Proceedings of the

Annual Stability Conference

Structural Stability Research Council

Orlando, Florida, April 12-15, 2016

Effect of Imperfections on the Compression Behavior of SC Walls

Saahastaranshu R. Bhardwaj1, Amit H. Varma2

Abstract

Steel-plate composite (SC) walls are increasingly being used in the construction of safety related

nuclear facilities. Appendix N9 of the Supplement No.1 to AISC N690-12 (N690s1) provides

specifications for design of SC walls. SC walls need to be designed for the SC specific limit state

of faceplate buckling. The spacing of steel anchors and tie bars can be checked to ensure that

limit state of faceplate yielding precedes faceplate buckling. The compression behavior of SC

walls is affected by faceplate slenderness, faceplate waviness, shear stud and tie bar spacing,

concrete pour height, and strength of faceplates and concrete infill. There is a need to better

understand how these parameters modify the compression behavior and failure mode of SC

walls. This paper outlines a procedure to incorporate the effects of these parameters on the

compression behavior of SC walls. The implementation of the procedure is illustrated by means

of a sample analysis. Benchmarked finite element models have been developed to study the

effect of imperfection, and concrete casting pressure on the compression capacity of SC walls. It

is observed that nonslender faceplates do not undergo significant reduction in SC wall capacity

due to imperfection and concrete casting pressure. However, the capacity of SC walls with

slender faceplates is expected to reduce significantly. The paper presents a specimen matrix

discussing the future work that will be performed to understand the effect of various parameters

on the compression behavior of SC walls.

Introduction

Modular steel-plate composite (SC) walls are increasingly being used in the construction of

safety related nuclear facilities. SC walls consist of concrete infill sandwiched by steel plates

(faceplates) on two sides. The faceplates are connected to each other by means of tie bars.

Composite action between the faceplates and concrete infill is provided by steel anchors.

Modular SC construction consists of different phases. SC wall panels and sub-modules are

typically fabricated in the shop. The empty modules are then shipped to the field. The modules

are combined and erected at site, where concrete is poured. The faceplates may have

imperfections before fabrication of sub-modules, or may develop imperfections during

transportation or assembly of sub-modules to sub-modules. These faceplate imperfections will be

amplified due to the pressure exerted by unhardened concrete. The imperfections in the faceplate

1 Graduate Research Assistant, Purdue University, <sbhardwa@purdue.edu> 2 Professor, Purdue University, <ahvarma@purdue.edu>

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can alter the buckling behavior of the faceplates thus affecting the compression capacity of SC

walls. The effect of variations in these parameters needs to be addressed in the design of SC

walls.

American Institute of Steel Construction (AISC) has published Supplement No. 1 to

Specification for Safety-Related Steel Structures for Nuclear Facilities, AISC N690s1 (AISC,

2015). Appendix N9 to the supplement provides provisions for the design of SC walls. Bhardwaj

et al. (2015) present an outline and a brief discussion on the use of Appendix N9 for design of

SC walls. Appendix N9 provides permissible concrete and faceplates strengths for the provisions

to be applicable. 36 ksi steel is not permitted to prevent: (i) residual (locked-in) stresses from

concrete casting, and (ii) thermally induced stresses, from causing premature yielding and

limiting the strength or ductility of the SC walls. The possible effects of construction and

erection procedures on faceplate imperfections are addressed by the dimensional tolerance

provisions of Chapter NM of N690s1. The chapter provides the tolerance limits for faceplates

during fabrication, assembly, before casting and after casting. The faceplate waviness

requirement limits the out-of-plumbness of faceplates after concrete hardening. The Appendix

also provides faceplate slenderness requirements to ensure that the faceplate yields in

compression before undergoing local buckling. This requirement is based on the study by Zhang

et al. (2014).

Variation and uncertainty in the construction procedures for modular SC walls may lead to some

of these requirements being violated. Appendix N9 limits the applicability of its design

provisions in case these requirements are not met. Reconciliatory analysis may need to be

performed to verify the design of these SC walls. This paper presents a procedure for simulation

of the construction sequence for SC wall panel sections. The simulation includes the effect of

initial imperfections and concrete casting pressure on the compression behavior of the SC wall

panel sections. The procedure can be employed to understand the effects of faceplate

slenderness, faceplate waviness, tie bar spacing (spaced at section thickness or half the section

thickness), concrete pour height, faceplate yield strength, and concrete compressive strength on

the compression behavior of the SC wall panel sections.

Previous Studies

Zhang et al. (2014) studied the effect of shear connector (and tie bar) spacing on the faceplate

buckling and composite behavior of SC walls. Based on the existing experimental database and

supplementary parametric studies, the authors recommended a faceplate slenderness requirement

to prevent faceplate buckling from occurring before faceplate yielding. The faceplate slenderness

limit is required to be satisfied per Eq. A-N9-2 of AISC N690s1. Benchmarked finite element

models from this study were employed to study the effect of faceplate waviness on the

compression capacity of the SC walls. Commentary to Section NM2.7 of AISC N690s1

discusses the basis for faceplate waviness requirement. However, the study considers

imperfections up to 0.6 times the faceplate thickness, whereas the faceplate waviness

requirement may result in higher magnitude of permissible imperfections. Table 1 shows that

faceplate waviness equation (Equation NM2-1 of AISC N690s1) may result in imperfections of

the magnitude of 1.5 to 2 times the faceplate thickness. Additionally, the study does not consider

the effect of other parameters such as concrete pour height, tie bar spacing, etc., on the

compression behavior of SC walls.

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This paper presents a procedure to simulate the construction sequence to understand the effect of

these parameters on faceplate buckling and SC wall compression behavior. The parametric

studies would help understand the influence of these parameters. Additionally, the stability

provisions of AISC N690s1 will be corroborated by these studies.

Procedure for considering effect of slenderness and concrete casting pressure

Fig. 1 presents the procedure for considering the effect of geometric imperfection and concrete

casting pressure on the compression behavior of SC walls. The procedure involves three step

sequentially coupled finite element analysis. The finite element model is subject to eigenvalue

perturbation analysis to obtain the buckling mode shape. The buckling mode is scaled to 0.9

times the faceplate waviness limit and imported to the pressure stress analysis model. The stress

analysis for concrete pouring pressure is performed and the concrete stresses are zeroed. The

final stress state from the analysis is imported to stress analysis for compression loading. The

stress analysis for compression loading is performed and the results are compared to a control

specimen without any imperfections and concrete pouring pressure. The proposed parametric

studies and the implementation of the procedure is presented in a sample analysis in the

following sections.

Parametric Studies

The compression behavior of SC walls is affected by the faceplate slenderness, faceplate

waviness, shear stud and tie bar spacing, concrete pour height, and strength of faceplates and

concrete infill. The procedure discussed in Fig. 1 can be employed to perform parametric studies

aimed at understanding the effect of these parameters. Table 1 presents the matrix for studying

the effect of faceplate slenderness and steel grade on the compression capacity of a typical SC

wall panel section. The stud spacing (Column G) is decided to meet the slenderness criteria

(Column F). The tie bar spacing (Column H) has been considered as three times the stud spacing.

The section thickness (Column I) is considered to be twice the tie bar spacing. It is observed that

some of the specimen do not meet the reinforcement ratio (ρ) [Column J] requirements of

Appendix N9 to AISC N690s1. The study will provide insight into the effect of not meeting the

reinforcement ratio requirement. Section dimensions (Column K) are decided to be three times

the tie bar spacing to accommodate two rows of tie bars in the specimen. The faceplate waviness

limit (Column L) is determined based on Equation NM2-1 of AISC N690s1. Tie bar diameter

(Column M) is determined based on tensile strength requirements of Equation A-N9-5) of AISC

N690s1. Columns N and O compare the minimum shear reinforcement required by AISC

N690s1 (based on the tensile strength requirement) with that required by Table 9.6.3.3 of ACI

318 (ACI, 2014). It is observed that the AISC requirement is mostly conservative. The

highlighted specimen (SP-50-6-1) is analyzed in the sample analysis.

Similar parametric study matrices will be constructed to study (a) the effect of slenderness ratio

and steel grade for tie bar spaced at section thickness, (b) the effect of variation in concrete pour

height, and (c) the effect of variation in concrete strength on the faceplate buckling and

compression behavior of SC wall panel sections.

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Figure 1: Procedural flowchart for analysis of SC wall panel sections for compression loading (including

imperfection and concrete casting pressure)

Perform the Eigenvalue analysis of the model 1. Obtain the Eigen shapes for the steel faceplate assembly

Build a finite element model for the panel section

1. Model the panel section with symmetry boundary conditions

2. Explicitly model the faceplates, concrete infill, steel studs and tie bars, and their interactions

Perform the stress analysis for concrete casting pressure. 1. Import the mode shape corresponding to faceplate buckling from the eigenvalue analysis. 2. Scale the mode shape such that the maximum initial deformation meets the faceplate waviness

requirement of Chapter NM of the Nuclear Specification 3. Apply the casting pressure due to unhardened concrete on the faceplates

4. Lock the model state and remove the concrete pressure load 5. Release the stresses in concrete

Perform the stress analysis for compression loading. 1. Import the final state from the concrete casting pressure analysis as the initial model state

2. Harden the concrete infill 3. Unlock the model state and enforce symmetry boundary conditions.

4. Apply the compression load on the model

Post-process the analysis results

1. Obtain the force displacement behavior of the SC wall panel section

2. Compare the compression behavior of this model (including the faceplate imperfection and

concrete casting) with a control model (not including the faceplate waviness and concrete casting

pressure).

3. Observe the failure limit state (compression yielding or compression buckling) of the faceplates in

the two models

End analysis of SC wall panel section

Begin analysis of SC wall panel section

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Table 1: Parametric study matrix for effect of slenderness ratio and steel grade

Sample Analysis

The procedure presented in Fig. 1 is implemented in the sample analysis discussed in this

section. Specimen SP-50-1-6 with parameters as shown in Table 1 is modeled in commercial

finite element software ABAQUS Version 6.14 (Simulia, 2014). This configuration consists of

grade 50 steel for the steel and 6 ksi concrete infill. The section thickness is 24 in. with 0.2 in

thick faceplates on each end. The stud spacing meets the faceplate slenderness requirements of

AISC N690s1 (Equation A-N9-2). The reinforcement ratio meets the requirements of Section A-

N9.1 of AISC N690s1 for Appendix N9 to be applicable. The tie diameter is decided based on

the tensile strength requirements of Section N9.1.5 (Equation A-N9-6) of AISC N690s1. The

details of the model are presented in Figure 2. The specimen is modeled with faceplate initial

imperfections based on faceplate waviness requirements of Chapter NM of AISC N690s1 (AISC,

2015). The SC wall panel section is analyzed for concrete casting pressure and the compression

capacity of the specimen is determined. The capacity of the specimen is compared with the

compression capacity of a control specimen with no imperfections and casting pressure.

Figure 2. Model Parameters for Sample Analysis

Finite Element Model

Benchmarked compression models by Zhang et al. (2014) were developed further for the purpose

of this study. The steel faceplates were modeled using shell (S4R) elements. Concrete infill was

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modeled using solid elements (C3D8R). The shear studs and tie bars were modeled using beam

elements (B31). Beam elements were embedded into the concrete infill. Therefore, holes in the

concrete infill were not modeled. The interface between the steel faceplates and concrete infill

was represented by connector elements (CONN3D2). The connector elements connect

corresponding nodes of shear studs (or tie bars) and steel faceplates. Load-displacement

relationship proposed by Ollgard et al. (1971) was used to define the interfacial behavior of SC

composite walls.

Steel Behavior was modeled as elastic-perfectly plastic with a yield stress of 50 ksi and an elastic

modulus of 29000 ksi. Concrete Damaged Plasticity (CDP) model is used for concrete infill. The

uniaxial compression stress-strain behavior of concrete was defined using the modified

Popovic’s empirical stress-strain model recommended by Collins et al. (1993). Concrete

compressive strength was considered as 6 ksi. The uniaxial tension strength and the post-peak

behavior were defined using the equations for plain concrete provided in CEB-FIB Model Code

(CEB-FIP, 2010).

As discussed in Fig. 1, three-step sequentially coupled analysis approach is used for the

development and analysis of the finite element models. The analysis involves: (a) eigenvalue

buckling analysis, (b) stress analysis for structure response to concrete pouring pressure, and (c)

stress analysis to simulate structural response to axial compression loading.

Eigenvalue buckling analysis.

Eigenvalue buckling analysis is a linear perturbation procedure. The steel assembly was subject

to an incremental loading pattern to determine the modal response of the faceplates. Eigenmode

corresponding to the faceplate buckling is selected from the eigenvalue analysis and imported as

geometric imperfection to the stress analysis for concrete pouring pressure. The buckling mode

(mode 15) is presented in Fig. 3. The magnitude of these initial geometric imperfections in the

faceplates is scaled by the faceplate waviness requirements presented in Chapter NM (Equation

NM2-1) of AISC N690s1. The faceplate waviness limits, measured as the distance of the lowest

point (trough) from the straight line two adjacent high points (crests), are presented in column L

of Table 1. For the shear stud and tie bar configuration presented in Table 1, Equation NM2-1

limits the faceplate waviness to 0.3 in. (1.5tp).

Stress analysis for concrete pouring pressure

The faceplate buckling modeshape obtained from eigenvalue analysis is scaled to a maximum

imperfection of 0.27 in. (90% of the limiting faceplate waviness). The scaled modeshape is

imported as initial imperfection in the analysis. The model with imperfection is presented in in

Fig. 4. Symmetry boundary conditions are enforced to ensure that the response of the SC wall

panel section corresponds to the response of a typical SC wall panel section in the SC wall

expanse. The analysis procedure implemented is implicit dynamic.

This analysis determines the structure response to concrete casting. Therefore, the concrete is

considered unhardened. This is achieved by reducing the concrete elastic modulus to a

thousandth of its long term modulus. Since the concrete is considered unhardened, it will take the

shape of the faceplates with initial imperfections. This is achieved by tying the concrete surface

nodes to faceplate nodes before imperfections are applied. As observed in Fig. 4, concrete

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maintains contact with the faceplates at the start of the analysis. SC wall construction typically

consists of concrete being cast in pour height increments of 10ft. The analysis considers concrete

casting pressure corresponding to a pour height of 10 ft (0.01 ksi magnitude). The pressure load

is applied to the faceplates. Since the concrete is tied to faceplates, the pouring pressure leads to

stresses and strains in concrete, which will not physically happen during construction. The

stresses in concrete are removed by locking the model (fixing all degrees of freedom at all the

nodes of the model), deactivating and then reactivating the concrete. The final step of the

analysis retains the faceplate stresses and strains while removing the stresses in concrete. This is

illustrated in Fig. 5, which is the model state at last step of stress analysis for concrete pouring

pressure. It is observed that the pouring pressure leads to peak faceplate steel stress of the

magnitude 7 ksi. The corresponding peak strain in the faceplates is 0.0002.

Figure 3. Buckling mode for the faceplates (eigenvalue

buckling analysis)

Figure 4. Initial Imperfection imported in the model

(scaled modeshape from eigenvalue buckling analysis)

a) Faceplate stresses (outer face) b) Concrete stresses

Figure 5. Stress states at the end of analysis for concrete pouring pressure

Stress analysis for uniaxial compression loading

The model state at the end of the stress analysis for concrete pouring pressure is imported as an

initial state for this analysis. The analysis procedure implemented is dynamic explicit. The

concrete is hardened with the model locked. This is done by defining temperature dependent

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elastic modulus for concrete and then raising the concrete temperature to harden the concrete.

The coefficient of thermal expansion for concrete is defined as zero. The model is unlocked after

the concrete hardens and symmetry boundary conditions are enforced. Unlocking the model

allows the steel faceplates to try to elastically rebound and push against hardened concrete. The

model is then subject to uniaxial compression in displacement control.

The specimen reaches its peak compression load at an axial displacement of 1.12 in. (time step

0.35). The stress and strain states of concrete infill and faceplates are presented in Fig. 6 and 7

respectively. As observed in Fig. 6a, concrete infill reaches its peak stress (6 ksi) at a strain of

0.003. The faceplates (Fig. 7a) reach the yield stress at these strain values. The faceplates yield

before buckling, in spite of the initial imperfections and the concrete casting pressure. This was

expected as the specimen meets the faceplate slenderness requirement (it ensures the faceplate

yields before buckling) and the faceplate waviness requirement (is based on the maximum

waviness a faceplate can have before any reduction in the compression capacity) of AISC

N690s1.

a) Compressive stress b) Compressive strain

Figure 6. Concrete infill state at peak compressive load

a) Faceplate compressive stress b) Faceplate compressive strain

Figure 7. Faceplate state at peak compressive load

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Control Specimen

The effect of geometric imperfections and concrete casting pressure on the compression capacity

of SC wall panel sections is observed by comparing the behavior of the specimen with a control

specimen without any imperfections that is not subject to concrete casting pressure. The control

specimen has the same parameters as SP 50-6-1. The force-displacement behaviors of the two

specimen are compared in Fig. 8. The axial force is normalized with the expected compression

capacity of the specimen ( 0.85 's y c cA F f A , where As is the area of steel faceplates, Fy is the

steel yield stress, Ac is the area of concrete infill, and f’c is the concrete compressive strength).

The figure presents the force vs axial strain behavior for the specimen with imperfections and

concrete casting pressure (SP-50-6-1) and the control specimen [SP-50-6-1 (Control)], and the

theoretical stiffness of the specimen [ ( / )AE L ]. It is observed that the reduction in

compression capacity of SP-50-6-1 is less than 1%. The reduction in the force carried by steel

faceplates is less than 5%. Additionally, there is no change in the axial stiffness of SP-50-6-1 in

comparison to the control specimen. The axial stiffness of the two specimen (SP-50-6-1 and

control) matches the theoretical specimen of the SC wall panel section. The peak normalized

axial force for the two specimen is greater than one because the finite element model does not

consider the reduction in concrete contribution to the axial capacity (the 0.85 factor in the

expected capacity that corresponds to variability in cylinder strength).

Figure 8. Reduction in Compression capacity of SC wall due to geometric imperfection and concrete casting

pressure

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Conclusions

The procedure for simulation of the construction sequence for a typical SC wall panel section has

been presented in this paper. The simulation includes the effect of initial imperfections and

concrete casting pressure on the compression behavior of the SC wall panel sections. The

procedure can be employed to understand the effects of faceplate slenderness, faceplate

waviness, tie bar spacing (spaced at section thickness or half the section thickness), concrete

pour height, faceplate yield strength, and concrete compressive strength on the compression

behavior of the SC wall panel sections.

The study illustrates the implementation of the procedure on a sample SC wall panel section (SP-

50-6-1). The specimen meets the faceplate slenderness, faceplate waviness, reinforcement ratio,

and tie bar spacing and strength requirements of AISC N690s1. The specimen is detailed to

ensure that the faceplates yield before buckling in compression (based on AISC N690s1

requirements). This behavior is confirmed by the sample example. It is observed that the

reduction is compression capacity due to geometric imperfections and concrete casting pressure

corresponding to a pour height of 10 ft. is negligible (less than 1%). There is no loss of axial

stiffness due to the geometric imperfections and concrete casting pressure.

Future Work

The compression behavior of SC wall panel sections will be affected by a change in the faceplate

slenderness, tie bar spacing, concrete pour height, and steel and concrete strengths. The influence

of these parameters on the compression behavior of the SC wall panel section will be studied by

conducting parametric studies. The proposed specimen matrices for these studies have been

discussed earlier. The effect of geometric imperfections is expected to be more significant for SC

wall panel sections that (a) do not meet the faceplate slenderness criteria of AISC N690s1, and

(b) have tie bars spaced at section thickness. The parametric studies will also highlight how the

concrete pour height can be changed to counter the effect of other parameters and vice versa. The

effect of concrete casting pressure and geometric imperfections is expected to be significant for

faceplates with a yield stress of 36 ksi.

Refined material models will be used for steel to better simulate the post-peak behavior of

faceplates, shear studs and tie bars. These models will include strain hardening and damage

modeling for the steel.

Acknowledgments

The authors are grateful to Dr. Kai Zhang for his contribution to the development of this

methodology.

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