NIST Technical Note 1752 

Digital image correlation measurements during gusset

plate connection testing to structural failure. 

Mark A. Iadicola 

http://dx.doi.org/10.6028/NIST.TN.1752 

NIST Technical Note 1752 

Digital image correlation measurements during gusset

plate connection testing to structural failure. 

Mark A. Iadicola 

Metallurgy Division

Material Measurement Laboratory

http://dx.doi.org/10.6028/NIST.TN.1752 

August 2012 

U.S. Department of Commerce 

Rebecca Blank, Acting Secretary

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director
Certain commercial entities, equipment, or materials may be identified in this document 

in order to describe an experimental procedure or concept adequately. Such 

identification is not intended to imply recommendation or endorsement by the National 

Institute of Standards and Technology, nor is it intended to imply that the entities, 

materials, or equipment are necessarily the best available for the purpose. 

National Institute of Standards and Technology Technical Note 1752 

Natl. Inst. Stand. Technol. Technical Note 1752, 118 pages (August 2012) 

CODEN: NTNOEF 
1 

Abstract 

This report describes the use of three-dimensional (3D) digital image correlation to measure the shape, displacement, and in-plane strain fields, during testing of gusset plate structural connections. Twelve full-scale bridge gusset plate connections of various geometries and 

boundary conditions were tested at the the Federal Highway Administration (FHWA) TurnerFairbank Highway Research Center (Ocel et al., 2012). These experiments are part of the verification of numerical models as part of the National Cooperative Highway Research Program 

(NCHRP) Project 12-84 “Guidelines for the Load and Resistance Factor Design and Rating of 

Riveted and Bolted Gusset Plate Connections for Steel Bridges”. The measurements described 

here are in regards to the tests performed to failure (i.e., maximum load carrying capacity of 

the connection). During each of the twelve tests to failure, a series (typically about 150) of 

image pairs were taken for subsequent digital image correlation analysis. Although all of the 

image pairs were processed, only a very small portion of the results are explicitly presented 

here. General access to the overall data set will be given to other researchers. Overall, the 

measurements showed reasonable uncertainties on the order of ± 175 μm/m of maximum inplane shear strain, and the measured out of plane initial shapes of the plates typically matched 

qualitative inspections of the connections. 

In this report, the layout, calibration, and measurement procedure associated with the digital image correlation system are described in detail to aid in understanding of the results. The 

results shown here include a sample of the measured and derived variables for one experiment 

at two conditions, to inform the reader of the type of data that is available. The results also 

include an abbreviated set of results that show the evolution of the out of plane shape and maximum shear strain field at four points in loading from the initial condition to failure. These are 

very useful in visualizing the mechanisms (buckling and/or shear failure of the plate) that lead 

to eventual failure of the connection. The evolution of strain bands of maximum in-plane shear 

is seen quite clearly in many of the plates. These localized bands of deformation frequently 

extended from the bolt lines of one member to another member through the large open areas 

of the plate. Comparison between all of the plates at failure, in terms of the maximum in-plane 

strain fields, is also presented. This comparison helps delineate plates that failed after significant shearing versus the ones that failed with minimal or no shearing. The comparison also 

shows very clearly the effect of reduced thickness, which was used as an analog to section loss 

due to corrosion. 

Keywords: digital image correlation, strain measurement, buckling, gusset plate connections, steel truss bridges 
2
 
3 

Contents 

1 INTRODUCTION 4
 

2 SETUP 7
 

3 SPECIMEN PREPARATION 11
 

4 CALIBRATION 13
 

5 PROCEDURE AND ACQUISITION 14
 

6 POST PROCESSING 16
 

7 RESULTS 21
 

7.1 Example Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
 

7.2 Key Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
 

7.2.1 GP307-SS3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
 

7.2.2 GP307-LS3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
 

7.2.3 GP307-SL3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
 

7.2.4 GP307-SL4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
 

7.2.5 GP307-SS3-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
 

7.2.6 GP307-SS3-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
 

7.2.7 GP307-SS3-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
 

7.2.8 GP307-SS3-4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
 

7.2.9 GP490-SS3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
 

7.2.10 GP490-SS3-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
 

7.2.11 GP490-LS3-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
 

7.2.12 GP490-LS3-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
 

7.3 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
 

8 SUMMARY 97
 

REFERENCES 117
 
4 

1 INTRODUCTION 

The work reported here was performed in collaboration with the Federal Highway Administration 

(FHWA) on the National Cooperative Highway Research Program (NCHRP) Project 12-84 titled 

“Guidelines for the Load and Resistance Factor Design and Rating of Riveted and Bolted Gusset 

Plate Connections for Steel Bridges”. For this project, large-scale gusset-plate experiments were 

performed at the FHWA Turner-Fairbank Highway Research Center in the Structures Laboratory 

(Ocel et al., 2012). Researchers from the National Institute of Standards and Technology (NIST) 

worked in conjunction with FHWA to perform digital image correlation (DIC) deformation measurements during these experiments, and this report presents the results of the NIST measurements 

taken during loading to failure of the specimen connections. 

The type of connection being tested is a five member structural connection joined by gusset 

plates on each side of the members (Fig. 1). The load frame setup is designed to permit testing of a 

variety of gusset plates to failure using the same set of members (i.e., a new specimen is comprised 

only of two new gusset plates and associated chord splice plates, cover plates, and any retrofits 

being tested). Failure is defined here as the point when the connection can no longer carry more 

load (i.e., maximum load). The five members engage reaction walls (shear walls) through four 

sets of hydraulic actuators. The Vertical member can be in either tension or compression during 

loading, whereas the East Chord is set in either the compression only or tension only configuration 

from the time of the connection assembly. The West Chord is grouted and post-tensioned to the 

West abutment allowing horizontal reaction to be either tension or compression depending upon 

the particular loading scenario. The symmetric design of the connection results in a South and a 

North gusset plate that are mirror images of each other. 

In this report, the test specimens are referred to by the FHWA selected labeling convention as 

GPvvv-wxy-z, where vvv is the bolt type (either “307” for standard A307 or “490” for high-strength 

A490 7/8-9 UNC bolts), w refers to the gap between the corner of the Compression Diagonal and 

the Chord member (“S” for short,“L” for long), and x refers to the edge length or connection length 

(“S” for short or “L” for long), y is the plate thickness where 3 refers to 3/8 in (9.5 mm) and 4 

refers to 1/2 inch (12.5 mm), and z differentiates repeat tests of the same plate geometries. For 

example, the first repeat test with A490 bolts, a 3/8 in (9.5 mm) thick plate, a long gap to the chord 

and short edges is named GP490-LS3-1. Figure 2 shows the plates schematically as viewed from 

the North side of the connection (detailed dimensions of the plates may be found in Ocel et al. 

(2012)). The five member edges are also shown in the figure. As an analog to section loss due to 

corrosion, one plate geometry GP307-SS3 was further machined (from the interior face) to reduce 

the plate thickness between the members and along the chords in three patterns. These are shown 

schematically as grey areas with dashed lines in Fig. 2 (again detailed dimensions of the plates may 

be found in Ocel et al. (2012)). A special case occurs for the test on plate GP307-SS3-4, which 

added a shingle plate to the North face of the connection. These plates which cover a portion of 

the gusset plate and connect all five members are intended as a retrofit to reinforce a plate with 

substantial corrosion. This shingle plate is denoted as GP307-SS3-shingle in the remainder of this 

report. It should also be noted that although most of the North and South plate connections are 
5 

X

Y

X

Z

North Plate

South Plate

X’

Y’

X’

Z’

(a)
 

(b) 

Figure 1: Structural connection being tested in the load frame: (a) schematic of load frame with 

East Chord hydraulic cylinders in the compression configuration (hydraulic jacks used to apply 

loads are shown in grey; the vertical uses a different type of actuator that can apply tension or 

compression) and (b) shape and dimensions of member cross-sections in mm. Note: section B-B 

is as viewed from North side of the load frame unlike Ocel et al. (2012). 
6 

symmetric, there were a couple exceptions. Specimens GP307-SS3-3 and GP307-SS3-4 had the 

reduced thicknesses shown in Fig. 2 only for the North gusset plates, and only the GP307-SS3-4 

North plate had an added shingle plate to reinforce the plate. For more details on these particular 

connections see Ocel et al. (2012). 

There are four main deformation/strain measurement methods used in the tests to failure: 3D 

laser point tracking, foil strain gauges, DIC, and a brittle coating method. Most of the methods are 

used on a dedicated side of one plate to prevent interference from the other methods during testing. 

Additionally before and after each test, the laser tracking system is used to perform thorough scans 

of the 3D shape of the gusset plates (including both plate external surfaces, and plate edges). 

During the test, the laser tracker is used to measure the displacement of specific bolt ends and 

member reference points on the North face of the connection, while DIC is performed on the outer 

surface of the North plate, and the brittle coating is used on the outer surface of the South plate. 

Strain gauges are attached to the members, splice plates, and the inner surfaces of both the North 

and South gusset plates (i.e., the South face of the North plate and the North face of the South 

plate). 

Full-field shape and strain mapping data is very desirable for the testing of structural connections. Point measurement methods like strain gauges and point displacement sensors may be used 

in large deformation testing, but sensor placement is selected a priori and may not detect local 

deformations that do not occur at those exact locations. Laser trackers, like the one used in these 

experiments, is a special case that can be used as a single point tracker or can scan many points to 

form a point cloud to approximate the full-field behavior. Unfortunately, there is no indexing of 

these points to exact locations on the plate, therefore the current shape can not be indexed to the 

original shape making strain field calculation impossible. Photo-elastic techniques can be used in 

the elastic range, but can not extend very far into the plastic strain range. An example of photoelastic measurements applied in the elastic range for these same experiments see Iadicola et al. 

(2012). The brittle coating method does produce some full-field data, but it is not very quantitative. Even if calibrated, the method acts as a threshold for one strain level. DIC, however, is not 

only a quantitative full-field method to measure 3D shape, but it is also capable of quantitative 

measurement of surface strains during plastic deformation. 

The use of DIC for full-scale in situ testing of civil engineering structures as a method of 

structural health monitoring or inspection has been suggested (Junda et al., 2007; Kitagawa et al., 

2007; Kohut et al., 2008; Kujawinska et al.  ́ , 2010; Kujawinska et al.  ́ , 2009; Malesa et al., 2010;

McCormick and Lord, 2010; Wei and Xiaoyuan, 2009; Yoneyama et al., 2007). Often this is 

done only for a small portion of the structure. In the case of bridges, the displacement of a span 

might be measured at specific points (Malesa et al., 2010) along the length, along the entire length 

(Yoneyama et al., 2007), or used to determine the full-field strain response at a single connection of 

interest (Junda et al., 2007; Malesa et al., 2010; McCormick and Lord, 2010). Laboratory testing 

that incorporates DIC typically uses reduced-scale structures for testing and focuses on either a 

connection (De Roover et al., 2002; Junda et al., 2007; McCormick and Lord, 2010; Sadowski 

et al., 2010; Smith et al., 2011; Souid et al., 2009; Sozen and Guler, 2011; Wei and Xiaoyuan, 

2009) or other small area of interest (Hild et al., 2011; Kujawinska et al., 2011). Yoneyama et al. 
7 

(2005) performed laboratory tests on a reduced-scale single girder “bridge” before their field load 

testing of a single span bridge (Yoneyama et al., 2007). The laboratory and in situ testing verified 

DIC performance with and without an added pattern for correlation by comparing the DIC results 

to point displacement transducers. The work presented here is the laboratory testing of a single 

full-scale bridge connection. Unlike some of the previous work that only looked at the strain fields 

for a small section on the connection, the measurements here use DIC over the entire plate. These 

experiments are keenly interested in the evolving strain fields over the plate, as well as the out of 

plane displacements, as the specimen approaches failure. Comparisons can be made to the other 

measurement methods in common displacement and strain ranges (Iadicola et al., 2012), but are 

not the focus of this report, nor is the modeling of the results (Mentes et al., 2011). 

A stereo (two-camera) digital image correlation system and processing software from Correlated Solutions Inc. is used to perform 3D displacement measurements on the outer surface of 

the North gusset plate. The system uses a combination of stereo-photogrametry and digital image 

correlation to measure and track a semi-random surface pattern to determine 3D displacements on 

a surface and derive strains from those displacements. The method requires a high contrast pattern 

that moves with the surface of the specimen and clear line of sight to both cameras. A black and 

white pattern is applied to the plate surface for all the experiments reported here. Plate surface 

areas obscured directly by the washer, nuts, and bolt ends are not measurable, as well as the areas 

to either side of the bolt end that are obscured in the images viewed from either the left or right 

camera. 

The coordinate system used for the DIC measurements performed on the outer surface of the 

North gusset plate shown here has an origin approximately at the lower East corner of the plate 

(Figs. 1a). The X-axis is nominally aligned with the bottom edge of the North gusset plate, with 

a Y-axis aligned with the vertical face of the plate. A more detailed definition of the coordinate 

system is presented in Section 6 below. Note: an alternative coordinate system is used by the 

other measurement methods that essentially has its origin at the lower West corner of the North 

gusset plate with the X’-axis to the East and the Y’-axis vertically along the west edge of the plate 

(Figs. 1a). This alternate system has a positive Z’ direction toward the South, which is in the 

opposite direction from the DIC Z-axis. 

Table 1 describes the nomenclature used in this report. The report details the setup (Section 2), 

specimen preparation (Section 3), calibration (Section 4), procedures (Section 5), and post processing (Section 6) associated with the digital image correlation measurements. A selection of results 

(Section 7) for the test to structural failure of the connections is shown to illustrate some key results 

and describe the data that is available for further detailed analysis. 

2 SETUP 

In the measurements described here, black and white CCD cameras are used in combination with 

compact 8 mm lenses with locking focus rings and apertures. The cameras are mounted to a continuous aluminum bar to ensure that their spacing and orientation remain unchanged during each 

experiment (Fig. 3a). The bar is mounted horizontally level on a tripod setting the lens centerline 

height to the center height of the plate (Fig. 3c). The bar is approximately parallel to the surface of 
8 

GP307-SS3
 

GP307-LS3
 

GP307-SL3;
 

GP307-SL4
 

Figure 2: Schematic view of the gusset plate specimens as viewed from the North similar to Figs. 1 

(Tension Diagonal on the left and Compression Diagonal on the right). The member edge locations 

are also shown. Four GP307-SS3 samples are described with areas of reduced thickness (shown in 

grey with dashed edges). 
9 

t

b

t

a

t

GP307-SS3-1: ta = 6.48 mm, tb = 4.75 mm;
 

GP307-SS3-2: ta = 4.75 mm, tb = 6.48 mm
 

GP307-SS3-3: t = 4.70 mm;
 

GP307-SS3-4: t = 7.87 mm
 

GP490-LS3-1;
 

GP490-LS3-2
 

(has added L3”x3”x1/2” angle sections, not
 

shown)
 

GP490-SS3; 

GP490-SS3-1; 

GP490-SS3-2; 

GP490-SS3-3 

Figure 2 (continued) 
10 

Table 1: Nomenclature
 

Symbol Symbol in Plot Legends Units Description 

X X [mm] mm 3-dimensional orthogonal coordinate 

Y Y [mm] mm 3-dimensional orthogonal coordinate 

Z Z [mm] mm 3-dimensional orthogonal coordinate 

U U [mm] mm displacement in X-direction 

V V [mm] mm displacement in Y-direction 

W W [mm] mm displacement in Z-direction 

εXX exx [um/m] - Lagrange μm/m Lagrangian strain in X-direction 

εYY eyy [um/m] - Lagrange μm/m Lagrangian strain in Y-direction 

εXY exy [um/m] - Lagrange μm/m Lagrangian shear strain in XY-plane 

ε1 e1 [um/m] - Lagrange μm/m 1st principal in-plane Lagrangian strain 

ε2 e2 [um/m] - Lagrange μm/m 2nd principal in-plane Lagrangian strain 

(εXY)max Tresca Strain [um/m] - Lagrange μm/m max. in-plane Lagrangian shear strain 

θ n/a o included angle between cameras 

A n/a mm camera spacing from one another 

B n/a mm standoff, camera to plate distance 

S n/a pixels digital image correlation subset size 

P n/a pixels digital image correlation subset spacing 

t n/a mm gusset plate thickness in reduced section 

ALF n/a N/N applied load fraction 

DIC n/a n/a digital image correlation 
11 

the plate (Fig. 3b). The cameras are mounted with an included angle between θ = 30o and 35o with 

the bisector of that angle passing through the centerline of the plate width (Fig. 3b). The cameras 

are spaced at about distance A and set back from the plate by approximately distance B, resulting 

in the intersection of the optical centerlines of the cameras being located behind the plate surface 

(Fig. 3b). This was necessary to fill as much of the field of view as possible with the plate. Since 

the cameras are angled there is no single magnification for either image, but an average magnification value for the plate area of each image can be calculated for the specific camera/lens position 

for each experiment (see Table 2). 

Table 2: Parameters describing the DIC camera orientations. Included angle and spacing between 

cameras values are based on the system calibration, and are reported here to the same number of 

decimal places as used in the software. 

Camera Exposure Angle Spacing Standoff Magnification Plate ID Resolution Time (

o) A (mm) B (mm) (pixel/mm) (Mpixel) (ms) 

GP307-SS3 2 30.7367 1062.10 1995 1.04 50 

GP307-LS3 2 34.2315 1350.50 1850 0.92 50 

GP307-SL3 5 32.6439 1151.84 1565 1.41 40–50 

GP307-SL4 5 33.3695 1129.11 1570 1.41 25–34 

GP307-SS3-1 5 32.8026 1012.12 1420 1.57 35–45 

GP307-SS3-2 5 33.0080 1012.04 1390 1.59 25–40 

GP307-SS3-3 5 32.6243 1011.84 1395 1.59 30–40 

GP307-SS3-4 5 32.7176 1012.09 1385 1.57 25–39 

GP307-SS3-4 

after reassembly 5 32.7176 1011.81 1385 1.57 25–40 

GP490-SS3 2 32.2019 1028.62 1570 1.10 50 

GP490-SS3-1 5 32.6302 937.919 1280 1.72 25–38 

GP490-LS3-1 5 33.0275 1024.93 1370 1.62 40 

GP490-LS3-2 5 33.6706 1025.19 1395 1.60 40–62 

Two photographic lights were used to reduce shadowing on the plate surface from the bolt ends 

and allow the aperture diameters to be reduced (to increase the depth of field). These lights were 

located behind each of the cameras about 2.7 m from the plate (Fig. 3), and were only on when 

acquiring images to reduce excessive heating. 

3 SPECIMEN PREPARATION 

Each North plate specimen was sand blasted after machining to remove the mill-scale and was 

cleaned of dirt and oil. Subsequently, the surface pattern was applied prior to connection assembly. 
12 

30-35o

Lighting North

Gusset

Plate Left 

Camera

(East)

Right 

Camera

(West)

Aluminum

Bar

(a)
 

A

B

2.7 m

θ

Lighting

North

Gusset

Plate

Left 

Camera

(East)

Right 

Camera

(West)

Aluminum

Bar

(b)
 

North

Gusset

Plate

Lighting

 Camera

(c)
 

Figure 3: DIC setup (a) annotated photo, (b) schematic plan view, and (c) schematic side view.
 
13 

Figure 4: Pattern used for digital image correlation measurements as painted on a gusset plate 

specimen. A 19.0 mm diameter coin is shown for reference. 

The North gusset plate was first painted matte white, then patterned with matte black ink stamped 

on the surface. Minor scratches and other damage to the pattern due to assembly were touched-up 

using paints of both black and white before testing began. The stamp pattern is 130 mm by 180 mm, 

which results in a slight chance of aliasing during correlation, due to the pattern repetition. This is 

rarely an issue because of the natural variation in the quality of the stamped pattern. This aliasing 

did occasionally occur during post processing, but was corrected through a combination of adjusted 

correlation thresholds or in extreme cases trimming of problem areas from the correlation analysis. 

The stamp pattern is designed to be semi-random with a nearly equal amount of area that is black 

or white (Fig. 4). The size of the pattern is such that the black and white features are each about 

5 mm wide. This results in two to three edges being visible in any 15 mm length on the plates. 

4 CALIBRATION 

A two-step calibration procedure is used here: first for the cameras/lenses, and then second for the 

orientation of the cameras to one another. A reference dot pattern target is used to calibrate each 

combination of camera and lens. Since the target does not fill the field of view, multiple images 

are needed to interrogate the entire field of view and determine the necessary lens corrections for 

each camera (see number of images left and right in Table 3). A known length within an area of 

correlation is required to determine the spacing and orientation of the cameras to one another. A 

bar with two target panels attached at a known spacing between features (see Fig. 5b and Table 3) 

is used where each target has a pattern similar to the pattern painted on the plate. Image pairs 

of this bar at three tilts to the horizontal are used to calibrate and verify the camera spacing and 

orientation. The calibration is done with one of the image pairs of the bar in the horizontal position 
14 

(Fig. 5a), and then the images of the bar in other positions are checked using that calibration to 

verify the measured panel spacing is correct to within an acceptable error (see length errors shown 

in Table 3). The resulting camera positions based on the calibration are shown in Table 2. 

Table 3: Number of images used to perform the DIC system calibration. Length of reference targets 

used for system calibration, and error in measured length with targets in angled positions. 

Target Length Length Images Images Plate ID Spacing Error Error Left Right (mm) Tilt 1 (%) Tilt 2 (%) 

GP307-SS3 64 40 1262.130 <0.01 -0.02 

GP307-LS3 45 45 1236.980 -0.01 -0.04 

GP307-SL3 50 74 1237.107 0.06 -0.06 

GP307-SL4 208 212 1160.145 <0.01 0.01 

GP307-SS3-1 162 162 1160.209 -0.07 0.02 

GP307-SS3-2 166 149 1160.145 0.03 0.02 

GP307-SS3-3 171 159 1160.145 <0.01 0.01 

GP307-SS3-4 195 203 1160.145 -0.04 0.02 

GP307-SS3-4 

after reassembly 188 188 1160.145 -0.01 -0.02 

GP490-SS3 35 42 1237.107 0.02 <0.01 

GP490-SS3-1 100 95 1083.945 0.06 <0.01 

GP490-LS3-1 52 49 1236.980 0.03 0.06 

GP490-LS3-2 68 67 1236.92 -0.02 -0.01 

5 PROCEDURE AND ACQUISITION 

Before the start of each test to failure, but after calibration of the DIC system, approximately three 

image pairs are acquired (while the connection is in an unloaded state). One of the pairs will be 

used as the reference state while the other two will be used to determine systematic uncertainties 

during post processing. For each test to failure, an equilibrium load ratio combination on the five 

members is selected (Table 4), and loads are applied as incremental steps of this load combination 

on four members (with the West Chord a fixed reaction member) through a feed back control 

loop. These values are targets, but during the testing actual values are measured. The applied load 

fraction (ALF) values given in this report are based on the current load for the dominant member 

divided by a reference load value (4448 kN or 1000 kips). During the load steps in the elastic range 

and for initial yield, the loading is held for extended periods (approximately 5 minutes) for other 

measurements to be made using the laser tracker system. At the start of these static holds, a set 

of DIC image pairs was acquired, and if any imaging problems occurred, then a second set was 
15 

(a)
 

(b) 

Figure 5: Left camera image of a horizontally positioned DIC calibration reference bar and targets 

(a), with cropped images showing targets (b) with two features at a known distance used for system 

calibration. 
16 

taken after the laser tracking measurements were complete. As the specimen approached failure 

these extended hold times were no longer needed (laser tracking measurements were suspended) 

and DIC images were acquired at regular time intervals. The frequency of image acquisition was 

increased as the specimen loading approached the predicted failure load. The maximum image 

acquisition rate used in the experiments was 0.1 Hz. Each image is acquired with an exposure 

time between 25 ms and 62 ms (Table 2), and typically three image pairs were taken at each static 

hold point in deformation. Along with the image file times, four analog signals (Tension Diagonal 

master hydraulic cylinder load, Tension Diagonal position, Compression Diagonal master hydraulic 

cylinder load, and Compression Diagonal position) were sampled simultaneous to each image pair 

to help synchronize the image acquisition with the other data systems. 

Table 4: Approximate applied load ratio combinations for each gusset plate tested. Values have no 

units. To obtain the target applied load combination for a given plate, multiply the tabulated ratio by 

the current applied load fraction (ALF) times the reference load of 4448 kN (or 1000 kilo-pounds, 

kips). Tensile values are positive, and compressive values are negative. 

East Tension Compression West Chord Plate ID Vertical Chord Diagonal Diagonal (reaction) 

GP307-SS3 -0.707 0.707 0.207 -1.000* 0.500 

GP307-LS3 0.261 0.348 0.246 -0.697 1.000* 

GP307-SL3 -0.707 1.000 0.000 -1.000* 0.707 

GP307-SL4 -0.707 1.000 0.000 -1.000* 0.707 

GP307-SS3-1 -0.707 0.707 0.207 -1.000* 0.500 

GP307-SS3-2 -0.707 1.000* -0.207 -0.707 0.500 

GP307-SS3-3 -0.707 1.000* -0.207 -0.707 0.500 

GP307-SS3-4 -0.707 1.000* -0.207 -0.707 0.500 

GP490-SS3 -0.707 1.000 0.000 -1.000* 0.707 

GP490-SS3-1 -0.600 1.000* -0.282 -0.600 0.531 

GP490-LS3-1 -0.600 1.000* -0.282 -0.600 0.531 

GP490-LS3-2 -0.600 0.600 0.282 -1.000* 0.531 

* dominant member used for calculation of ALF values in this report 

6 POST PROCESSING 

The image pairs for each test to failure are analyzed using stereo digital image correlation techniques to measure the 3D displacement of the gusset plate surface. For any selected subset of 

pixels in one image of each pair, a correlation can be performed to the pixels in the other image 

of each pair using the measured system calibration. If both of these subsets view the same grey 

scale pattern the correlation errors will be minimized, and the 3D location of the subset will be 
17 

known based on the orientation of the system calibration, and this location is attributed to a point 

located at the center of the subset. Parameters are set in the algorithm to reject data points at subsets 

that exceed user-defined tolerances for the correlation errors. A series of subset correlations can 

be performed to cover the area of interest in the images (i.e., the gusset plate), thus reproducing 

the current shape of the plate indexed to the pattern being interrogated. These same subsets can 

be correlated to subsequent image pairs to determine the new 3D positions of each subset. The 

changes in 3D positions of each subset define the measured displacements of that subset. A coordinate transformation may be defined to rotate these data from the camera system coordinates to an 

arbitrary coordinate system (e.g., the plate surface system as shown in Fig. 1a). 

An assessment of the errors associated with the system setup, pattern, and analysis parameters 

is performed using a series of image pairs taken with the specimen resting in the unloaded state. 

The first image pair acts as the reference shape and the subsequent image pairs as data with known 

displacements equal to zero. The measured displacements not equal to zero represent the error in 

the measured variables. For each plate before the test to failure, the system setup and pattern are 

adjusted to reduce the errors associated with the correlation. The analysis parameters, including 

the subset size and spacing, are optimized during the post processing of the test as described below. 

The DIC analysis requires the user to define the region of analysis in one image of the pair, 

as well as the subset size for correlation and subset spacing. The subset size (S) defines the area 

over which each position and displacement measurement is averaged. The subset spacing (P) 

determines the amount of overlap between the subsets, where a spacing size equal to the subset size 

results in each subset being an independent measurement (i.e., no overlap). Overlapping subsets 

results in some smoothing of the data, but this is only an issue when there are sharp gradients in 

shape or displacement. Since the results here are for a contiguous specimen, this is not a concern. 

The smallest possible subset spacing is one, but this requires substantially more processing for 

limited added data for a specimen with a smoothly varying shape. A typical subset size is shown 

as a red square in Fig. 6b. For all of the results shown here, the region of analysis was selected 

in the left image to be the edge of the plate or plates (Fig. 6a), which included the bolt heads that 

obscure the pattern and have no pattern and thus do not correlate. This results in many areas that 

have no pattern to correlate (Fig. 7a), but was determined to be less time consuming than manually 

removing the correlation region around each bolt end. The required subset size also limits how 

close to the plate edges or other features the data can be measured (Fig. 7a and b). Consequently, 

there is useful DIC data only in the field areas of the plate and between some of the bolts where both 

cameras could view enough of the surface pattern. Initially it also resulted in some areas of poor 

correlation that included the edges of the washer, nuts, and bolt ends (in Fig. 7a subset shown below 

the bolt end). Tolerances on the correlation were adjusted for each test to remove the correlation 

areas that included the bolt ends and washers. In extreme cases, some of the region of interest was 

trimmed to remove the problem areas. When aliasing occurred due to pattern repetition, it was 

typically located at points that were visible only in one image such as the area just to the left or 

right of a bolt end (Fig. 7a). These were easily corrected by trimming this area from the region of 

analysis. 

The DIC measured positions and displacements are rotated to a user defined orthogonal coordi­
18 

(a)
 

(b) 

Figure 6: Images of GP307-LS3 (a) DIC region of analysis (semitransparent red area) selected in 

left image of the image pair shown. (b) Close up images with approximate DIC subset (red square 

with red center spot) in left and right images. 
19 

(a) (b) 

Figure 7: DIC subsets (red square with red center spot) near edges of the correlation region (a) 

around bolt ends and (b) near plate edges (dashed lines). 

nate system, which is based on reference marks offset from the bottom edge of the plate that were 

made during painting of the plate. The X-axis origin is the lower East corner of the North plate 

(Fig. 1a). The Y-axis projection on to the XZ-plane is normal to the X-axis and approximately 

follows the East vertical edge of the plate. The Z origin is based on three points in the field of the 

plate: one below the Tension Diagonal, one below the Compression Diagonal, and one between 

the top bolts of the Vertical. Figure 8 shows the approximate location of these three points for 

one plate as viewed in the left image. The initial Z shape shows the zero-contour intersects these 

three points. A color map with a transition from brown (negative values) to blue (positive values) 

is typically used in this report for plots of Z-shape, since it is the deviation from perfectly flat that 

is of primary interest. The measured displacements in the X, Y, and Z directions are defined as U, 

V, and W respectively. 

Strains are derived from the measured displacement fields. The Lagrangian formulation of 

strain was used for all the measurements, since it is typically used for finite element modeling. The 

axial strains in the X-direction (εXX), Y-direction (εY Y ), and shear strain in the XY-plane (εXY ) 

are calculated from the measured displacements, 

 2 2 2 ∂U 1 ∂U ∂V ∂W

εXX = + + + (1) ∂X 2 ∂X ∂X ∂X

 2 2 2 ∂V 1 ∂U ∂V ∂W

εY Y = + + + (2) ∂Y 2 ∂Y ∂Y ∂Y
20 

Figure 8: Out-of-plane shape (Z positive outward from the plate) after coordinate rotation to specimen GP307-SL3. Three points shown as red crosses locate the Z = 0 mm plane. 
 

 

21 

2 2 2 1 ∂U ∂V 1 ∂U ∂U ∂V ∂V ∂W ∂W

εXY = + + + . (3) 2 ∂Y ∂X 2 ∂X ∂Y ∂X ∂Y ∂X ∂Y

Note: the higher order (large strain) terms are used in the calculation. The calculation is performed 

for the each analysis point using the nearest neighboring points. The calculations are performed 

individually on a triangle formed by the point of interest and two of neighboring points, and then 

these values are averaged for all of the neighboring points. This results in strains that are calculated 

near the edge of the analysis region using only one to three of these triangles, where as points in the 

center of the analysis region use four triangles. The resulting strains are smoothed with other data 

points within a two subset radius of the point of interest using a Gaussian weighted (10 % at the 

highest radius) filter. This results in slightly larger strain uncertainty near any edge of the region 

of analysis (i.e., plate edge or near a bolt end) since less triangles are averaged. In the figures 

presented here, the nomenclature for the strains (and the associated units) is slightly revised to 

not require Greek lettering (Table 1). The maximum in-plane shear strains (εXY )max (or “Tresca 

Strain” as described in the software) are also calculated. Note that the Tresca strains are based on 

the tensor definition, 

 

εXX − εY Y

2

(εXY )max = + (εXY )2, (4) 2

1 that is (εXY )max = (γXY )max (i.e., the Tresca strains are the radius of Mohr’s circle of in-plane 2

strain as opposed to the typical definition of (γXY )max which is the diameter of Mohr’s circle). All 

of the strains are determined for the outer surface of the plate. The variation of strain through the 

thickness of the plate, due to bending, is not considered or discussed here. 

Assessments of the noise level in the calculated maximum shear strains for two images taken in 

the unloaded reference state were used to determine an optimal square interrogation subset size (S) 

and a subset spacing (P) for each experiment, which balanced the reduction of the noise error while 

keeping the subset as small as possible. These settings and the resulting uncertainties are shown 

in Table 5. The uncertainties for the Tresca strain, W, εXX and εY Y are based on plus/minus 

one standard deviation from the expected zero value for all of the plate data. These are somewhat 

conservative values since they include edges of the correlation areas (i.e., plate edges and near bolt 

ends). If only the areas between the members that do not have an edge of the correlation area are 

considered the uncertainties reduce to about half the values shown in Table 5. Kujawinska et al. 

(2011) and Smith et al. (2011) both report uncertainties for W of ±0.030 mm which is of a similar 

value as those calculated here. Unfortunately they do not report uncertainties for any other of the 

variables of interest here. 

7 RESULTS 

A total of 12 tests to failure are presented in this report. For each test, between 100 and 800 

image pairs were acquired and processed. In this section, a small, but representative, portion of 

these results are presented. This section is broken down into three main subsections. The Example 

Case Section 7.1 includes a sample of the results for one test to failure (GP307-SL3) at just two 
22 

Table 5: Parameters describing the DIC analysis and resulting uncertainties.
 

S P Uncertainty 

Plate ID actual 

(pixels) 

average 

(mm) 

actual 

(pixels) 

average 

(mm) 

Tresca 

(μm/m) 

W 

(mm) 

εXX

(μm/m) 

εY Y

(μm/m) 

GP307-SS3 19 18.2 7 6.7 246 0.040 337 346 

GP307-LS3 19 20.7 7 7.6 85 0.030 105 134 

GP307-SL3 23 16.3 7 5 142 0.023 181 177 

GP307-SL4 23 16.3 7 5 195 0.021 147 380 

GP307-SS3-1 23 14.6 7 4.5 251 0.019 151 490 

GP307-SS3-2 23 14.5 7 4.4 144 0.028 142 243 

GP307-SS3-3 23 14.5 7 4.4 124 0.016 146 168 

GP307-SS3-4 

gusset 23 14.7 7 4.5 226 0.018 269 318 

GP307-SS3-4 

shingle 23 14.7 7 4.5 126 0.015 161 167 

GP307-SS3-4 

shingle after 23 14.7 7 4.5 169 0.024 203 265 

reassembly 

GP490-SS3 19 17.3 6 5.4 180 0.031 167 251 

GP490-SS3-1 23 13.4 7 4.1 140 0.018 160 229 

GP490-LS3-1 23 14.2 7 4.3 254 0.029 256 430 

GP490-LS3-2 23 14.4 7 4.4 188 0.025 325 325 
23 

load steps and includes the different positions, displacements, and strains measured for each image 

pair. The Example section is intended to inform the reader of the type of data that is available for 

further analysis. The Key Points Section 7.2 includes the results of a few notable variables for all 

twelve tests to failure at four key points during the loading of each plate. This is intended to show 

how the deformations evolved during the tests to failure. The Comparison Section 7.3 presents the 

failure results for all twelve tests together for one strain variable on a common scale to permit cross 

comparison of the tests. 

All of the results are presented as contour plots with varying color maps and scales that overlay 

the left image at the current stage of loading. This means the chord members are in the lower part 

of the plot, and the Vertical and Diagonal members are in the upper part of the plots. The left side 

of the image is to the East and the right is toward the West (see Fig. 1). The Tension Diagonal 

member is in the upper left of the image and the Compression Diagonal member is on the upper 

right. When applicable, the current load level is described as the applied load fraction (ALF), which 

is the ratio of the current load on the dominant member (for a given load ratio combination on all 

five members, see Table 4) divided by a 4448 kN (1000 kip) reference load on that same member. 

Recall that for each test to failure a particular equilibrium load combination (Table 4) on the five 

members (with the reference load on a specific member) is selected prior to the start of the test. 

During loading, the ratio of the loads on the members is approximately matched at every step to the 

selected load combination, thus the ALF along with knowledge of the selected load combination 

generally describes the current load condition. 

7.1 Example Case 

A sample of the results for the test of GP307-SL3 to failure is presented in Fig. 9–12. The positions 

X, Y, and Z are in reference to the selected coordinate system described in the Section 6 above 

(approximately shown in Fig. 1). Figure 9 plots the initial (ALF = 0) plate shape in the X-Y-Z 

system where each legend uses the same color map, but different value ranges. The initial outof-plane plate shape (Z positive toward the camera system, see Fig. 1a), shown in Fig. 9c, was 

qualitatively verified using a straight edge to check the locations of the high and low points. For 

some of the tests, this shape was spot checked more quantitatively through comparison to the 

measurements of the laser tracker system. In some tests, patterned covers were attached to selected 

bolt ends to see if the motion of the bolt ends could be tracked (see four red areas on the bolt 

ends in Fig. 9c, two on the Chord members and two on the Compression Diagonal). Although 

the measurements of these covers are shown in the plots the details of the measurements are not 

discussed here. 

Figure 10 plots the displacements (U, V, and W) from the initial shape (Fig. 9) at the point 

of maximum load (ALF = 0.95). The X-direction displacement (U) shows that the entire plate 

has shifted to the East (left), with the upper half of the plate shifting by about 8 mm more than 

the lower half. This is consistent with the Tension and Compression Diagonals having a force 

resultant in the negative X-direction, while the Chord members are loaded from the East (left) in 

the positive X-direction. The Y-direction displacement (V, Fig. 10b) shows that the East (left) half 

of the plate has shifted up pulled by the Tension Diagonal, while the West (right) half of the plate 
24 

(a)
 

(b)
 

(c)
 

Figure 9: Initial positions (a) X, (b) Y, and (c) Z at zero load (ALF = 0) for specimen GP307-SL3.
 
25 

has shifted down pushed by the Compression Diagonal. The out of plane displacement (W) shows 

that on average the plate shifted away from the camera (toward the South), but that the plate at the 

Compression Diagonal swayed out to the North, with buckling along the free edges between both 

the Compression Diagonal and the Vertical, or Compression Diagonal and the West Chord. 

The Lagrangian strains are calculated from the displacement fields, as described above. The 

results are the axial strains εXX and εY Y , in the X and Y-directions respectively, as well as the inplane shear strains εXY , for each measurement point referenced to the selected coordinate system. 

These results are shown as contour plots of strain, Fig. 11. The most prominent strains are the εXY

(Fig. 11c), which shows shear strain bands that extend between the bolt lines of the various members. With knowledge of the in-plane components the principal in-plane strains can be calculated 

at each analysis point. Note that the orientation of the direction of the principal strains in the XYplane can vary with location on the plate. Fig. 12a and b plot the first and second principal in-plane 

strains, respectively, with the second plotted with reverse color map (red being the minimum strain 

value). If ε1 = −ε2 then that point has an orientation that is in a state of pure shear. Deviations 

from this equality result for areas that deviate from pure shear. 

The combined strain measure described in Section 6, and shown here, is the Tresca strain 

((εXY )max), which combines all of the in-plane strain components into one strain measure. Tresca 

strains are plotted in Fig. 12c, where the color map now includes a grey portion at the lowest strain 

level. The upper limit of the grey bar is set at the static yield strain (1040 μm/m) for this strain 

measure based on material property tests for this particular plate. This allows the reader to delineate 

the area that is elastically loaded (grey) from the area that is plastically deforming (spectrum of 

colors). A similar color map will be used in the next two sections for cases when the maximum 

plastic strains are quite large (i.e., five or more times yield). This Tresca yield strain value for each 

plate is calculated from the uniaxial data from coupon tests of the same plate material through, 

1 1 + ν [(εXY) ] = max σY, (5) Y 2 E

where ν is the Poisson’s ratio (value of 0.3 assumed), E is the elastic modulus (value of 29 000 ksi 

= 200 GPa assumed), and σY is the static yield stress as measured from the coupon test data for 

each plate. 

7.2 Key Points 

In this section, the evolution of each specimen from the initial state through four steps to failure 

are described for each specimen. Based on a general assessment of the data, three variables were 

selected for more detailed presentation here. The first is the initial shape of the plate in terms of Z, 

which could be a factor when considering the effect initial imperfections can have on imperfection 

sensitive testing. The second is the out-of-plane displacement (W) as it evolves with loading, which 

may be used to determine if and when buckling occurs. The third is the Tresca strain (maximum 

in-plane shear strain), which is useful in determining localized strain mechanisms (such as shear 

banding). For each plate tested, the results for out-of-plane displacement and Tresca strain are 

presented at four representative load levels (in terms of ALF, see Table 4), in addition to the initial 

shape at the zero load level (ALF = 0). A brief discussion of the results for each plate follows. 
26 

(a)
 

(b)
 

(c) 

Figure 10: Displacements (a) U, (b) V, and (c) W measured for GP307-SL3 at failure (maximum 

load, ALF = 0.95). 
27 

(a)
 

(b)
 

(c) 

Figure 11: Strains (a) εXX, (b) εY Y , and (c) εXY for GP307-SL3 measured at failure (maximum 

load, ALF = 0.95). 
28 

(a)
 

(b)
 

(c) 

Figure 12: First principal strain (a) ε1, second principal strain (b) ε2, and (c) Tresca strain measured 

for GP307-SL3 at failure (maximum load, ALF = 0.95). 
29 

Figure 13: Out-of-plane shape of specimen GP307-SS3 at zero load (ALF = 0). 

7.2.1 GP307-SS3 

Figure 13 shows the initial shape of GP307-SS3 at the start of the failure test under no load. The 

location of Z = 0 mm was set using three points as described above. After the rotation, the plate 

is slightly convex about the end of the Vertical member, and has an overall twist with the Tension 

Diagonal toward the positive Z and the East Chord in the negative Z-direction. Figure 14 shows 

the evolution of W (Z-direction displacement) from the initial shape in Fig. 13. The ALF values 

are in reference to the Compression Diagonal load (see Table 4). During the test, the entire plate 

shifted toward the negative Z-direction from an early stage, with final buckling of the Compression 

diagonal in that direction (Fig. 14d). Figure 15 plots the maximum in-plane shear strains at the 

same four ALF levels shown in Fig. 14. The yield strain in terms of Tresca strain is approximately 

820 μm/m, based on standard material testing of the same material. Figures 15a–c have strain 

ranges predominately in the elastic range, and use a pseudorandom color map. Figure 15d has a 

strain range predominately in the plastic strain range (spectrum color map) with grey being used 

for areas of the plate that have not yet reached the yield strain. The results show that the Tresca 

strains were concentrated between the ends of the Compression and Tension Diagonals from the 

early stages of loading, with the largest strains occurring at the end of the Compression Diagonal 

and along the Chord bolt lines. The strain field is more uniform in the early stages of loading, but 

the later two stages show more strain localizations, which extend between the various bolt lines by 

the point of failure (ALF = 0.71). 
30 

(a)
 

(b) 

Figure 14: Out-of plane displacement (W) fields from the reference state to current plate shape for 

GP307-SS3 at ALF of (a) 0.30, (b) 0.40, (c) 0.57, and (d) 0.71 (failure). 
31 

(c)
 

(d)
 

Figure 14 (continued)
 
32 

(a)
 

(b) 

Figure 15: Maximum in-plane shear strain for GP307-SS3 at ALF of (a) 0.30, (b) 0.40, (c) 0.57, 

and (d) 0.71 (failure), with initial yield at 820 μm/m. 
33 

(c)
 

(d)
 

Figure 15 (continued)
 
34 

7.2.2 GP307-LS3 

Figure 16 shows the initial shape of GP307-LS3 at the start of the failure test under no load. This 

is the only plate tested with the East Chord in the tension configuration, which required moving 

of the hydraulic jacks (shown on Fig. 1a) to the outside of the East Abutment. The location of 

Z = 0 mm again was set using three points as described above. After the rotation, the plate has 

a saddle shape with the Tension Diagonal and West Chord in the positive Z-direction and the 

Compression Diagonal and East Chord in the negative Z-direction. The general shape is consistent 

with the measurements from the 3D laser point tracker, but the magnitude of the shape is four 

times larger as measured by DIC. The reason for this inconsistency could not be determined, but 

the laser system, which is designed to be very accurate in this range of measurement, is more likely 

correct. The uncertainties in W shown in Table 5 for GP307-LS3 are consistent with those seen by 

other researchers (Kujawinska et al., 2011; Smith et al., 2011), but Iadicola et al. (2012) showed a 

0.6 mm maximum difference between the DIC and laser measured Z coordinates. Further analysis 

is needed to determine the reason for the large difference seen here, but none of the other variables 

(i.e., displacements or strains) show a similar distribution across the plate. Therefore these other 

values seem to not be affected, but should be checked against the other measurement methods (i.e., 

strain gauges or laser tracker) for verification similar to Iadicola et al. (2012). 

Figure 17 shows the evolution of the Z-direction displacement from the initial shape in Fig. 16. 

The ALF values are in regards to the West Chord load (Table 4). During the test, the entire plate 

initially shifted toward the positive Z-direction (Fig. 17a and b), with the largest positive motion 

at the Tension diagonal. At higher load levels, the West half of the plate shifts in the negative Zdirection, with final buckling of the Compression Diagonal in that direction (Fig. 17d). Figure 18 

plots the maximum in-plane shear strains at the same four ALF levels shown in Fig. 17. The 

yield strain in terms of Tresca strain is approximately 1080 μm/m, based on standard material 

testing of the same material. All the plots (Figures 18a–d) have strain ranges predominately in the 

elastic range and use a pseudorandom color map. The results show that the Tresca strains were 

concentrated between the ends of the Compression Diagonal and the West Chord from the early 

stages of loading, with the largest strains occurring at the end of the Compression Diagonal and 

along the Chord bolt lines. The strain field is more uniform in the early stages of loading, but the 

later two stages show more strain localization, which started to extend between the various bolt 

lines by the point of failure (ALF = 1.14). 

7.2.3 GP307-SL3 

Figure 19 shows the initial shape of GP307-SL3 at the start of the failure test under no load, after 

the plate was rotated to the selected coordinate system. After that rotation, the plate is relatively 

flat with a slight depression near the East Chord bolt line. Figure 20 shows the evolution of the 

Z-direction displacement from the initial shape in Fig. 19. The ALF values are in regards to the 

Compression Diagonal load (Table 4). During the test, the entire plate shifted toward the negative Z-direction from an early stage, until the final buckling of the Compression Diagonal in the 

positive Z-direction (Fig. 20d). Figure 21 plots the maximum in-plane shear strains at the same 

four ALF levels shown in Fig. 20. The yield strain in terms of Tresca strain is approximately 
35 

Figure 16: Out-of-plane shape of specimen GP307-LS3 at zero load (ALF = 0). 

1040 μm/m, based on standard material testing of the same material. Figures 21a–c have strain 

ranges predominately in the elastic range and use a pseudorandom color map. Figure 21d has a 

strain range predominately in the plastic strain range (spectrum color map) with grey being used for 

areas of the plate that have not yet reached the yield strain. The results show that the Tresca strains 

were concentrated between the ends of the Compression and Tension Diagonals during the early 

stages of loading (Fig. 21a and b), with the largest strains occurring at the end of the Compression 

Diagonal and along the Chord bolt lines. The strain field is more uniform in the early stages of 

loading (Fig. 21a and b), but the later two stages (Fig. 21c and d) show more strain localizations, 

which extend across the plate between the diagonal bolt lines through the end of the Vertical bolts. 

Additional strain localizations of lower magnitude extend from this bands down to the Chord bolt 

lines. 

7.2.4 GP307-SL4 

Figure 22 shows the initial shape of GP307-SL4 at the start of the failure test under no load. The 

location of Z = 0 mm was set using three points as described above. After rotation, the plate has a 

slight saddle shape with the Tension Diagonal and West Chord in the positive Z-direction, and the 

Compression Diagonal and East Chord in the negative Z-direction. Figure 23 shows the evolution 

of the Z-direction displacement from the initial shape in Fig. 22. The ALF values are in regards to 

the Compression Diagonal load (Table 4). During the test, the plate shifted continuously toward 

the negative Z-direction. The Compression Diagonal, which started in the negative Z-direction 

(Fig. 22), shifted further in that direction through the buckling of the plate (Fig. 23a–d). Figure 24 

plots the maximum in-plane shear strains at the same four ALF levels shown in Fig. 23. The yield 

strain in terms of Tresca strain is approximately 740 μm/m, based on standard material testing of 
36 

(a)
 

(b) 

Figure 17: Out-of plane displacement (W) fields from the reference state to current plate shape for 

GP307-LS3 at ALF of (a) 0.21, (b) 0.40, (c) 0.98, and (d) 1.14 (failure). 
37 

(c)
 

(d)
 

Figure 17 (continued)
 
38 

(a)
 

(b) 

Figure 18: Maximum in-plane shear strain for GP307-LS3 at ALF of (a) 0.21, (b) 0.40, (c) 0.98, 

and (d) 1.14 (failure), with initial yield at 1080 μm/m. 
39 

(c)
 

(d)
 

Figure 18 (continued)
 
40 

Figure 19: Out-of-plane shape of specimen GP307-SL3 at zero load (ALF = 0). 

the same material. Figures 24a and b have strain ranges predominately in the elastic range and 

use a pseudorandom color map. Figure 24c and d have strain ranges predominately in the plastic 

strain range (spectrum color map) with grey being used for areas of the plate that have not yet 

reached yield. The results show that the Tresca strains were concentrated between the ends of 

the Compression and Tension Diagonals from the early stages of loading, with the largest strains 

occurring at the ends of the diagonal bolt lines and along the Chord bolt lines (Fig. 24b). The strain 

field is more diffuse in the early stages of loading (Fig. 24a and b). In the later stages (Fig. 24c and 

d) more strain localizations are present, starting in Fig. 24c and extend between the Tension and 

Compression Diagonal bolt lines though the end of the Vertical bolt line with various extensions 

down to the Chord bolt lines. The highest strains were seen along the Chord bolt line starting as 

early as ALF = 0.52 (Fig 24b). 
41 

7.2.5 GP307-SS3-1 

Figure 25 shows the initial shape of GP307-SS3-1 at the start of the failure test under no load, 

after rotation to the selected coordinate system. Note that GP307-SS3-1 is one of the plates that 

has a reduced thickness as an analog for section loss due to corrosion (Fig. 2). The thinner section 

is on the Compression Diagonal half of the plate. After the rotation, the plate has a slight saddle 

shape with the Tension Diagonal and West Chord in the positive Z-direction, and the Compression 

Diagonal and East Chord in the negative Z-direction. Figure 26 shows the evolution of the Zdirection displacement from the initial shape in Fig. 25. The ALF values are in regards to the 

Compression Diagonal load (Table 4). During the test, the majority of the plate shifted toward 

the negative Z-direction with the exception of the Tension Diagonal that moved in the positive Zdirection. The Compression Diagonal, which started in the negative Z-direction, shifted further in 

that direction through the buckling of the plate always with a convex bulge of the plate under the 

Compression Diagonal (Fig. 26a–d). Figure 27 plots the maximum in-plane shear strains at the 

same four ALF levels shown in Fig. 26. The yield strain in terms of Tresca strain is approximately 

1060 μm/m, based on standard material testing of the same material. Figures 27a–c have strain 

ranges predominately in the elastic range and use a pseudorandom color map. Figure 27d has a 

strain range predominately in the plastic strain range (spectrum color map) again with grey being 

used for areas of the plate that have not yet reached yield. The results show that the Tresca strains 

were concentrated between the end of the Compression Diagonal and the West Chord from the 

early stages of loading, with the largest strains occurring at the end of the Compression Diagonal 

(Fig. 27c and d). This is the area of the plate with the thinnest cross-section, and this thinned down 

area is somewhat visible in the strain field (compare Fig. 27c to Fig. 2 for GP307-SS3-1). Unlike 

many of the other tests to failure, the strain field did not localize into bands extending from the 

bolt lines, but instead showed highest strain at the Compression Diagonal bolt line nearest to the 

buckling (Fig. 27d). 
42 

(a)
 

(b) 

Figure 20: Out-of plane displacement (W) fields from the reference state to current plate shape for 

GP307-SL3 at ALF of (a) 0.33, (b) 0.52, (c) 0.68, and (d) 0.95 (failure). 
43 

(c)
 

(d)
 

Figure 20 (continued)
 
44 

(a)
 

(b) 

Figure 21: Maximum in-plane shear strain for GP307-SL3 at ALF of (a) 0.33, (b) 0.52, (c) 0.68, 

and (d) 0.95 (failure), with initial yield at 1040 μm/m. 
45 

(c)
 

(d)
 

Figure 21 (continued)
 
46 

Figure 22: Out-of-plane shape of specimen GP307-SL4 at zero load (ALF = 0).
 
47 

7.2.6 GP307-SS3-2 

Specimen GP307-SS3-2 also is one of the samples that had a section machined to represent section 

loss due to corrosion, with the area near the Tension Diagonal being the thinnest cross-section 

(Fig. 2). Figure 28 shows the initial shape of GP307-SS3-2 at the start of the failure test under no 

load, after the location of Z = 0 mm was set using three points as described above. After the rotation, 

the plate has a slight overall tilt from positive Z at the bottom of the chords to negative Z at the 

upper edge of the plate, with the Compression Diagonal being farthest in the negative Z-direction. 

Figure 29 shows the evolution of the Z-direction displacement from the initial shape in Fig. 28. The 

ALF values are in regards to the Tension Diagonal load (Table 4). During the test, the plate shifted 

toward the negative Z-direction through the final buckling of the plate at the Compression Diagonal 

(Fig. 29a–d). The plate at maximum load (Fig. 29d) shows three convex bulges. Two exist from the 

early stages of the test in areas that have reduced thickness: one between the Compression Diagonal 

and West Chord, and one between the Tension Diagonal, Vertical, and East Chord. The last convex 

bulge occurred under the Tension Diagonal starting sometime after ALF = 0.36. Figure 30 plots 

the maximum in-plane shear strains at the same four ALF levels shown in Fig. 29. The yield strain 

in terms of Tresca strain is approximately 1070 μm/m, based on standard material testing of the 

same material. Figures 30a and b have strain ranges predominately in the elastic range and use a 

pseudorandom color map. Figure 30c and d have strain ranges predominately in the plastic strain 

range (spectrum color map) with grey being used for areas of the plate that have not yet reached 

yield. The results show that the Tresca strains were concentrated from an early stage in the field 

areas of the plate, between the end of the diagonals and the chord, with the largest strains occurring 

at the end of the Tension Diagonal in the thinnest portion of the machined section. Unlike many of 

the other tests to failure, the strain field did not localize into bands extending from the bolt lines, 

but instead showed the strain concentrated in the thinned sections of the plate or near the limits of 

the thinned sections (see Fig. 2 GP307-SS3-2, Fig. 30c and d). 
48 

(a)
 

(b) 

Figure 23: Out-of plane displacement (W) fields from the reference state to current plate shape for 

GP307-SL4 at ALF of (a) 0.36, (b) 0.52, (c) 0.80, and (d) 1.07 (failure). 
49 

(c)
 

(d)
 

Figure 23 (continued)
 
50 

(a)
 

(b) 

Figure 24: Maximum in-plane shear strain for GP307-SL4 at ALF of (a) 0.36, (b) 0.52, (c) 0.80, 

and (d) 1.07 (failure), with initial yield at 740 μm/m. 
51 

(c)
 

(d)
 

Figure 24 (continued)
 
52 

Figure 25: Out-of-plane shape of specimen GP307-SS3-1 at zero load (ALF = 0).
 
53 

7.2.7 GP307-SS3-3 

Specimen GP307-SS3-3 is one of the samples that had a long thin section machined above the 

Chord bolt line to represent section loss due to corrosion (Fig. 2). Figure 31 shows the initial shape 

of GP307-SS3-3 at the start of the failure test under no load, after rotation to the selected coordinate 

system. After that rotation, the plate has a slight saddle shape with the Tension Diagonal and West 

Chord in the positive Z-direction, and the Compression Diagonal and East Chord in the negative 

Z-direction. Figure 32 shows the evolution of the Z-direction displacement from the initial shape 

in Fig. 31. The ALF values are in regards to the Tension Diagonal load (Table 4). During the test, 

the plate shifted continuously toward the negative Z-direction. The Compression Diagonal, which 

started in the negative Z-direction, shifted further in that direction through the final buckling of the 

plate (Fig. 32b and c), and always with a slight convex bulge of the plate near the West Chord bolt 

line under the Compression Diagonal (Fig. 32b–d). Figure 33 plots the maximum in-plane shear 

strains at the same four ALF levels shown in Fig. 32. The yield strain in terms of Tresca strain 

is approximately 850 μm/m, based on standard material testing of the same material. Figures 33a 

and b have strain ranges predominately in the elastic range and use a pseudorandom color map. 

Figure 33c and d have strain ranges predominately in the plastic strain range (spectrum color map) 

with grey being used for areas of the plate that have not yet reached yield. The results show that 

the Tresca strains were concentrated from an early stage in the section of the plate with reduced 

thickness, just above the Chord bolt lines. Unlike many of the other tests without reduced sections, 

the strain field did not localize into bands extending from the bolt lines, but instead showed the 

strain concentrated in the thinned section of the plate from the early stages of plastic deformation 

(Fig. 33a–d). Some strain localization is seen along the Vertical bolt line and extending from the 

Tension Diagonal, but the magnitude is much less then the thinned section (Fig. 33c and d). 
54 

(a)
 

(b) 

Figure 26: Out-of plane displacement (W) fields from the reference state to current plate shape for 

GP307-SS3-1 at ALF of (a) 0.12, (b) 0.26, (c) 0.35, and (d) 0.45 (failure). 
55 

(c)
 

(d)
 

Figure 26 (continued)
 
56 

(a)
 

(b) 

Figure 27: Maximum in-plane shear strain for GP307-SS3-1 at ALF of (a) 0.12, (b) 0.26, (c) 0.35, 

and (d) 0.45 (failure), with initial yield at 1060 μm/m. 
57 

(c)
 

(d)
 

Figure 27 (continued)
 
58 

Figure 28: Out-of-plane shape of specimen GP307-SS3-2 at zero load (ALF = 0).
 
59 

7.2.8 GP307-SS3-4 

Specimen GP307-SS3-4 was tested with the addition of a shingle plate (GP307-SS3-shingle) on 

the North face of the connection. GP307-SS3-4 has a long thin section of the plate with reduced 

thickness just above the Chord bolt line (Fig. 2) as an analog to a corroded gusset plate. The shingle 

plate covers most, but not all, of this thinner section. This test is also unique in that there was a 

premature failure of the Tension bolts prior to failure of either plate. After this premature failure, 

some bolt holes in the plate along the Tension Diagonal had to be enlarged to permit reassembly 

of the connection. This substantially damaged the DIC pattern on the shingle plate, but did only 

minor damage to the pattern on the visible portion of the gusset plate. For the gusset plate, the 

damaged pattern still permitted correlation of the gusset plate from the start of testing through the 

bolt failures and to failure (after reassembly), but this is not the case for the shingle plate. For the 

shingle plate, the extent of the pattern damage near the Tension Diagonal made it impossible to 

correlate from the reassembled state to the original condition of the plate. Therefore the results 

presented are split into two sets: one set for for the visible portion of GP307-SS3-4 that covers 

the entire test to failure (using the calibration for GP307-SS3-4 in Tables 2 and 3), and one set 

GP307-SS3-shingle that references the original shape up to the bolt failure (using the calibration 

for GP307-SS3-4 in Tables 2 and 3) and references the after reassembly shape for the final failure 

(using the calibration for GP307-SS3-4 after reassembly in Tables 2 and 3). A simple addition of 

the results is not possible, since the exact locations of the correlation points do not match for the 

two correlations performed for GP307-SS3-shingle. 

Figure 34a and b show the initial shape of GP307-SS3-4 and GP307-SS3-shingle, respectively, 

at the start of the failure test under no load. Figure 34c shows the out-of-plane shape of GP307­

SS3-shingle after reassembly at zero load. The location of Z = 0 mm was set using three points 

on the gusset plate similarly to that described above. After the rotation, GP307-SS3-4 and GP307­

SS3-shingle have a slight saddle shape (Fig. 34a and b) with the Tension Diagonal and West Chord 

in the positive Z-direction and the Compression Diagonal shifted in the negative Z-direction. After 

reassembly, the shingle plate is at rest in a slightly different position and the overall shape is somewhat concave. Note that the ranges of the Z-position for the shingle plate in Fig. 34b and c are 

centered about the approximate thickness of the plate (9.53 mm or 3/8 inch). Figure 35 shows the 

evolution of the Z-direction displacement for GP307-SS3-4 from the initial shape in Fig. 34a. The 

ALF values are in regards to the Tension Diagonal load (Table 4). During the test, GP307-SS3-4 

shifted toward the negative Z-direction from an early stage, with the exception of the Tension Diagonal which generally did not move out-of-plane (Fig. 35a–c). Figures 35a–c are from before the 

premature bolt failure, and only Fig. 35d is from after the reassembly. The displacements plotted 

in Fig. 35d are still in regards to the original shape shown in Fig. 34a, but after reassembly the 

connection was sitting in a position that was in the negative Z-direction from its original position 

(between W = −15 mm to −9 mm). Figure 35d shows that the plate finally buckled at the Compression Diagonal in the negative Z-direction. During the test, GP307-SS3-shingle also shifted toward 

the negative Z-direction from an early stage (Fig. 36a–c), until the premature bolt failure (Fig. 36d, 

when the plate unloaded and settled in the positive Z-direction). Figures 36a–c are from before 
60 

(a)
 

(b) 

Figure 29: Out-of plane displacement (W) fields from the reference state to current plate shape for 

GP307-SS3-2 at ALF of (a) 0.23, (b) 0.36, (c) 0.57, and (d) 0.67 (failure). 
61 

(c)
 

(d)
 

Figure 29 (continued)
 
62 

(a)
 

(b) 

Figure 30: Maximum in-plane shear strain for GP307-SS3-2 at ALF of (a) 0.23, (b) 0.36, (c) 0.57, 

and (d) 0.67 (failure), with initial yield at 1070 μm/m. 
63 

(c)
 

(d)
 

Figure 30 (continued)
 
64 

Figure 31: Out-of-plane shape of specimen GP307-SS3-3 at zero load (ALF = 0). 

the premature bolt failure. Figure 36d is from just after the premature failure, after unloading, and 

only Fig. 36e is from after the reassembly. The displacements shown in Fig. 36a–d are in reference 

to the original shape shown in Fig. 34b, but the displacements shown in Fig. 36e are in reference 

to unloaded state after reassembly shown in Fig. 34c. Figure 36e also shows that the Compression 

Diagonal buckled in the negative Z-direction similar to Fig. 35d. 

Figure 37 plots the maximum in-plane shear strains for the visible portion of GP307-SS3­

4 at the same four ALF levels shown in Fig. 35. The yield strain in terms of Tresca strain is 

approximately 850 μm/m, based on standard material testing of the same GP307-SS3-4 material. 

Figures 37a and b have strain ranges predominately in the elastic range and use a pseudorandom 

color map. Figure 37c and d have strain ranges predominately in the plastic strain range (spectrum 

color map) with grey being used for areas of the plate that have not yet reached the yield strain. The 

results for GP307-SS3-4 show that the Tresca strains were concentrated near the thinned section 

(above the Chord bolt line) and along the Tension bolt lines prior to the premature bolt failure 

(Fig. 37a–c). After reassembly and at maximum load (ALF = 0.99), the strains along the Tension 

bolt lines are reduced as compared to the strains near the thinned section (Fig. 37d). 

Figure 38 plots the maximum in-plane shear strains for GP307-SS3-shingle at the same four 

ALF levels shown in Fig. 36. The initial yield strain in terms of Tresca strain is approximately 

1040 μm/m, based on standard material testing of the same GP307-SS3-shingle material. Figures 38a and b have strain ranges predominately in the elastic range and use a pseudorandom color 

map. Figure 38c–e have strain ranges predominately in the plastic strain range (spectrum color 

map) with grey being used for areas of the plate below the yield strain of 1040 μm/m. The results 
65 

for GP307-SS3-shingle show that the Tresca strains were concentrated near the bolts prior to, and 

just after, the premature bolt failure (Fig. 38a–d). The strains shown in Fig. 38e are in reference to 

the reassembled connection, thus the area in grey does not delineate areas of strain below yield, but 

does describe areas that have not exceeded 1040 μm/m since reassembly. The total strain would 

be the addition of these strains to the unloaded state just after the premature bolt failure (Fig. 38d). 

The strains at failure (Fig. 38e) show similar strain localization to earlier gusset plates, with the 

highest strains along the Chord bolt lines and between the Tension and Compression Diagonal bolt 

lines (through the end of the Vertical bolt line). Also similar to the earlier gusset plate tests, these 

two bands of highest strain are connected by many lower magnitude strain bands. 
66 

(a)
 

(b) 

Figure 32: Out-of plane displacement (W) fields from the reference state to current plate shape for 

GP307-SS3-3 at ALF of (a) 0.24, (b) 0.30, (c) 0.63, and (d) 0.74 (failure). 
67 

(c)
 

(d)
 

Figure 32 (continued)
 
68 

(a)
 

(b) 

Figure 33: Maximum in-plane shear strain for GP307-SS3-3 at ALF of (a) 0.24, (b) 0.30, (c) 0.63, 

and (d) 0.74 (failure), with initial yield at 850 μm/m. 
69 

(c)
 

(d)
 

Figure 33 (continued)
 
70 

(a)
 

(b)
 

(c) 

Figure 34: Out-of-plane shape at zero load of specimen (a) GP307-SS3-4 before the start of testing, 

(b) GP307-SS3-shingle plate before the start of testing, and (c) GP307-SS3-shingle plate after 

premature bolt failure and reassembly. 
71 

7.2.9 GP490-SS3 

Figure 39 shows the initial shape of GP490-SS3 at the start of the failure test under no load. The 

location of Z = 0 mm was set using three points as described above. After the rotation, the plate is 

slightly concave about the ends of the two chord members. Figure 40 shows the evolution of the 

Z-direction displacement from the initial shape in Fig. 39. The ALF values are in regards to the 

Compression Diagonal load (Table 4). During the test, the entire plate shifted toward the negative 

Z-direction from an early stage, with final buckling of the Compression diagonal in that direction 

(Fig. 40d). Figure 41 plots the maximum in-plane shear strains at the same four ALF levels shown 

in Fig. 40. The yield strain in terms of Tresca strain is approximately 1040 μm/m, based on standard 

material testing of the same material. Figures 41a–c have strain ranges predominately in the elastic 

range and use a pseudorandom color map. Figure 41d has a strain range predominately in the 

plastic strain range (spectrum color map) with grey being used for areas of the plate that have not 

yet reached the yield strain. The results show that the Tresca strains were concentrated between 

the ends of the Compression and Tension Diagonals from the early stages of loading, with slightly 

larger strains occurring at the end of the Compression Diagonal and along the Chord bolt lines. The 

strain field is more uniform in the early stages of loading, but the last stage (ALF = 0.73) shows 

substantial strain localization, along the Chord bolt lines. Additional strain localizations of lower 

magnitude extends from the Compression bolt line to the Tension bolt line with small extensions 

to the Chord bolt lines and the Vertical bolts. 
72 

(a)
 

(b) 

Figure 35: Out-of plane displacement (W) fields from the reference state to current plate shape for 

GP307-SS3-4 at ALF of (a) 0.27, (b) 0.54, (c) 0.89, and (d) 0.99 (after premature bolt failure and 

reassembly). 
73 

(c)
 

(d)
 

Figure 35 (continued)
 
74 

(a)
 

(b) 

Figure 36: Out-of plane displacement (W) fields from the reference to current plate shape for
 

GP307-SS3-shingle at ALF of (a) 0.27, (b) 0.54, (c) 0.89, (d) after unload from ALF = 0.89, and
 

(e) 0.99 with W referenced to the unloaded position after reassembly (Fig. 134c). 
75 

(c)
 

(d)
 

Figure 36 (continued)
 
76 

(e)
 

Figure 36 (continued)
 
77 

7.2.10 GP490-SS3-1 

Figure 42 shows the initial shape of GP490-SS3-1 at the start of the failure test under no load, 

after rotating to the selected coordinate system. After that rotation, the plate is relatively flat with 

a slight depression near the East Chord bolt line, and a slight twist along the West edge of the 

plate. Figure 43 shows the evolution of the Z-direction displacement from the initial shape in 

Fig. 42. The ALF values are in regards to the Tension Diagonal load (Table 4). During the test, the 

entire plate shifted toward the negative Z-direction from an early stage, through the final buckling 

of the Compression Diagonal in the negative Z-direction with a convex bulge of the plate under 

the Compression Diagonal (Fig. 43d). Figure 44 plots the maximum in-plane shear strains at the 

same four ALF levels shown in Fig. 43. The yield strain in terms of Tresca strain is approximately 

1030 μm/m, based on standard material testing of the same material. Figures 44a–c have strain 

ranges predominately in the elastic range and use a pseudorandom color map. Figure 44d has a 

strain range predominately in the plastic strain range (spectrum color map) with grey being used 

for areas of the plate that have not yet reached yield. The results show that the Tresca strains were 

concentrated between the ends of the Compression and Tension Diagonals from the early stages of 

loading, with the largest strains occurring at the end of the Tension Diagonal and along the Chord 

bolt lines. The strain field is more diffuse in the early stages of loading (Fig. 44a and b), then the 

later two stages (Fig. 44c and d) which show more strain localizations. These long localized bands 

extend along the Chord bolt line and from the bolt lines of the diagonals to one another, with added 

bands of high strain reaching from the chord band to the other long band between the diagonals. 

This is similar to Figure 41d for GP490-SS3, but the magnitude of strain is much higher in Fig. 44d 

and more weighted to the Tension Diagonal half of the plate. 
78 

(a)
 

(b) 

Figure 37: Maximum in-plane shear strain for GP307-SS3-4 at ALF of (a) 0.27, (b) 0.54, (c) 0.89, 

and (d) 0.99 (failure), with initial yield at 850 μm/m. 
79 

(c)
 

(d)
 

Figure 37 (continued)
 
80 

(a)
 

(b) 

Figure 38: Maximum in-plane shear strain for GP307-SS3-shingle at ALF of (a) 0.27, (b) 0.54, (c) 

0.89, (d) after unload from ALF = 0.89, and (e) at ALF = 0.99 after reassembly where Tresca strain 

values are in addition to the strains shown in (d). Initial material yield strain is at 1040 μm/m. 
81 

(c)
 

(d)
 

Figure 38 (continued)
 
82 

(e)
 

Figure 38 (continued)
 
83 

Figure 39: Out-of-plane shape of specimen GP490-SS3 at zero load (ALF = 0).
 
84 

(a)
 

(b) 

Figure 40: Out-of plane displacement (W) fields from the reference state to current plate shape for 

GP490-SS3 at ALF of (a) 0.59, (b) 0.61, (c) 0.63, and (d) 0.73 (failure). 
85 

(c)
 

(d)
 

Figure 40 (continued)
 
86 

(a)
 

(b) 

Figure 41: Maximum in-plane shear strain for GP490-SS3 at ALF of (a) 0.59, (b) 0.61, (c) 0.63, 

and (d) 0.73 (failure), with initial yield at 1040 μm/m. 
87 

(c)
 

(d)
 

Figure 41 (continued)
 
88 

Figure 42: Out-of-plane shape of specimen GP490-SS3-1 at zero load (ALF = 0).
 
89 

7.2.11 GP490-LS3-1 

Figure 45 shows the initial shape of GP490-LS3-1 at the start of the failure test under no load. The 

location of Z = 0 mm was set using three points as described above. After the rotation, the plate 

has a slight saddle shape with the Tension Diagonal and West Chord in the positive Z-direction 

and the Compression Diagonal and East Chord in the negative Z-direction. Figure 46 shows the 

evolution of the Z-direction displacement from the initial shape in Fig. 45. The ALF values are 

in regards to the Tension Diagonal load (Table 4). During the test, the entire plate shifted toward 

the negative Z-direction from an early stage, until the final buckling of the Compression diagonal 

in the positive Z-direction (Fig. 46d). Figure 47 plots the maximum in-plane shear strains at the 

same four ALF levels shown in Fig. 46. The yield strain in terms of Tresca strain is approximately 

1040 μm/m, based on standard material testing of the same material. Figures 47a–c have strain 

ranges predominately in the elastic range and use a pseudorandom color map. Figure 47d has a 

strain range predominately in the plastic strain range (spectrum color map) with grey being used 

for areas of the plate that have not yet reached the yield strain. The results show that the Tresca 

strains were concentrated between the ends of the Tension and Compression Diagonals from the 

early stages of loading, with the largest strains occurring at the end of the Tension Diagonal and 

along the Chord bolt lines. The strain field is more diffuse in the early stages of loading (Fig. 47a 

and b). In the later stages (Fig. 47c and d) more strain localizations are present. These begin by 

ALF = 0.68 (in Fig. 47c) extending from the Tension Diagonal bolt line to the Vertical bolt line, 

and later (in Fig. 47d) extending between the Tension and Compression Diagonal bolt lines though 

the end of the Vertical bolt line with various extensions down to the Chord bolt lines. 

Attempts were made to apply a brittle coating to the outside face of the South gusset plate with 

limited success. In many cases, the coating did not flake off as intended even at the maximum 

strains achieved during the tests to failure. One of the tests where the coating was successful was 

for GP490-LS3-1. Figures 48 and 49 show the brittle coating results on the South face of the 

connection compared to the Tresca strains on the North face. In both figures, the brittle coating 

results for the South face are mirror images of the South plate, thus the Tension Diagonal is on 

the upper left and the Compression Diagonal is on the upper right. Also in both figures, the first 

image is of the brittle coating before testing began at zero load (ALF = 0). The second image in 

each figure is the brittle coating after the specified amount of loading in terms of ALF. The brittle 

coating was not calibrated so the strain level to cause flaking is not known quantitatively, but in the 

images the results of straining is a change from an initial grey or black color to a white in specific 

areas. For example, the distinct thin bands of white under the Tension Diagonal in Fig. 48a that do 

not appear in Fig. 48b. The third plot in each figure is a plot of the Tresca strain where the plastic 

strain range is shown in color and the strains below the expected yield for the material (1030 μm/m) 

is shown in grey. When comparing the results for the brittle coating and the DIC measurements 

two details should be kept in mind: (1) the brittle coating and DIC measurements are made on two 

different sides of the connection, and although the connection is designed as symmetric the out of 

plane motion (Fig. 46) could suggest some bending thus creating a difference in strain from the 

South to the North plate; (2) the spatial resolution of the strain system is on the order of the DIC 
90 

(a)
 

(b) 

Figure 43: Out-of plane displacement (W) fields from the reference state to current plate shape for 

GP490-SS3-1 at ALF of (a) 0.19, (b) 0.45, (c) 0.69, and (d) 0.92 (failure). 
91 

(c)
 

(d)
 

Figure 43 (continued)
 
92 

(a)
 

(b) 

Figure 44: Maximum in-plane shear strain for GP490-SS3-1 at ALF of (a) 0.19, (b) 0.45, (c) 0.69, 

and (d) 0.92 (failure), with initial yield at 1030 μm/m. 
93 

(c)
 

(d)
 

Figure 44 (continued)
 
94 

subset spacing (average S = 5 mm, Table 5) while the brittle coating may capture much finer areas 

of high strain. 

In Fig. 48b and c, the bands of high Tresca strain are located in similar position to some of 

the white lines on the brittle coating at the same load level. These areas along the East Chord bolt 

line, between the Chord and Vertical bolts, and between the lower Tension Diagonal bolts and the 

Vertical and East Chord. There also exists additional white lines in the brittle coating (Fig. 48b) 

extending from the Tension diagonal bolt closest to the Vertical and extending from the second 

bolt from the plate edge on the East Chord. These two lines do not have a clear corresponding 

band in Fig. 48c, which shows these areas are only being elastically deformed. There also exists 

an area of plastic strain in Fig. 48c above the West Chord that is somewhat diffuse, that does not 

correspond to any visible change in the brittle coating (Fig. 48b). The lower spatial resolution 

of the DIC versus the brittle coating may explain the white bands where the DIC measures only 

elastic strain, but does not explain the area that has DIC measured plastic strains where there is no 

change in the brittle coating. This latter result could be a result of the the out of plane shape near 

the Compression Diagonal (Fig. 45) which starts concave to the North and continues developing in 

that direction (Fig. 46), which suggests the South plate may be concave in the same location. This 

could result in some bending and increased tensile strains in the North plate and decreased tensile 

strains in the South plate below the Compression Diagonal. 

Figure 49 shows similar behavior to Fig. 48 after the failure load (ALF = 0.88) had been reached 

and the connection had been unloaded. Most of the bands seen in the brittle coating (Fig. 49b) are 

also seen in the DIC results (Fig. 49c) although not to the same level of spatial refinement. Again 

there are areas below the Tension Diagonal that show bands that are not fully reflected in the DIC 

data. Although areas near the Compression Diagonal that show plastic strains in the DIC results 

(Fig. 49c) that are not reflected in the brittle coating image (Fig. 49b) are also visible in (Fig. 49), 

there also are some bands to the West of the Vertical that appear in both the brittle coating and DIC 

results. 
95 

Figure 45: Out-of-plane shape of specimen GP490-LS3-1 at zero load (ALF = 0).
 
96 

7.2.12 GP490-LS3-2 

Figure 50 shows the initial shape of GP490-LS3-2, with two angles added on the upper plate edge 

and the West plate edge, at the start of the failure test under no load. The location of Z = 0 mm 

was set using three points as in the other cases. After the rotation, the plate has a slight saddle 

shape with the Tension Diagonal and West Chord in the negative Z-direction and the Compression 

Diagonal and East Chord in the positive Z-direction. Figure 51 shows the evolution of the Zdirection displacement from the initial shape in Fig. 50. The ALF values are in regards to the 

Compression Diagonal load (Table 4). During the test, the entire plate shifted toward the negative 

Z-direction from an early stage, through the final buckling of the Compression Diagonal in the 

negative Z-direction with a convex bulge of the plate under the Compression Diagonal (Fig. 51d). 

Figure 52 plots the maximum in-plane shear strains at the same four ALF levels shown in Fig. 51. 

The yield strain in terms of Tresca strain is approximately 1020 μm/m, based on standard material 

testing of the same material. Figures 52a–c have strain ranges predominately in the elastic range 

and use a pseudorandom color map. Figure 52d has a strain range predominately in the plastic 

strain range (spectrum color map) with grey being used for areas of the plate that have not yet 

reached the yield strain. The results show that the Tresca strains were concentrated between the 

end of the Compression Diagonal and the West Chord from the early stages of loading, with the 

largest strains occurring at the end of the Compression Diagonal and along the West Chord bolt 

lines (Fig. 52c). The strain field is more diffuse in the early stages of loading (Fig. 52a and b). 

In the later stages (Fig. 52c and d) more strain localizations are present, starting in Fig. 52c and 

extend between the Compression Diagonal bolt lines to the Vertical and West Chord bolt lines. 
97 

7.3 Comparison 

Figures 53a–n replot the Tresca strain results shown at the highest ALF values in the Section 7.2, 

but on a common legend range with grey being used for areas of the plate that have strains <

970 μm/m (the average yield value). Figure 53h is for GP307-SS3-4 referenced to the initial 

unloaded plate at maximum load. However, Fig. 53i and j are for GP307-SS3-shingle after the 

premature bolt failure (unloaded) referenced to the initial unloaded plate, and at maximum load 

after reassembly referenced to the reassembled (but deformed) unloaded plate, respectively. The 

total strain for GP307-SS3-shingle is the addition of the strains in Fig. 53j to the strains at the 

unloaded state just after the premature bolt failure in Fig. 53i. The predominant strain pattern at 

failure for most of the plates tested is bands of localized strain that extend between the adjacent 

bolt lines and along the top Chord bolt line. Two plates, GP307-SS3-1 in Fig. 53e and to a lesser 

extent GP307-LS3 in Fig. 53b, show buckling related strains being the dominant strains present. 

Only plates GP307-SS3-2 and GP307-SS3-3 (Figs. 53f and g, respectively), which have sections 

reduced in thickness as an analog to corrosion related section loss, show more uniform areas of high 

strain (in the reduced thickness areas). The only localized bands of strain seen in these two cases 

are of much lower magnitude between the Vertical and the diagonals (blue bands in Fig. 53g). One 

could separate the plates with distinct localized strain bands into two groups based on the maximum 

strain achieved using the middle value of the common range (17 460 μm/m) as a threshold. The 

plates with strains higher than 17 460 μm/m (Fig. 53c, d, h/j, and l) have undergone substantial 

shear strain, typically well in excess of the threshold, along the Chord bolt lines and/or in the 

plate areas between the two diagonals. The plates with maximum strains lower than 17 460 μm/m 

(Fig. 53a, k, m, and n) have developed some distinct localized strain bands, but the plate seems to 

have failed by buckling before the shear strain on the plate could become dominant. 

8 SUMMARY 

An overview of 3D digital image correlation measurements during testing of large structural connections has been presented. Twelve full-scale bridge gusset plate connections were tested with 

various geometries and boundary conditions (Ocel et al., 2012). These experiments are part of 

the NCHRP Project 12-84 “Guidelines for the Load and Resistance Factor Design and Rating of 

Riveted and Bolted Gusset Plate Connections for Steel Bridges”. The measurements described 

here are in regards to the tests performed to failure (i.e., maximum load carrying capacity of the 

connection). This report only presents a very small portion of the overall DIC measurements, but 

the remainder of the results will be made available. 

The layout, calibration, and measurement procedure associated with the digital image correlation system were described in detail to aid in understanding of the results. A specially designed 

black on white pattern was applied to the samples for the correlation analysis to track throughout 

the loading process. During each of the twelve tests to failure, a series (typically about 150) of image pairs were taken for subsequent digital image correlation analysis. Although all of the image 

pairs were processed, only a very small portion of the results are presented here. In the Results 

(Section 7), an Example Case (Section 7.1) of the variables that are measured and derived from 
98 

(a)
 

(b) 

Figure 46: Out-of plane displacement (W) fields from the reference state to current plate shape for 

GP490-LS3-1 at ALF of (a) 0.43, (b) 0.53, (c) 0.68, and (d) 0.88 (failure). 
99 

(c)
 

(d)
 

Figure 46 (continued)
 
100 

(a)
 

(b) 

Figure 47: Maximum in-plane shear strain for GP-490LS3-1 at ALF of (a) 0.43, (b) 0.53, (c) 0.68, 

and (d) 0.88 (failure), with initial yield at 1040 μm/m. 
101 

(c)
 

(d)
 

Figure 47 (continued)
 
102 

(a)
 

(b)
 

(c) 

Figure 48: Comparison of brittle coating and maximum in-plane shear strain for GP490-LS3-1 

connection. Mirror images of brittle coating on South gusset plate (a) unloaded initial condition 

and (b) at ALF = 0.75, and (c) maximum in-plane shear strain for North gusset plate at ALF = 0.75. 
103 

(a)
 

(b)
 

(c) 

Figure 49: Comparison of brittle coating and maximum in-plane shear strain for GP490-LS3-1 

connection. Mirror images of brittle coating on South gusset plate (a) unloaded initial condition 

and (b) unloaded after ALF = 0.88 (failure), and (c) maximum in-plane shear strain for North gusset 

plate at ALF = 0.88. 
104 

Figure 50: Out-of-plane shape of specimen GP490-LS3-2 (and reinforcement structural angles) at 

zero load (ALF = 0). 

those measurements was presented for one plate (GP307-SL3) at two points during testing (i.e., the 

initial condition and at failure). These same data are available for every image pair from the initial 

condition through the failure condition of each plate tested. Since it is impossible to describe all of 

these results in a report format, it was decided to present just two additional subsets of the overall 

digital image correlation data. 

The Key Points (Section 7.2) results, show the evolution of the out of plane shape and maximum 

shear strain field at four points in loading from the initial condition to failure. These are very useful 

in visualizing the mechanisms (buckling and/or shear failure of the plate) that lead to eventual 

failure of the connection. Often shearing of the plate dominated the early stages of loading, but by 

the point of failure there was an out of plane motion of the Compression Diagonal more typical 

of a buckling failure. This evolution is often seen as even more gradual when looking at all of the 

data for a given test. The evolution of maximum in-plane shear strain bands is seen quite clearly in 

many of the plates. These localized bands of deformation frequently extended from the bolt lines 

of one member to another through the large open areas of the plate, while these bands also occurred 

along the top bolt lines of the two Chord members. 

The final section of the results again plots the failure strain fields of Section 7.2, but on a 

common contour scale to permit Comparison (Section 7.3) of the strain fields from one plate to 

another. It is in this section that one can more easily see the plates that failed after significant 

shearing versus the ones that failed with minimal or no shearing. The comparison also shows very 

clearly the effect of the plates with reduced thickness as an analog to section loss due to corrosion. 

Overall the measurements showed reasonable uncertainties on the order of ± 175 μm/m of 
105 

maximum in-plane shear strain. The measured out of plane initial shapes of the plates typically 

matched qualitative inspections of the connection, and with the exception of one plate (GP307­

LS3). These shapes were generally on the same order (about ± 4 mm) as measurements through 

other methods. The large (about ± 20 mm) out of plane twisted initial shape does not seem reasonable, and puts the calibration for plate GP307-LS3 into question. The same effect was not seen in 

the uncertainty analysis for the out of plane displacements from the initial shape or the maximum 

shear strains calculated at zero load. Further, the results for the deformed shapes and strains did 

not show a similar variation based on the location in the images suggesting the results were not 

effected as dramatically. 
106 

(a)
 

(b) 

Figure 51: Out-of plane displacement (W) fields from the reference state to current plate shape for
 

GP490-LS3-2 (and reinforcement structural angles) at ALF of (a) 0.31, (b) 0.48, (c) 0.68, and (d)
 

0.87 (failure). 
107 

(c)
 

(d)
 

Figure 51 (continued)
 
108 

(a)
 

(b) 

Figure 52: Maximum in-plane shear strain for GP490-LS3-2 (and reinforcement structural angles) 

at ALF of (a) 0.31, (b) 0.48, (c) 0.68, and (d) 0.87 (failure), with initial yield at 1020 μm/m. 
109 

(c)
 

(d)
 

Figure 52 (continued)
 
110 

(a)
 

(b) 

Figure 53: Failure strains on a common color scale range: (a) GP307-SS3, (b) GP307-LS3, (c) 

GP307-SL3, (d) GP307-SL4, (e) GP307-SS3-1, (f) GP307-SS3-2, (g) GP307-SS3-3, (h) GP307­

SS3-4, (i) GP307-SS3-shingle (after premature bolt failure and unload), (j) GP307-SS3-shingle 

(referenced to the reassembled, but deformed, specimen) (k) GP490-SS3, (l) GP490-SS3-1, (m) 

GP490-LS3-1, and (n) GP490-LS3-2 
111 

(c)
 

(d)
 

Figure 53 (continued)
 
112 

(e)
 

(f)
 

Figure 53 (continued)
 
113 

(g)
 

(h)
 

Figure 53 (continued)
 
114 

(i)
 

(j)
 

Figure 53 (continued)
 
115 

(k)
 

(l)
 

Figure 53 (continued)
 
116 

(m)
 

(n)
 

Figure 53 (continued)
 
117 

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