the connection subelements.

3.1 Bolts

The 1994 Load and Resistance Factor Design (LRFD) Manual (Manual of 1994) uses the following equation to predict the load-deformation behavior of high strength bolts.

R = Rult(1 - e-μΔ)λ Eq(1)

Where:

Δ = Total deformation of fastener and bearing deformation of the connected material (in.)

μ = 10

λ = 0.55

Rult = Ultimate shear strength of a single fastener

e = Base of natural logarithm

The form of the equation was originally developed by Fisher (1965), while the values of the coefficients were determined by Crawford and Kulak (1971) based on six single bolt shear tests. The bolts in these shear tests were fully tensioned A325 3/4-in. bolts placed in double shear and the test specimen was loaded in compression.

Despite the fact that the coefficients of Eq 1 are based on only six tests, the equation is used to predict the bolt load-deformation behavior in the eccentrically loaded connection design aids in the LRFD Manual (Manual of 1994). This is done without regard to bolt diameter, whether the bolt is in single or double shear, whether the elements being bolted together are in compression or tension, whether the failure mode of the bolt is shear of the bolt or bearing tearout of the plate, and other parameters that could be associated with this type of element.

To better determine the load-to-deformation behavior of bolted plates in single shear, Richard, et al (1980) conducted a series of 126 bolt tests. These tests consisted of fully tensioned single bolts being placed in single shear and the plates were loaded in tension. Thirty different combinations of plate thicknesses, plate strengths, bolt diameters, edge distances, and bolt strengths were studied. Three typical failure modes were observed in the elemental tests; shear failure of the bolt, bearing failure of the plate, transverse tension tearing of the plates. Linear regression analyses were performed to determine coefficients for an equation that could be used for additional analytical modeling. This equation is referred to as the Richard Formula and the coefficients determined from the regression analysis are Kp, Ro, and n. The equation is given by:

(Continues...)

Excerpted from CONNECTIONS IN STEEL STRUCTURES III Copyright © 1996 by Elsevier Science. Excerpted by permission of Pergamon. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site. Content: Introductory Notes. Composite Connections. Special Connections. Design Methods. Modelling of Connections. Frame Behaviour. Cyclic Response. Design Standards. State of Practice. Connections in Australia. Appendix. Abstract: This book publishes the proceedings from the Third International Workshop on Connections in Steel Structures: Behaviour, Strength and Design held in Trento, Italy, 29-31 May 1995. The workshop brought together the world's foremost experts in steel connections research, development, fabrication and design. The scope of the papers reflects state-of-the-art issues in all areas of endeavour, and manages to bring together the needs of researchers as well as designers and fabricators. Topics of particular importance include connections for composite (steel-concrete) structures, evaluation methods and reliability issues for semi-rigid connections and frames, and the impact of extreme loading events such as those imposed by major earthquakes. The book highlights novel methods and applications in the field and ensures that designers and other members of the construction industry gain access to the new results and procedures This work consists of the third International Workshop on Connections in Steel Structures, held in Italy in 1995. It includes assessments of research and developments in steel construction, considering connections as key elements. Topics covered include connection modelling and cyclic response.