Ductile Knee-Braced Frames for Seismic Applications

Leelataviwat, S. & Doung, P. Department of Civil Engineering, King Mongkut’s University of Technology Thonburi, Thailand; sutat.lee@kmutt.ac.th

Junda, E., & Chan-anan, W. Department of Civil and Environmental Engineering, Nakhon Pathom Rajabhat University, Thailand

ABSTRACT:

This paper presents the behavior and design concept of efficient structural steel systems based on innovative

applications of knee braces. Advantages of knee-braced frames (KBF) include relatively simple connections for

ease of construction and reparability after an earthquake and less obstruction as compared to conventional bracing

systems. Various configurations of KBFs can be designed and detailed for different levels of strength, stiffness,

and ductility. KBFs are designed so that all inelastic activities are confined to the knee braces and designated

yielding elements only. Key design concepts to ensure ductile behavior of KBFs are first summarized. Finally,

results from experimental and analytical studies into the behavior of KBFs are briefly presented. The results show

that KBFs can provide viable alternatives to conventional structural systems.

Keywords: Knee Braces, Knee-Braced Frames, Seismic Resistant Steel Structures, Cyclic Tests

1. INTRODUCTION

Knee braces were widely used in the past for wind-resistant design. However, the application of knee

braces for seismic resistant structures is still limited. In the past several years, the authors have conducted

extensive experimental and analytical studies to develop ductile knee-braced frames for seismic

applications (Srechai 2007, Suksen 2007, Leelataviwat et al. 2011a, Leelataviwat et al. 2011b, Junda

2011, Wongpakdee 2014, Doung 2015). Knee-braced frames (KBFs) utilize relatively simple

connections for ease of construction and reparability after an earthquake. More importantly, the knee

braces provide much less obstruction as compared to the braces of conventional systems, making this

system architecturally attractive. With a slight modification in the brace connections, knee braces can

also be utilized in the seismic strengthening of existing steel frames. Various configurations of KBFs

can be designed and detailed for different levels of strength, stiffness, and ductility. Figure 1 shows

various KBF configurations that have been investigated by the authors to date.

(a) (b) (c) (d)

Figure 1. Various Knee-braced systems: (a) Knee-Braced Moment Frame; (b) Knee-Braced Moment

Frame with Partially Restrained Connections; (c) Knee-Braced Frames; and (d) Knee-Braced Truss

Moment Frame.

PPartially Restrained Connections

BRBs

Simple (Shear) Connections

BRBsBuckling Braces/BRBs

In Figure 1(a), knee braces are combined with a moment frame to provide largest strength and stiffness.

This system can utilize either conventional buckling braces or buckling restrained braces (BRBs) for

higher ductility. For this system, the frame is designed so that the knee braces will yield under seismic

loads followed by plastic hinging of beams at the ends of the beam segments outside the knee portions.

In Figure 1(b), partially restrained (PR) connections are used instead of rigid connections. PR

connections such as bolted top and seat angle with double web angle connections can be used for beam-

column connections. These PR connections make the erection of the frame relatively simple and allow

the frame to be repaired after an earthquake. Properly detailed, these PR connections can exhibit

considerable ductility and energy dissipation capacity. In Figure 1(c), simple or shear connections are

used. For this system, the beam is designed to be fully elastic under the largest forces generated by the

knee braces. This system is most efficient in terms of ease of construction and reparability after an

earthquake. Hence, it ranks highly on ductility and resiliency but may lack the strength exhibited by the

back-up moment frames. In Figure 1(d), open-web truss frames replaces the solid beams used in other

systems. This system is suitable for long-span applications.

The design of all the KBF systems above can be carried out based on a capacity design concept that

results in ductile behavior. The frames are designed so that the knee braces will yield. All inelastic

activities are confined to designated yielding elements and are directed away from the critical areas,

decreasing the dependence of the performance on the material and quality of workmanship.

In this paper, the key concepts for the design of ductile KBF systems are summarized first. Examples of

the response from cyclic tests of selected systems are presented. Finally, an example of the dynamic

response of a selected system is provided. This paper provides a comprehensive overview of the design

concept and behavior of viable seismic resistant structural systems based on knee bracing concept.

2. DESIGN CONCEPT OF KNEE-BRACED FRAMES

Based on the past experimental and analytical studies, the ductile behavior of KBFs hinges on two

important design considerations, controlling the deformation demands on the knee braces and the design

of the columns to resist the forces induced by the knee braces. The following sections elaborate on these

two key aspects. It should be noted that the following discussions focus on a KBF with simple

connections. However, the concepts are also applicable to all the systems presented in Figure 1.

2.1 Knee Braces Design

For the systems shown in Figure 1, knee braces are the primary designated yielding elements. Hence,

they are expected to deform well into the inelastic range. For this reason, BRBs are more suitable than

conventional braces. Compared to the braces in a conventional braced frame, knee braces may

experience larger axial strain demand for a given frame drift. Figure 2 compares the deformation and

the strain demand of the braces in a KBF and a conventional concentrically braced frame (CBF). The

strain demands shown in Figure 2 were computed assuming rigid beams and columns. Figure 3 shows

the brace strain versus drift angle plots for the KBF and CBF. As can be seen, comparing to the diagonal

brace in the CBF, knee braces in the KBF can experience larger of smaller deformation demand

depending of the frame configuration and brace angle (φ). For shorter braces like knee braces, the

deformation capacity are generally smaller than that of a conventional brace because the deformation

can only distribute over a short length. Therefore, one of the most important aspects in the design of a

KBF is to ensure that the deformation or strain demand can be safely accommodated by the knee braces.

Longer knee braces (with large brace angle, φ) can generally accommodate larger deformation demand

but longer braces may also obstruct the passage in the bay.

In a KBF, the size and brace angle must be chosen based on the balance between function, deformation

demand, and brace ductility. Figure 4 shows the brace strain demands as a function of knee brace angle

(φ) for different drift angles. The strain varies depending primarily on the brace angle and becomes

largest for φ = 45 degrees. Based on Figure 4, the type of braces and brace angle can be chosen according

to the expected level of frame drift.

Figure 2. Deformation and the strain demand of the braces in a KBF and a conventional CBF.

0

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0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

L/H = 1.5

CBF

KBF (45 Degrees)

KBF (60 Degrees)

Bra

ce

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KBF (45 Degrees)

KBF (60 Degrees)B

race

Str

ain

Drift

Figure 3. Brace Strain in a KBF and CBF.

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20 30 40 50 60 70

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Ove

rall

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ce

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Brace Angle (Degrees)

Drift Angle

Figure 4. Brace Strain as a function of brace angle for different frame drifts.

As mentioned earlier, one of the most important design considerations is the controlling of the

deformation demands on the knee braces. For this reason, KBF is most suited for a displacement-based

design procedure. For a given brace angle, a plot such as Figure 4 can facilitate the selection of a target

drift of the frame. Once the target drift is chosen, a displacement-based design method can be used to

obtained the require frame strength to ensure that frame drift remains within the target. Any

displacement-based design procedures can be used for this purpose. One displacement-based design

method that has been successfully used by the authors is called Performance-based Plastic Design

(PBPD) method (Goel and Chao 2008).

In the PBPD method, the design base shear for a selected hazard level and a target drift is calculated

using energy balance concept. The required frame strength is computed by equating the work needed to

push the structure monotonically up to the target drift to that required by an equivalent elastic-plastic

single degree of freedom system to achieve the same state. For KBFs, a target deformation can be

selected (based on Figure 4) and the required base shear strength can be computed. The sizes of the

BRBs or knee braces can then be chosen based on the required frame strength. It has been found that

the PBPD method is very effective in controlling the deformation of frame and the braces to within the

target. The details of the PBPD method as applied to KBFs can be found elsewhere (Srechai 2007, Geol

and Chao 2008, Wongpakdee 2014).

2.2 Column Design

One of the concerns regarding the use of KBFs is that the knee braces may induce large flexural moments

in the columns leading to a soft-story type mechanism under seismic excitations. However, recent

developments in the design and assessment of structural systems under seismic excitation allow KBFs

to be designed with a high degree of accuracy and confidence. For KBF systems, the columns should be

designed to remain fully elastic (except at the bases) under the maximum forces induced by fully strain-

hardened braces. In order to achieve this objective, the columns can be designed based on the capacity

design concept.

One approach that has been used successfully is to apply the concept of plastic design with the

corresponding yield mechanism shown in Figure 1. To remain fully elastic, the columns must be

designed to resist the knee brace forces adjusted to fully-yielded and strain-hardened conditions. Based

on the PBPD approach, a capacity design method that considers the equilibrium of the entire column

subjected to all forces can be carried out. This method is sometimes referred to as “column tree” analysis.

Figure 5 shows the example of a column tree analysis. The forces associated with the beams and BRBs

are applied to the column tree. The columns can also be designed using pushover analysis. Once the

brace sizes have been determined, the frame can be “pushed” up to the target drift level by assuming

elastic columns except at the bases where plastic hinges are allowed to form. The moment and axial

force diagrams of the elastic columns are then used to design the member sizes. This process can be

done iteratively until the column sizes satisfy the elastic behavior objective.

Figure 5. Column tree design based on pushover analysis.

3. EXPERIMENTAL RESULTS

Large-scaled experiments have been carried out to assess the performance of KBFs with different

configurations. Specimens in the form of a portal frame and a T-shaped sub-assemblage have been tested

under cyclic loading. Some selected results from the tests are reviewed in this paper. Figure 6 shows a

V

Drift

test specimen of a knee-braced moment frame with partially restrained connections. For this specimen,

the beam-to-column joints consisted of top and seat angle connections. Angles were also used to connect

the beam web to the column flange. Regular braces made of a hollow circular section were used for this

specimen. The knee braces connected to beams and columns by bolted connections. In the test, the

specimen was subjected to quasi-static, cyclic loading until failure.

The hysteretic loops are shown in Figure 6c. The results show a stable hysteretic response through the

entire loading history. The pinching behavior which is the characteristic of a frame with partially

restrained connections is also apparent. The pinching is mainly due to the combination of the opening

and closing of gaps and slippage at bolt holes. The specimen was able to deform upto 4% drift when the

fracture initiated in the braces.

(a) Test Set-up (b) Beam-to-Column Connection Region

(c) Cyclic Test Result

Figure 6. KBMF with PR Connections.

Figure 7 shows one of the test specimens for a KBF with BRBs (Figure 1d). A T-shaped sub-assemblage

representing half of a beam and half of a column was tested. Single plate shear connection was used at

the beam-to-column connection. The column was mounted to the strong floor. The cyclic load was

applied at the end of the beam. The BRB was oriented at a 60 degree angle to minimize the strain as

shown in Figure 4. The specimen shows very ductile behavior with full and stable hysteretic loops. The

test was stopped due to fracture of one of the bolts at the single plate shear connection. However, even

with the loss of one of the bolts at the shear connection, there was only a minor decrease in the lateral

load resistance of the frame. The specimen was able to deform more than 5%. The connection was

designed primarily to carry the shear force and was unable to accommodate the rotation of the beam.

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-6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0

Story drift (%)

Late

ral lo

ad

(kN

)

Analytical

Experimental

Figure 7. KBF with Single Plate Shear Connections.

4. DYNAMIC RESPONSE

A 3-story building shown in Figure 8 was selected as an example to illustrate the dynamic response of

KBFs. The building was assumed to be an office building. In this study, the frame was designed as KBF

with BRBs and single plate shear connections. The study frame was designed in accordance with the

PBPD method described above. The structural system was designed for a Design Category D with S1 =

0.6g and Ss = 1.5g following ASCE 7-10 (2010). The design base shear of the study frame was evaluated

at two hazard levels, DBE and MCE, for 2% and 3% target drifts respectively. Nonlinear static pushover

and dynamic time history analyses were conducted using a set of 44 ground motions based on FEMA

P695 (2009).

Sample results from pushover and time history analyses are shown in Figures 9 and 10. As can be seen,

the inelastic activities occurred only at the designated locations. The frame performed as intended in the

design. The story drifts were within the target limits for both DBE and MCE levels.

Figure 8. Example 3-Story KBF with Single Plate Shear Connections.

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Load

(kN

)

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Figure 9. Pushover Analysis Results

(a) DBE Level (b) MCE Level

Figure 10. Time History Analysis Results

3. SUMMARY

The behavior and design concept of efficient structural systems based on innovative applications of knee

braces are presented in this paper. Selected experimental and analytical study results are reviewed and

discussed. Two key design issues to achieve ductile behavior for KBFs consist of limiting the

deformation demand in the knee braces and designing the columns to remain elastic. Design approaches

to control the deformation demands of the knee braces and the design of the columns are presented.

Based on research carried out thus far, it was found that KBFs with various configurations represent

viable alternatives to conventional structural systems. Various configurations of KBFs can be designed

and detailed for different levels of strength, stiffness, and ductility.

ACKNOWLEDGEMENTS

The research presented in this paper has been supported by different agencies over a number of years. The authors

would like to acknowledge funding from the Thailand Research Fund (TRF), National Research Council of

Thailand, and King Mongkut’s University of Technology, Thailand.

0

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0 0.5 1 1.5 2 2.5 3 3.5

First Yielding

Column Base Yielding

BRB Fracture

Roof drift (%)

Base s

hear

coeffic

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(V/W

)

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