Numerical and experimental investigation of the in-plane behavior

of rectangular steel-plate composite walls

Siamak Epackachi1, Nam H. Nguyen2, Efe G. Kurt3, Andrew S. Whittaker4, and Amit H. Varma5

1 PhD Candidate, Dept. of Civil, Structural and Environmental Engineering, University at Buffalo,

Buffalo, NY 14260. Email: siamakep@buffalo.edu 2 PhD Candidate, Dept. of Civil, Structural and Environmental Engineering, University at Buffalo,

Buffalo, NY 14260. Email: namnguye@buffalo.edu 3 PhD Candidate, School of Civil Engineering, Purdue University, West Lafayette, IN 47907. Email:

ekurt@purdue.edu 4 Professor and Chair; Director, MCEER; Dept. of Civil, Structural and Environmental Engineering,

University at Buffalo, Buffalo, NY 14260. Email: awhittak@buffalo.edu 5 Associate Professor, School of Civil Engineering, Purdue University, West Lafayette, IN 47907.

Email: ahvarma@purdue.edu

ABSTRACT

Steel-plate composite (SC) walls are composed of steel faceplates, infill

concrete, shear studs bonding the faceplate to the infill, and tie rods linking the

faceplates. In new build nuclear power plants, elastic response is sought of SC walls

in design basis earthquake shaking and numerical and experimental studies on SC

walls have focused primarily on response to design basis loadings. The inelastic

response of SC walls for beyond design basis earthquake shaking has yet to be

explored and characterized.

The experimental and numerical response of four SC walls subjected to cyclic

in-plane loading is summarized in this paper. The walls have an aspect ratio of 1.0 and

are flexure-critical. A number of design parameters are investigated, including infill

concrete thickness, reinforcement ratio, stud spacing, and tie bar spacing. Numerical

models of these walls are constructed using the general-purpose finite element code

LS-DYNA. The numerical analyses, and key experimental results are presented.

INTRODUCTION

Steel-concrete (SC) composite walls are being used for the construction of

containment internal structures and shielding structures in large light water reactors in

the United States and abroad. SC walls have been proposed for other nuclear

construction, including small modular reactors. To date, design of SC walls has been

based in part on proprietary test data and limited data available in the literature (e.g.,

Akiyama et al. (1989), Takeda et al. (1995), Takeuchi et al. (1995), Usami et al. (1995),

Kazuaki et al. (2001), Emori (2002), Clubley et al. (2003), Ozaki et al. (2004), Eom et

al. (2009), Varma et al. (2011), Cai et al. (2012)). Most of these tests were conducted

at small scales and have focused on the essentially elastic range of response.

This paper presents results of a numerical and experimental investigation on the

behavior of large-scale steel-plate composite (SC) walls subjected to cyclic lateral

loading. The testing program involved four rectangular SC wall specimens with an

aspect ratio (height-to-length) of 1.0. The design parameters considered in the

investigation included wall thickness, reinforcement ratio, stud spacing, and tie bar

spacing. Details of the testing program are provided in Epackachi et al. (2014). The

general-purpose finite element code LS-DYNA (2012a and 2012b) is used for the

numerical studies. The finite element models are validated using the test data of

rectangular SC walls.

EXPERIMENTAL PROGRAM

Test specimen description

Four large-size specimens (SC1 through SC4) were built and tested under

displacement-controlled cyclic loading. The tests were conducted in the NEES

laboratory at the University at Buffalo with support from the Bowen Laboratory at

Purdue University. The design variables considered in the testing program include

reinforcement ratio, tie-rod and stud spacing. The aspect ratio (height-to-length, H/L)

of all walls was 1.0. Information on the four walls is provided in Table 1. In this table,

studs and tie rods serve on connectors, spaced at distance S, the overall thickness of

the wall is T, the thickness of each faceplate is tp, the reinforcement ratio is 2tp/T, and

the faceplate slenderness ratio is S/tp.

Table 1. Test specimens

Specimen

Wall dimension

(H×L×T)

(in. × in. × in.)

Stud

spacing

(in.)

Tie rod

spacing

(in.)

Reinforcement

ratio

(%)

Faceplate

slenderness

ratio

Day-of-test

wall concrete strength

(ksi)

SC1 60×60×12 4 12 3.1 21 4.5

SC2 60×60×12 - 6 3.1 32 4.5

SC3 60×60×9 4.5 9 4.2 24 5.3

SC4 60×60×9 - 4.5 4.2 24 5.3

The diameter of the studs and tie rods was 0.375 in. for all walls; the studs and

tie rods were fabricated from 50 ksi steel. The yield and ultimate strengths of the steel

faceplates calculated from three coupon tests, were 38 and 55 ksi, respectively. The

nominal compressive strengths of the infill concrete and the foundation concrete were

4 and 6 ksi, respectively.

Each SC wall was installed on top of a re-usable foundation block. The base of

each wall included a 1-in. thick base plate to which the faceplates were CJP groove

welded. Two rows of 13 number 0.675-in. diameter studs were welded to the base

plate to bond the concrete and improve the transfer of shearing and tensile forces. The

base plate was installed atop a 1-in. thick base plate embedded in the foundation block

and was secured to the foundation block using 22 1.25-in. diameter threaded B7 bars

that were post-tensioned to 100 kips per bar. Figure 1 is a photograph of SC1 installed

on the foundation block.

Figure 1. Specimen SC1

Pre-test analysis

Pre-test predictions of the responses of trial SC walls were made to determine

whether the specimens were flexure-critical or shear-critical. Nominal material

properties were used. The flexural strength of the SC walls was estimated using the

cross-section program XTRACT (Chadwell et al. 2002); the corresponding maximum

shearing forces were 344 kips and 328 kips for SC1/SC2 and SC3/SC4, respectively.

The flexural strength calculation assumed perfect bond between the steel faceplates

and the infill concrete. The maximum shearing resistance of the walls per the draft

Appendix N9 to AISC N690 (AISC 2013), Ozaki et al. (2004), and Varma et al. (2011,

2012) was 870/855/815 kips for SC1/SC2 and 840/855/780 kips for SC3/SC4, which

assumes shear yielding of the faceplates. These calculations showed the walls to be

flexure critical, with a maximum resistance less than the capacity of the actuators

proposed for loading the walls.

Test setup

Two horizontally inclined high force-capacity actuators were used to apply

cyclic lateral loads to the top of the SC walls. The foundation block was post-tensioned

to the strong floor with 14 number 1.5 in. diameter Dywidag bars to prevent foundation

movement during testing. The test setup is shown in Figure 2.

The displacement-controlled, reversed cyclic loading was based on that

proposed by ACI Committee 374. Two cycles of loading were imposed at

displacements equal to fractions and multiplies of a reference displacement (=0.14

inch): 0.1, 0.5, 0.75, 1, 2 ... 15, where the calculation of the reference displacement is

described in Epackachi (2014). The loading speed was 0.01 in./sec.

Figure 2. SC wall test setup

Instrumentation

Krypton light-emitting diodes (LEDs), rosette strain gages, linear

potentiometers, Temposonic displacement transducers, and linear variable

displacement transducers were used to monitor the response of the walls.

Potentiometers and Temposonics were attached to the ends of the walls to measure in-

plane displacement. Potentiometers measured the out-of-plane displacements of the

walls. The movement of the foundation block relative to the strong floor was

monitored using potentiometers and Krypton LEDs.

Krypton LEDs were attached to one steel faceplate per wall to measure in-

plane and out-of-plane displacements. Rosette strain gages were installed at three

levels on the other faceplate to directly measure strains at discrete locations. The lateral

load applied to each wall was calculated as the sum of the in-plane components of the

actuator forces.

POST-TEST ANALYSIS OF SC WALLS

Data from the tests of the four large-scale rectangular SC walls were used to

benchmark the finite element model. The numerical study was undertaken using the

general purpose finite element code LS-DYNA (2012a and 2012b).

The Winfrith concrete model (LS-DYNA 2012b) in LS-DYNA (MAT085)

was used for the infill concrete. The piecewise-linear-plasticity material model

(MAT024) in LS-DYNA (2012b) was used for steel faceplates and connectors.

Friction between the infill concrete and the steel faceplates, the infill concrete and the

baseplate, and the base plate and the steel plate embedded in the foundation block was

considered using CONTACT-AUTOMATIC-SURFACE-TO-SURFACE

formulation available in LS-DYNA (2012a). The friction coefficients for the

concrete/steel and steel/steel interfaces were set equal to 0.3 and 0.4, respectively. The

steel faceplates were tied to the baseplate using the kinematic constraint, CONTACT-

TIED-SHELL-EDGE-TO-SURFACE, available in LS-DYNA (2012a).

Neglecting slip between the connectors and the infill concrete, the studs and

tie rods were coupled to the infill concrete using the CONSTRAINED-LAGRANGE-

IN-SOLID formulation in LS-DYNA.

Beam elements were used to represent the studs and tie rods. Eight-node solid

elements were used to model the infill concrete and the base plates; four-node shell

elements were used for the steel faceplates. Post-tensioning bars connecting the SC

wall to the foundation block were modeled using spring elements. The infill concrete

was modeled with 1 in × 1 in × 1 in elements and the steel faceplates were modeled

with 1 in × 1 in elements.

The constant stress formulation (ELFORM=1 in LS-DYNA) and Belytschko-

Tsay formulation were used for the solid elements and shell elements, respectively.

The cross section integrated beam element (Hughes-Liu beam in LS-DYNA (2012a))

was used for shear studs and tie rods. Springs were modeled using discrete element

formulation. The LS-DYNA model is shown in Figure 3.

(a) Infill concrete (b) Specimen SC2

Figure 3. LS-DYNA model of SC wall

ANALYSIS AND TEST RESULTS

Summary of test results

Key test results are provided in Table 2. The initial stiffness of SC3 and SC4

was less than that of the thicker SC1. The initial stiffness of SC2 was substantially less

than SC1, which was not expected and is attributed to flexibility at the base of the wall.

Buckling of the faceplates occurred at their free edges prior to achieving peak load,

noting that studs were not provided at the vertical free edges. Plate buckling extended

towards the center of wall during subsequent cycles of loading and was affected by the

connector spacing.

Yielding of the faceplates occurred prior to peak load. Peak load was observed

at a relatively high drift angle of 1.1+%. The peak loads developed in SC1 and SC2,

and SC3 and SC4 are similar, which indicates that connector spacing in the range

provided does not impact the peak shearing resistance in flexure-critical walls. The

peak loads in SC1 and SC2 are greater than SC3 and SC4 because the infill concrete

in SC1 and SC2 is 3 inches thicker. The drift angle at 80% of peak load provides some

insight into the importance of the connector spacing (or faceplate slenderness ratio).

Given that the walls sustained their peak loads at the same drift angle of 1.18%, the

greater the drift angle at 80% peak load, the slower the deterioration of strength with

increasing displacement. Wall SC1 had the smallest slenderness ratio of 21 and the

greatest drift angle at 80% peak load.

Table 2. Results summary for SC1 through SC4

Specimen

Initial

stiffness

(kips/in.)

Data point

Onset of

steel plate

buckling

Onset of

steel plate

yielding

Peak load Drift angle

at 80%

peak load

(%)

Pos/Neg Drift angle

(%)

Load

(kips)

Drift

angle

(%)

Load

(kips)

Pos/Neg

Drift angle

(%)

Pos/Neg

SC1 1680 0.48 240 0.48 317/320 1.18/1.18 2.42/2.56

SC2 1240 0.48 200 0.48 314/319 1.18/1.18 1.85/1.74

SC3 1380 0.70 185 0.48 265/275 1.40/1.18 1.69/1.88

SC4 1310 0.70 200 0.48 270/275 1.18/1.18 1.94/2.40

Predicted and measured damage to SC walls

The damage progression in the four walls was identical, namely cracking and

crushing of infill concrete at the toes of the walls, outward buckling and yielding of

the steel faceplates near the base of the wall, and tearing of the faceplates at their

junction with the base plate. Buckling of the faceplates would have been delayed if a

vertical row of studs had been provided near the boundaries of the walls. The damage

to the infill concrete was concentrated around the level of the first row of connectors

in all four walls.

The predicted damage and a photograph of damage to SC2 are presented in

Figure 4a. As seen in Figure 4a, the damage to SC2 including tensile cracking and

crushing of the concrete at the ends of the wall, and outward buckling and tearing of

the steel faceplates at the base of the wall are captured using the developed finite

element model of SC walls.

Damage to the infill concrete of specimen SC2 is presented in Figure 4b. The

damage was both observed and predicted above the base plate, at the level of the heads

of the studs attached to the base plate.

(a) Damage to specimen SC2; test (Left), and analysis (Right)

(b) Damage to infill concrete in specimen SC2; test (Left), and analysis (Right)

Figure 4. Predicted and measured damage to specimen SC2

Load-displacement cyclic response

The DYNA-predicted and experimentally-measured force-displacement

relationships for SC1 through SC4 are presented in Figure 5. The measured load-

displacement relationships are similar, with higher peak loads in the two thicker walls:

SC1 and SC2. Prior to the yielding of the steel faceplates, the residual drift ratios were

less than 0.08%. The intra-cycle reduction of stiffness was observed first at

displacements greater than those associated with yielding of the steel faceplates.

Pinched hysteresis and loss of strength and stiffness were observed for all walls at

displacements greater than those corresponding to peak strength. The pinching and

strength degradation are attributed to faceplate buckling, cracking and crushing of the

infill concrete, and tearing of the steel faceplate immediately above the baseplate.

There is a good agreement between the measured and predicted cyclic

responses of SC walls. The predictions of the initial stiffness, the peak shearing

resistance and the rate of the reloading/unloading stiffness deteriorations compare

favorably to the test results. The predicted post-peak response correlated well with the

experimental results in SC2 and SC4, but the rate of the post-peak deterioration are

under- and over-estimated in SC1 and SC3, respectively. Pinching is successfully

simulated using a robust smeared crack concrete model, which considers three

orthogonal crack planes per element and allows cracks to close and re-open during the

analysis.

(a) SC1 (b) SC2

(c) SC3 (d) SC4

Figure 5. Predicted and measured lateral load - displacement relationships of SC walls

CONCLUSIONS

Four large-scale SC walls (SC1 through SC4) were constructed at the NEES

facility at the University at Buffalo as part of a NSF-funded NEES project on low

aspect ratio conventional and composite shear walls. The walls had an aspect ratio of

1.0 and were flexure critical. The walls were tested under reversed cyclic loading. The

design space for the walls included reinforcement ratio and faceplate slenderness ratio.

Finite element models of the steel-plate composite shear walls were developed using

the general-purpose finite element code LS-DYNA. Verification studies were

undertaken through simulation of the nonlinear cyclic in-plane behavior of the four SC

walls.

The four flexure-critical walls sustained peak loads close to those predicted by

pre-test calculations using commercially available software. Faceplate slenderness

ratio did not influence the peak resistance of the walls, for the range of slenderness

ratio studied (21 to 32).

The developed finite element model of SC wall successfully simulated the damage in

SC walls. The measured initial stiffness, peak shearing strength and cyclic response of

four tested SC walls were successfully predicted using LS-DYNA.

ACKNOWLEDGEMENTS

This project was supported in part by the US National Science Foundation

under Grant No. CMMI-0829978. This support is gratefully acknowledged. We also

thank the technical staff of the NEES laboratory at the University of Buffalo, and the

Bowen Laboratory at Purdue University, and LPCiminelli Inc. for their contributions

to the project.

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