Cyclic inelastic buckling of steel braces

INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING

Volume 2, No 4, 2012

© Copyright 2010 All rights reserved Integrated Publishing services

Research article ISSN 0976 – 4399

Received on March, 2012 Published on May 2012 1129

Cyclic inelastic buckling of steel braces Supratik Bose

Indian Institute of Technology, Kanpur, Student, M. Tech, Civil Engineering Department

[email protected]

doi:10.6088/ijcser.00202040011

ABSTRACT

This paper presents the results from an experimental program on cyclic inelastic buckling of

steel braces. The objective of the experiment is to determine the force deformation

characteristics, critical buckling load, axis of failure and failure mode. The brace (single

angle section of 40 * 40 * 6 and length 1220 mm) is mounted in a shear loading frame (pin

connected at its ends) and a servo-hydraulic actuator is used to apply the lateral cyclic load to

the test specimen. The load applied was displacement controlled with the displacement

applied increasing from 0.5 mm to 30mm (with three trials for each displacement). Strain

gauges and LVDTs were attached at various points to obtain the experimental results. The

buckling load is obtained analytically from IS 800:2007 (both for flexural and flexural torsion

buckling) and compared with the experimental results. There was an evidence of flexural

torsion buckling as anticipated in IS 800 for single angle sections with one leg connected.

There was also an evidence of shear lag effect in the brace member which leads to non

uniform distribution of stresses.

Keywords: Steel braces, cyclic loading, buckling, backbone curve, shear lag.

1. Introduction

In engineering, buckling is a failure mode characterized by a sudden failure of a structural

member subjected to high compressive stresses, where the actual compressive stress at the

point of failure is less than the ultimate compressive stresses that the material is capable of

withstanding.

Braced steel frame structures are popular in regions of high seismicity. The steel braces

improve the lateral strength and stiffness of the structural system and contribute to seismic

energy dissipation by deforming inelastically during an earthquake. Steel braces can be

designed to resist only tensile forces, or to resist both tensile and compressive axial forces.

Tension-only braces are thin structural members that buckle early under compressive load,

and hence their compressive capacity is ignored in design. Buildings that include tension-

only braces have performed rather poorly during strong earthquakes. Experiments have

shown that, in general, tension–compression braces provide better performance during an

earthquake, but their behaviour under severe cyclic loading is complicated and not yet well

understood

Flexural buckling: This type of buckling can occur in any compression member that

experiences a deflection caused by bending or flexure. Flexural buckling occurs about the

axis with the largest slenderness ratio, and the smallest radius of gyration.

Torsion buckling: This type of buckling only occurs in compression members that are

doubly-symmetric and have very slender cross-sectional elements. It is caused by a turning

Cyclic inelastic buckling of steel braces

Supratik Bose

International Journal of Civil and Structural Engineering

Volume 2 Issue 4 2012

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about the longitudinal axis. Torsion buckling occurs mostly in built-up sections, and almost

never in rolled sections.

Flexural-torsion buckling: This type of buckling only occurs in compression members that

have unsymmetrical cross-section with one axis of symmetry. Flexural-torsion buckling is

the simultaneous bending and twisting of a member. This mostly occurs in channels,

structural tees, double-angle shapes, and equal-leg single angles (H.T. Zhu, Michael C.H.

Yam, Angus C.C. Lam, V.P. Lu (2009)).

In steel construction, hot-rolled structural shapes such as angles, tee-sections and channels are

often used as tension members and as braces. These members are either bolted or welded to

the connecting elements (e.g. a gusset plate) as shown in Figure 1. It is common practice with

these sections to connect only part of the cross-section at the connections. Because of this,

only part of the section is effective in carrying the loads, and this leads to the phenomenon

known as shear lag. Shear lag results in the non-uniform distribution of stress in tension

members (Figure 1). In addition, since the line of action of the load usually does not coincide

with the centroidal axis of a tension member section, loading eccentricity is also created and

hence secondary bending of the member is induced. The combined effects of shear lag,

connection eccentricity and stress concentrations at the connected region would initiate

premature fracture of the section and the capacity of the member is significantly reduced

(Patxi Uriz, Filip C. Fillippou,Stephen A Mahin (2008)). This phenomenon is most common

in tensile members but is also possible in members where only one leg is connected (as in our

experiment).

Figure 1: Shear Lag of an angle

Backbone Curve: Relationship between the generalized force and deformation (or generalized

stress and strain) of a structural component or assembly that is used to characterize response

in a nonlinear analysis model (Waltario A Lopez and Rafael Sabelli (2004)). Slow-cyclic

testing technique provides a consistent and reliable set of experimental data on strength,

stiffness, energy dissipation potential, and failure mode of structures. As a result, the ability

of structures to resist earthquake loads is often assessed using this method.

In this article an experiment is conducted with a steel brace of single equal leg angle section

subjected to lateral cyclic load. The objective of this study is to investigate the force

deformation characteristics, lateral strength and stiffness, energy dissipation capacity, and

failure mode.


Supratik Bose



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2. Materials and method

2.1. Test specimens

Figure 2: Experimental Set-up for Cyclic Buckling Test

The brace (single angle section) is mounted in a shear loading frame in which four members

of hot-rolled steel sections of ISMB150 @ 149.0 N/m forming a rectangular loading space,

are pin connected at ends (Figure 1). A servo-hydraulic actuator (MTS make) of capacity 100

KN and stroke 75 mm is used to apply the lateral cyclic load to the test specimen. The

displacement and the corresponding lateral load applied to the specimen can be monitored by

the in-built load cell and LVDT of the actuator. Length of the brace between end connections

is 1220 mm. As seen in the figure the brace was welded to the gusset plate which was

connected only to the beams of the loading frame.

2.1.1 Description of the sensors

The location and purpose of the various sensors used in this experiment are as follows:

In addition to the sensors attached to the actuator, two types of sensors, namely, two strain

gauges and LVDT are used to monitor the behaviour of the brace specimen under the applied

lateral cyclic loading. Two strain gauges were used at about 300 mm distance from the base

(i.e., one-quarter of total length) to monitor the state of strain of brace at different

displacement levels. The two strain gauges were attached near the bottom corner of the brace

member with one attached to the connected leg and the other to the unconnected leg. Two

strain gauges are attached in order to find out whether the two legs of the equal angle section

are carrying equal strains (and consequently equal stresses) or not, so that the shear lag effect

can be examined.

2.2. Material properties

Properties (both physical and mechanical) of the angle section used as brace are as follows:

Equal Angle section: 40 * 40 * 6 (measured during the experiment)

Area = 444 mm^2., Rxx = Ryy = 11.9 mm., Ruu = 14.9 mm, Rvv = 7.7 mm

Yield strength: 375:0 MPa, Ultimate strength: 520:0 MPa.


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The load was applied in cyclic manner such that in alternate cycles the brace member

undergoes compression (where buckling is possible) and in the other cycles it undergoes

tension. The displacement amplitudes were varied from an initial value of 0.5 mm to 30 mm.

Each displacement excursion level is repeated for three times to study the behaviour of

specimen with repetitive cyclic loading (total 24 scan sessions were performed until buckling

failure was observed).

Figure 3: Schematic plot of a equal angle section used as brace with its axes

3. Results and discussions

3.1. Analytical prediction of flexural and flexural torsion buckling from IS 800

The brace was found to be welded to the gusset plate. Since in our experiment the ends of the

brace are welded to the gusset plate hence analytical results are calculated for fixed

connection case from IS 800: 2007.

Considering fixed end connections,

For both the ends fixed the effective length factor, K = 0.65.

λ = 1.385, Φ = 1.75.

fcd = 132.99 N/mm^2 (without considering the factor of safety)

So, flexural buckling load = 59.04 kN.

Now for torsion flexure buckling, from table 12 for fixed ends with no. of bolts at the end

more than 2, k1 = 0.20, k2 = 0.35, k3 = 20

λvv = 2.131, λφ = 0.08967.

λe = 1.396, so Φe = 1.768.

fcd= 131.41 N/mm^2 (without considering the factor of safety)

So, flexural torsion buckling load = 58.35 kN.


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3.2. Experimental evaluation of the buckling load

Figure 4: Plot of load (kN) taken by the brace member both in tension and compression for

all the scan sessions

Figure 5: Plot of load (kN) taken by the brace member both in tension and compression till

scan session 12 where buckling has occurred

Since the actuator was applying cyclic load, the brace was buckling only in the alternate

cycles (for our experiment the even cycles are under compression) when it was under

compression. In other cycles it was undergoing tension and hence no buckling is possible

(only yielding was possible). From analysis of the experimental results it has been seen that

the brace has started buckling only after the maximum displacement applied by the actuator

has increased 7.5 mm i.e for scan session 12 (also discussed in point no 2) and hence after

scan session 12 the maximum value taken by the compression member has decreased as the

member has already buckled. From Figure 4, 5, it can be seen that the maximum value taken

in compression is 37.8 kN. Hence this load can be taken as the load where buckling failure of

the member has occurred (as it is the absolute maximum value of the loads taken by the brace

under compression considering all the scan sessions). So, from experiment, the buckling

strength of the member is 37.8 * cos α = 31.62 kN.

3.3. Shear lag effect


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It has already been discussed in the introductions that shear lag results in non-uniform

distribution of stress. The values of the two strain gauges (one attached to the connected leg

and the other to the unconnected leg) show a huge difference.

Figure 6: Comparison of the strain gauge readings at the two legs (session 22)

Figure 7: Comparison of the strain gauge readings at the two legs (session 15)

The strain gauge 1 is attached to the connected leg while the strain gauge 2 is attached to the

unconnected leg (showing much lesser values compared to the strain gauge 1). Since the two

strain gauges are showing different values, it can be said that the stress in the two legs are

unequal. Obviously the stress in connected leg is greater. So there is an unequal distribution

of stress in the two legs of the angle section as evident from the values measured from the

strain gauges which is possibly an effect of shear lag. So it can be conferred the shear lag

effect is observed in measurement of the two strain gauges.

3.4. Analytical Prediction of the backbone curve

Figure 8: Envelope of Load (kN) Vs Displacement (mm) obtained analytically


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Backbone curve from experimental values: The load measured by the load cell of the actuator

for all the 24 scan sessions are plotted whose envelope of the hysteresis plot thus obtained

gives the backbone curve.

Figure 9: Backbone curve (load (kN) Vs displacement (mm) envelope) from the experiment

Comparison of analytical and experimental backbone curve

Figure 10: Analytical (dashed line) and experimental backbone curve (normal line)

So it can be seen from figure 10 that analytically a good prediction of the observed behaviour

of the backbone curve can be obtained.

3.5. Comments on the observed behavior

Axis of Buckling: The brace was observed to buckle along the vv axis (as shown in Figure 3

in the experimental setup section). The radius of gyration along this axis minimum and hence

the slenderness ratio is maximum (λ α 1/r). Also experimentally it was seen that the brace has

buckled along this axis.


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Buckling Mode: The brace has buckled in its 1st mode which was clearly evident from the

experiment. It is known that the load required for the structure to buckle in its first mode is

the least. Hence it is natural that the 1st mode of buckling will occur.

Inelastic Activities: As the displacement applied by the actuator has increased, the stress

strain plots (or load strain plots) has entered into the nonlinear zone as it is evident from the

plot in Figure 9.

Failure: Total failure of the brace member is seen at the end of the experiment. Permanent set

was observed and hence not possible to be used further. The member failed due to flexural-

torsion buckling. The ends of the bracing were seen to have twisted due to the torsion effect.

The bracing member was welded at the ends (which could be considered as a partial fixed

end connection.) Due to the fixity at the ends and only one leg connected, the member (equal

angle section) has twisted at its end which is evident from comparison with the analytical

results and also from the figure given below (Figure 25 and 26).

Figure 11: Buckling failure of the brace member twisting of the brace member near its

support showing evidence of flexure torsion buckling

There is an evidence of the flexural torsion buckling as anticipated in IS 800 for single angle

struts. After the buckling failure of the brace it was observed that not only there is flexure

buckling of the member but also it has twisted which is only possible due to torsion.

3.6. Comparison of the theoretical and experimental values

Flexural

Buckling load

(theoretical)

(kN)

Torsion

Buckling load

(theoretical)

(kN)

Experimentally

obtained

Buckling load

(kN)

Error from

Flexure

buckling load

(%)

Error from torsion

flexure

buckling load

(%)

59.04 58.35 31.62 46.44 45.81

So, the value of the buckling load obtained experimentally is slightly closer to the torsion

flexure buckling load (for both the cases) which again confirmed that the member was

twisted.

4. Conclusion / Suggestions/ Findings

1. The buckling strength obtained experimentally is considerably less than the value

obtained analytically.


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2. There was an evidence of shear lag effect in the brace member which leads to non

uniform distribution of stress and reduction of strength of the member under

compression (i.e. buckling).

3. There were also evidences of flexural torsion buckling as anticipated in IS 800 for

single angle sections with one leg connected.

4. The load measured by the actuator and the load calculated from the strain gauge

attached to the connected leg are giving more or less similar values as long as the

material is within the linear zone.

Acknowledgement

This article is written based on the experimental work performed in Structural Engineering

Lab, Indian Institute of Technology, Kanpur as a part of the course, CE 623, "Experimental

Methods in Structural Engineering". The author would like to acknowledge the course

instructor, Dr. Samit Ray Chaudhuri, and Dr. Durgesh C. Rai who has designed the original

experimental setup for the testing program. The author would also like to acknowledge Dr.

K.K. Bajpai, teaching assistants Harikrishnan Panikkaveettil and Varun Singla and other

students of the course CE 623. The author has found the results of the experiment interesting

and the article contains his own interpretation of the results.

5. References

1. B. V. Fell, A. M. Kanvinde, G. G. Deierlen, A. T. Myers., (2009), Experimental

Investigation of Inelastic cyclic buckling and Fracture of steel braces, Journal of

Structural Engineering, 135(1), pp 19-32.

2. H.T. Zhu, Michael C.H. Yam, Angus C.C. Lam, V.P. Lu., (2009), The shear lag

effects on welded steel single angle tension members, Journal of Constructional Steel

Research, 65(5), pp 1171-1186.

3. Jun Jin and Sherif el Tawil, Inelastic Cyclic Model for Steel Braces, ASCE

4. IS 800: 2007- General Construction in steel-Code of Practice

5. Luis F. Ibarra, Ricardo A. Medina and Helmut Krawinkler., (2005), Hysteretic models

that incorporate strength and stiffness deterioration, International Association of

Earthquake Engineering,34(12), pp 1489-1511,

6. Patxi Uriz, Filip C. Fillippou Stephen A Mahin., (2008), Model for Cyclic Inelastic

Buckling of Steel Braces, Journal of Structural Engineering, 134(4), pp 9-12.

7. Waltario A Lopez and Rafael Sabelli., (2004), Seismic Design of Buckling Restrained

Braced Frames, Structural Steel Education Council, pp 5-7.

8. Jun Jin and Sherif El-Tawil., (2003), Inelastic Cyclic Model for Steel Braces, Journal

of Engineering Mechanics, ASCE, 129(5), pp 548-557.

9. Buckling of Steel Elements., available at www.Eurocode-resources.com.

10. Gregory G. Deierlein, Andrei M. Reinhorn and Michael R. Willford., (2010),

Nonlinear Structural Analysis for Seismic Design, A Guide for Practicing Engineers,

Applied Technology Council (ATC), NEHRP Seismic Design Technical Brief No. 4,

National Institutes of Standards and Technology, US Department of Commerce.

11. Lutfi Al-Sharif., (2010), Euler’s Buckling Equation, Mechatronics Engineering,

STM_File, pp 1-2.

Cyclic inelastic buckling of steel braces

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