Current Reliability-Based Design State of the Art

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Chapter 2: Literature Review


This literature review summarizes the progression and current state of lateral connection design methodology as given by the NDS. Both design format options, ASD and LRFD, will be presented. In addition, two fracture models will be presented, which offer two viable alternatives for the prediction of capacity resistance of perpendicular to grain connections. A summary of the state-of-the-art of reliability-based design of connections will also be provided.

Current U.S. Connection Design Methodology

Wood structures are currently designed according to the National Design Specification for Wood Construction – ASD/LRFD (NDS) (AF&PA 2005), by one of two formats: allowable stress design (ASD) or load and resistance factor design (LRFD). Lateral connection design for both formats is based upon the European Yield Model, which will be described in this section. Prior to the 2005 edition of the NDS, the NDS manual contained only the ASD format, and a separate manual contained the LRFD format. The origin, supporting research, and design values pertaining to these two formats, will also be presented in this section.

Succession of Design Methodologies

The initial design methodology for laterally loaded single fastener dowel-type connections was based off of empirical equations derived from monotonic experimental testing of bolted timber connections by Trayer (1932). This research was the first significant investigation in the U.S. of design values for bolted connections, and also introduced the concept of basing design from the proportional limit of the connection load-displacement behavior. Included with the work was the identification of geometric requirements, meant to limit the occurrence of premature splitting before the achievement of design-level resistances, in the form of end distance, edge distance, and bolt spacings. Subsequent experimental investigations of bolted connections, conducted by Doyle and Scholten (1963), and Soltis et al. (1986), have supported the accuracy of the empirical equations formulated by Trayer (1932). Although a fundamental limitation of this design method was its basis on a finite number of connection materials and configurations, it served as the NDS protocol for laterally-loaded dowel-type connection design, through the 1986 edition.
An entirely different methodology for the design of laterally-loaded dowel type connections was introduced by Johansen (1949), known as the yield model or European Yield Model (EYM). The model facilitated prediction of connection resistance on the principle assumptions of ideal elastic-plastic behavior of the steel dowel and wood connection members, connectors loaded laterally with no gap present between members, negligible friction, and failures consisting of either an embedment failure below the dowel, one or two plastic hinges forming in the dowel, or a combination of the two mechanisms. Dowel embedment strength of the connection members, dowel bending strength, and geometry factors of the connection, were the key inputs of the model. Its accuracy in predicting monotonic yield resistance has been validated by the research of McLain and Thangjitham (1983), Aune and Patton-Mallory (1986), and Soltis and Wilkinson (1987), amongst others. Yield theory has been the basis of design for laterally-loaded dowel connections, since first being included in the 1991 NDS (Breyer et al. 2003). A more detailed description of the model as it appears in the NDS, is provided in Section 2.2.3.
Several models have been created more recently that extend prediction capabilities to include connection slip, and hysteretic considerations that permit the analysis of dynamic loads. The culmination of these efforts has been the load-slip model presented by Heine (2001), a model based upon elements of yield theory, non-linear response, and hysteresis elements selected from a genetic algorithm. The model also included an embedded stochastic model, allowances for system slack (i.e. oversized dowel holes) and a novel failure model termed the ‘Displaced-Volume-Method’. The model, instituted inside a computer program, was validated with experimental data of single and multiple-fastener, parallel to grain connections.

Research Relating to Embedment Strength

Embedment strength is an input included in all three models mentioned in Section 2.2.1. As such, much research pertaining to connection performance has concentrated on the relationship between embedment strength and the following variables: “angle between loading and grain direction, loading rate and/or duration, bolt angle with respect to load direction, bolt hole oversize, specific gravity, and moisture content” (Smart 2002).
With respect to grain orientation, research has shown that embedment strength perpendicular to grain is generally lower than parallel to grain, once past a critical dowel diameter (the two orientations are approximately equal for lower diameters). Soltis et al. (1987) found that for bolts, which typically have diameters exceeding 0.25 in., perpendicular to grain embedment strengths were significantly lower than respective values from the parallel to grain orientation. For the case of intermediate loading angles, where the angle of loading lies between the parallel and perpendicular to grain orientation, the Hankinson formula is used to quantify embedment strength. The formula is the following (Breyer et al. 2003): Where,
F = Embedment strength at angle of load θ, psi.
Fell = Embedment strength, parallel to grain, psi.
Fe   = Embedment strength, perpendicular to grain, psi.
Considerable research has also been directed towards the relationship between embedment strength and moisture content, which has been summarized by Rammer and Winistorfer (2001). Results of such work have concluded that embedment strength increases whenever moisture content decreases, and vice versa. Separate studies have found a relationship existing as a function of moisture content, between embedment strength and specific gravity. The specific relationship at 12% moisture content for softwoods (the typical equilibrium moisture content assumed for normal service conditions in wood construction), was determined for common bolt diameters by Wilkinson (1991) to be:
Fell = 11200G
Fe = 6100G1.45/√D
G = specific gravity or equivalent specific gravity (see below)
D = dowel diameter, in.
Equivalent specific gravity (ESG) is used in lieu of actual specific gravity, to facilitate the application of Equations 2-2 and 2-3 to SCL products. The specific ESG value for a SCL product is determined by inserting the test embedment strength (and dowel diameter for Equation 2-3) into the above equations, and solving for the corresponding specific gravity (Johnson and Woeste 2000). ESG values are typically included with the manufacturer’s design literature for each SCL product.
Time-dependent (also referred to as duration of load or DOL) effects have also been studied, and efforts have been summarized by Rosowsky and Reinhold (1999). Studies have shown that embedment strength values, and most other wood properties in general, are generally higher for shorter duration loads. However the connection-specific DOL testing program of Rosowsky and Reinhold (1999) revealed no significant trend tied to connection performance and load duration. Gutshall (1994) cyclically tested nail and bolted connections, and concluded that DOL adjustments were appropriate for seismic and wind loading conditions.
Studies have also considered the relationship between the connection dowel hole (bolt hole in the case of this research) and embedment strength. The importance of holes being properly drilled was highlighted by Goodell and Phillips (1944), who found that roughly-drilled holes afforded reduced connection resistances, in comparison with smooth holes. Considerations to hole oversizing, which is typical of bolt holes to provide assembly tolerance and to minimize splitting during connection fabrication, were given in the work of Wilkinson (1993). The work did not find oversizing itself to be a strength limiting practice (Smart 2002).
With the growing usage of structural composite lumber in wood structures, the research of Carstens (1998) addressed the need to investigate embedment strength values of engineered wood composites, and compare the two ASTM standards that exist for the measurement of embedment strength. Findings yielded good agreement with the previous study of Wilkinson (1991). It was also noted that composites typically had higher embedment strengths in comparison with lumber of the same species, for both principle orientations (Carstens 1998).

2005 NDS Design Methodology

As mentioned previously, both of the current design methodologies (ASD and LRFD) for laterally-loaded dowel-type connections are based from the European Yield Model, which uses a strength-of-materials approach and assumptions as described in Section 2.2.1. General design provisions for mechanical connections are given in Chapter 10 of the NDS, and specific provisions for dowel connections are given in Chapter 11 (AF&PA 2005).
For double shear connections, there are a total of 3 yield limit modes, and 4 yield mechanisms (Figure 2-1). Mode I failure is characterized by embedment failure in either the main (denoted as mode Im) or the side members (denoted as mode Is), with no presence of dowel bending or rotation. Mode IIIs failure is characterized by the formation of a plastic hinge in the fastener at each shear plane of the connection, and localized crushing of at least one of the members. Mode IV failure is characterized by the formation of two plastic hinges at each shear plane of the connection, and localized crushing of at least one of the members (Breyer et al. 2003). A schematic of these yield modes is shown in Figure 2-1.

Chapter 1 – Introduction 
1.1– Background
1.2– Objectives
1.3– Significance
Chapter 2 – Literature Review 
2.1 – Introduction
2.2 – Current U.S. Connection Design Methodology
2.3 – Fracture Mechanics-Based Models
2.4 – Current Reliability-Based Design State of the Art
2.5 – Summary
Chapter 3 – Materials and Methods 
3.1 – Introduction
3.2 – Materials
3.3 – Sample Size Determination
3.4 – Connection Tests
3.5 – Material Tests
3.6 – Property Definitions
Chapter 4 – Results and Discussion 
4.1 – General
4.2 – Connection Tests
4.3 – Material Property Tests
4.4 – Evaluation of TR-12
4.5 – Evaluation of Fracture Models
4.6 – Comparisons Between TR-12 and Fracture Models
Chapter 5 – Summary and Conclusions 
5.1 – Summary
5.2 – Conclusions
5.3 – Limitations
5.4 – Recommendations for Future Work

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