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1. Abstract

The experiment conducted deals with investigating the force-deformation characteristics,

lateral strength and stiffness, energy dissipation capacity, and failure mode of steel braces

subjected to cyclic loading. In this experiment, steel brace of equal leg angle section (hot-rolled

single angle sections of size ISA 40406 @26.0 N/m) is used and tested under lateral cyclic

load. Displacement level and corresponding level of lateral load applied on the specimen are

monitored by the in-built LVDT and load cell of the actuator which is used to apply the lateral

cyclic load to the test specimen. The cyclic inelastic buckling mode shape is observed. The

guidelines developed for loading history are based on a general concept of cumulative structural

damage in a component. Loading history considered in the present experiment for slow-cyclic

testing consisted of gradually-increased reversed-cyclic displacements. The theoretical bucklingload for the steel brace is computed as per IS 800:2007 both in flexure and flexural torsion and

compared with the experimental result. It is observed that flexural buckling load and flexural

torsional buckling load are less than observed value. Therefore in actual structure steel brace can

carry more load than that anticipated.

2.

Introduction

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 reasonably. Steel braces are

mainly provided in frame structure to enhance the lateral stiffness of a structure. Sometime these

are also used in structure as a viable alternative of energy dissipation device (such as viscous

damper, metallic yield damper, Magneto rheological damper), under cyclic loading (such as

seismic loading). Bracings are designed in such a way that it can dissipate substantial part of the

imparted seismic energy (into the structure) through its yielding (i.e. as hysteresis energy).

However, it is noteworthy to mention that the energy dissipation capacity of steel bracing can

reduce severely due to its premature buckling action, which becomes more adverse in

conjunction with yielding. To enhance the performance of a structure sometimes buckling

resisting braces (BRB) are provided, but that does not improve steel braced-structure

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performance significantly under near-fault motion. Slow-cyclic testing technique provides a

consistent and reliable set of experimental data on strength, stiffness, energy dissipation potential,

and failure mode of structures.

Careful planning of the entire test program is essential for obtaining meaningful results, which

includes fabrication of test specimen, test structure assembly, load application system, supporting

system, loading history, instrumentation, data acquisition, data reduction, analysis and presentation.

It is important to mention the boundary conditions, initial conditions, scale effects, etc. to interpret

the test results.

3.

Experimental Setup

The experimental setup consists of a steel brace of equal leg angle section (hot-rolled

single angle section ISA 40406).The brace 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). Length of the brace between end-to-end is 1400 mm.

Servo-hydraulic (SH) actuator (MTS make) of capacity 100 KN and stroke length 75 mm is used

to apply the lateral cyclic load to the test specimen.Two types of sensors, namely, strain gauge

and LVDT are used. To monitor state of strain of brace at different displacement levels two

strain gauges are used at about 300 mm distance from the base.One LVDT is used at the top

beam level at opposite end to actuator to measure horizontal displacement of the specimen and

another LVDT is placed at the back of actuator to measure displacement of reaction frame. Real-

time behavior of the test specimen is monitored by System 5000 Data Acquisition (DAQ)

System. Lateral load, strain and displacement of the specimen are suitably captured by the strain

and voltage channels.Analog output of the sensors is converted to digital format in the DAQ

system, which is further transferred to computer for storage as well as online display.

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Figure 1: Experimental setup

4.

Procedure

The SH actuator is started to apply horizontal cyclic load.

The strain gauge, LVDT and MTS LVDT and load cell readings are recorded

throughout the loading history.

It is generally observed that the contributions of large excursions are much larger

than small excursions. Further, the relative amount of damage caused by an

inelastic excursion is largest for the symmetric excursion and depends on the

sequence in which large and small excursions are applied. Loading history

considered in the present experiment for slow-cyclic testing consisted of

gradually-increased reversed-cyclic displacements as shown in Figure 2.

Displacement levels increases linearly from an initial magnitude of 0.5 mm with

an increment of 0.5 mm.

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

behavior of specimen with repetitive cyclic loading.

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Test specimen is loaded with increased magnitude until the failure is observed.

Figure 2: Loading history

5. Results and Discussions

The results obtained are analyzed and discussed as follows through answering the discussion

items.

Compare the observed buckling load of the brace with analytically predicted value

using Indian Standard IS:800-2007 provisions of flexural buckling as well as

flexural torsion buckling.

Maximum of load measured by the in-built load cell in the actuator = 28.9 kN.

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= tan-1

(800/1150) = 34.82 (APPROX.)

Carrying out the truss analysis, observed buckling load = load in the brace = 35.20 kN.

Analytically predicted value using IS 800:2007

Flexural buckling

From Cl. 7.1.2.1, the design compressive strength,

fcd = fym0/[ + (22)0.5]

Here = 0.5[1+ ( - 0.2) + 2]

= (fy/ fcc)0.5

fcc = 2E/(KL/r)

2

Now, from the steel test data, fy= 375 MPa.

fcc=2

x 2 x 105/ (0.65 x 1400/7.7)

2= 141.33 MPa.

= (375/141.33)0.5

= 1.63

Buckling class : c (For all Angle Sections Buckling Class is same)So, = 0.49.

= 0.5[1+0.49 (1.63 - 0.2) + 1.632] = 2.18

fcd= 375 x 1.1 / [2.18 + (2.1821.63

2)0.5

] = 113.7 MPa.

Area of the angle section = 447 mm2.

Therefore, buckling load in flexure = 447 x 113.7 N = 50.83 kN.

Flexural torsional buckling

As per cl. 7.5.1.2, equivalent slenderness ratio, e= (k1+ k2vv2+ k3

2)0.5

vv = (l/rvv) / (2E/fy)

0.5

= [(b1+ b2) /2t]/ (2E/fy)

0.5

= (250 / 375)0.5

= 0.816.

So, vv = (1400/7.7) / 0.816(2x 2 x 10

5/375)

0.5= 3.07.

28.9 kN

34.820

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= [(40 + 40) /(2 x 6)]/ 0.816(2x 2 x 10

5/375)

0.5= 0.11.

k1= 0.2

k2= 0.35

k3= 20

Therefore, e= (0.2 + 0.35 x 3.072+ 20 x 0.11

2)0.5

= 1.93

= 0.5[1+0.49 (1.93- 0.2) + 1.932] = 2.78.

fcd= 375 x 1.1 / [2.78 + (2.7821.93

2)0.5

] = 86.28 MPa.

Area of the angle section = 447 mm2.

Therefore, buckling load in flexural torsion = 447 x 86.28N = 38.56 kN.

Therefore, theoretical buckling load in flexure>theoretical buckling load in flexural torsion >

observed buckling load.

Compare force measurements using strain gauges with that of load cell in the

actuator arm. Explain sources of discrepancies, if any.

The loading history is as follows:

-60

-40

-20

0

20

40

60

80

100

0 200 400 600 800 1000 1200

Load

(kN)

Time elapsed (second)

Loading history

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Strain gauge SG1 is installed at the unconnected leg of the steel brace, while SG2 is on the

connected leg. Therefore, SG2 readings are more than SG1 readings.

Lets consider certain SG2 readings and corresponding load cell readings.

Connected

Leg Strain

Connected

Leg Area

Unconnected

Leg Strain

UnConnected

Leg Area

Connected

Leg Load

UnConnected

Leg Load

Total Load cell

values

201.61 223.50 139.38 223.50 9.01 6.23 15.24 3.47

200.66 223.50 138.91 223.50 8.97 6.21 15.18 3.48

200.18 223.50 138.91 223.50 8.95 6.21 15.16 3.48

199.22 223.50 138.91 223.50 8.91 6.21 15.11 3.47

200.66 223.50 138.43 223.50 8.97 6.19 15.16 3.47

200.18 223.50 138.43 223.50 8.95 6.19 15.14 3.47

200.18 223.50 137.95 223.50 8.95 6.17 15.11 3.47

200.66 223.50 137.95 223.50 8.97 6.17 15.14 3.47

200.18 223.50 138.43 223.50 8.95 6.19 15.14 3.47

201.13 223.50 138.43 223.50 8.99 6.19 15.18 3.47

200.18 223.50 137.47 223.50 8.95 6.15 15.09 3.46

Thus, it is observed that load in the steel brace obtained in the load cell in the actuator is less

than that obtained from strain gauge readings.

This discrepancy is because of the fact that in calculating loads from strain gauge readings,

we have assumed uniform strain and stress distribution for the whole angle section, but in reality

it is not so.

Do you observe any sign of shear lag effect in any of the measurements that

has been made during the test?

Shear lag effect has been observed in the strain gauge readings. Strain gauge SG1 is

installed on the unconnected leg, whereas SG2 on connected leg. Since the compression in the

steel brace is mostly resisted by the connected leg (due to shear lag effect), the strain in the

connected leg is more than that in the unconnected leg. Here are some data which shows that

SG1 readings are less than SG2 readings:

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Connected Leg Strain Unconnected Leg Strain Shear lag

201.61 139.38

200.66 138.91

200.18 138.91

199.22 138.91

200.66 138.43

200.18 138.43

200.18 137.95

200.66 137.95

200.18 138.43

201.13 138.43

200.18 137.47

Therefore shear leg effect is observed.

Obtain an analytical prediction for the observed back-bone curve of the specimen

and compare the observed behavior.

For the steel used in the brace, fy= 375 MPa. So, Fy= 375x 447 N = 167.625 kN.

E = 2 x 105 N/mm

2. Therefore, y = 167.625x1000 x 1400 / (447 x 2 x 10

5) = 2.625 mm.

Therefore the theoretical backbone curve is as follows:

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Fig. Theoretical backbone curve for steel

Fy= 167.625 kN

F 6 = 27.937 kN

= 2.625 mm

Fy/3 = 55.875kN

y/3 = 0.875 mm

2 = 5.25 mm

F

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Now, the observed cyclic load (lateral) applied by the actuator vs displacement curve is as

follows:

From truss analysis, it is obtained that the ordinates of the above curve have to be multiplied by

1.202 to obtain steel brace load vs displacement curve, as shown next:

Thus, from the experimental backbone curve, Fy = 72.23kN and y= 23.55 mm.

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Therefore, deviation of the theoretical values of:

Fy=

x 100 % = 56.31%.

y =

x 100 % = 88.85 %.

Comment on the observed behavior, such as the axis of buckling, buckling

mode, inelastic activities, failure, etc. Is there any evidence of flexural torsion

buckling as anticipated in IS 800 for single angle struts?

Comments on observed behavior

Axis of buckling

The axis of buckling was the minor axis of the channel section,v-v, as shown below.

Buckling mode

The buckling occurred in the first mode, since no nodes were observed.

Inelastic activities

The load displacement curve shows that loading and unloading didnt follow the same path.

Therefore, inelastic activities took place during the experiment.

Failure

Failure took place when a hinge was fully formed at a section (towards mid-section) of the steel

brace. At this stage the lateral load applied by the actuator was highest.

v

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

struts. As we have already seen, the theoretical flexural torsional buckling load of the angle

section is obtained as 38.56 kN, whereas the experimental buckling load was 28.9 kN. Thus,

although there is a deviation, this may be because of the factor of safety assumed in finding out

the theoretical value as per IS 800:2007. Moreover, during the experiment, it was observed that

torsion took place along with flexure in the buckling. Therefore, flexural torsional buckling took

place.

Quantify the errors in observed values as compared to theoretical results.

State the source of errors involved in this experimental study.

Lets consider the buckling load. From the experimental result, the buckling load of the steel

brace under cyclic loading is 28.9 kN.

Theoretically, the flexural buckling load as per IS 800:2007 is 50.83 kN and the flexural

torsional buckling load is 38.56 kN.

Thus, the error in buckling load (considering flexural buckling) =

x 100 % =

43.14 %.

Error in buckling load (considering flexural torsion) =

x 100 % = 25.05 %.

Here in obtaining the theoretical buckling loads, factor of safety has been used, whereas

the actual steel brace can carry more load before buckling. This is a source of error.

Besides, in the experiment cyclic load has been applied and the steel brace has reached

inelastic zone. But in obtaining the theoretical values inelasticity has not been considered. Also,

the theoretical values do not take into account cyclic loads. Thats why there is a deviation of

experimental result from theoretical value.

6. Conclusions

Interpretation of the experimental results leads to concluding that there is a substantial

difference between observed buckling loads and theoretical buckling load. This is because of

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inelasticity of the actual structure and cyclic loading. The deviation of the theoretical backbone

curve from the experimental one is also due to this fact. The factor of safety taken into account

also affects the theoretical values. Due to shear lag effects, the strains measured by two strain

gauges are different. Moreover, we can conclude that the buckling occurred in the first mode

about the minor axis. The buckling is actually flexural torsional buckling. The errors in observed

values are quite high due to the facts discussed earlier. Also, it is observed that a hinge is formed

at about the mid-point of the steel brace on account of buckling.