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Report on

Full-Scale Load Testing of Steel Strutting System

For

Yongnam Holding Limited

Prepared by

Dr Richard Liew PhD, MIStrutE, CEng, PE(S’pore)

Department of Civil Engineering National University of Singapore

08 December 2006 (This Report Contains 48 Pages)

1

CONTENTS Page

1 Modular Strutting System 3

2 Test Objectives 3

3 Test setup 4

4 Instrumentation

4.1 Displacement measurements

4.2 Stress measurements

5

5

6

5 Test Procedure 7

6 Mechanical Properties of Used Steel 7

7 Test Results

7.1 Axial load-displacement relationship

7.2 Applied load- vertical displacement relationship

7.3 Applied load- lateral displacement relationship

7.4 Stresses in the main struts

7.5 Force distribution in the ties and lacing members

7.6 Test Observations and failure modes

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9

9

9

10

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8 Comparison with Code’s Design Capacity 11

9 Conclusions 12

References 13

Table 1: Loading intervals and observation 14

Table 2: Table 2: Initial out-of-straightness deflection (downwards deflection) of

struts before loading

14

Table 3: Locations, alignment and direction of sensors 15

Table 4: Axial load capacity of laced strut -comparison of predicted results with test

result

17

Figure 1: Test and instrument layout 18

Figure 2: Load application using hydraulic actuators and high-strength strands 19

Figure 3: S Strut with the loading tendons in position 20

Figure 4: Base support allowing horizontal movement 21

Figure 5: Base support preventing lateral translations. 21

Figure 6: Transducer D3 measuring axial displacement at the real end of the strut. 22

Figure 7: Vertical displacement transducers D5 and D6 at the splice joint of strut. 23

Figure 8: Details of coupon specimens and extracted location 24

2

Figure 9: Applied load versus axial displacements 25

Figure 10: Applied load versus vertical deflection 26

Figure 11: Vertical deflection profile of the strut 27

Figure12: Load versus lateral displacement at mid-length 27

Figure 13: Stresses on top and bottom flanges of the strut sections at mid-length 28

Figure 14: Axial forces in the Channel Sections 28

Figure 15: Applied load versus axial forces in the lacing members 29

Figure 16: Buckling of the main struts and lacing members after collapse 30

Figure 17: Buckling of the mid-length strut section 31

Figure 18: Another view showing the buckling of the laced strut 32

Figure 19: Applied force versus lacing forces – comparison with EC3 approach 33

Appendix A: Certificate of Calibration for Digital Pressure Gauge 34

Appendix B: Coupon Test Results

35

Appendix C: Design Approaches for Calculating Buckling Resistance of Build-up Members

37

C.1 BS5950:Part1:2000 Approach

C.2 BS EN1993-1-1:2005 Approach

C.3 EC 3 approach to evaluate the shear force of the axially loaded

laced struts

C.4 Example

37

40

46

47

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Full-Scale Load Testing of Steel Strutting System

1 Modular Strutting System

Yongnam has developed a proprietary Modular System of components that may be assembled to

provide a structural strutting system appropriate for the majority of excavation support requirements.

The system comprises of:

• Laced universal beams of various cross-sections in modular lengths.

• Single and double waler beams in various lengths, intermediate supporting beams, king

posts, bracing and waler support brackets.

• Various strut to waler joints have been produced to suit to suit the site conditions as

required.

The Yongnam strutting system has been used in many basement construction and civil engineering

excavation works including high-rise and mass rapid transit projects in Singapore, Hong Kong and

the Middle East.

There are, however, a number of questions asked with regard to the performance of the modular

strutting system, such as the performance of the splice joint, strength of the reusable materials, force

distributions in the lacings and channels between the main struts. In response to these questions, a

full scale load test of “used” modular strutting system spanning about 20m was carried out in the

premise of Yongnam Holdings Limited, located at 51 Tuas South Street 5, Singapore 637644, on 8

November 2006. This report provides the test results and their interpretation with regard to the

performance of the strutting system in comparison with the code’s predicted results.

2 Test Objectives

The objectives of carrying out full scale test on the laced strut system are:

• To determine the maximum load capacity of the strut system and compare against the

design capacity

• To investigate the performance and to identify the possible failure mode of the strut system

• To ascertain the maximum induced forces on lacing members and compare them with

results predicted by the design equations given in BS5950:2000:Part 1 and Eurocode 3

• To investigate the force distributions on the lacing members along the length of the strut

4

• To study the load-displacement behaviour of the strut system

• To determine the strength of re-usable strut materials and their implication to structural

safety.

To accomplish the objectives, the strutting system was load tested to failure to establish its buckling

capacity and failure mode. The failure load is compared with the code’s predicted load to gain

insight to its ultimate strength behaviour. The load-displacement relationship and internal force

distribution in the main struts and lacing members were monitored on-line during the test.

3 Test Setup

The test specimen consists of two universal beams, UB 610x324x195 kg/m, inter-connected by

diagonal laces of equal angle section 80x80x9.66kg/m, and ties of channel sections C254x76 and

C254x90 as shown in Figure 1. The length of the strut is 19.6m consisting of three modular

segments of lengths 3.8m, 12m and 3.8m. The three strut segments were connected by using 8

number of M24 Grade 8.8 bolts via flush end plate connections. The two end-strut 3.8m segments

was about 4 years old and they were used in KPE strutting works for project C-421 and circle line

MRT project C-853. The central strut segment of 12m length was more than 6 years old and had

been used in Hong Kong MRT project and subsequently deployed to LTA projects C-421 and C-851

(Note: This information was provided by Yongnam Holdings on requested by the author).

The laced strut specimen was arranged in a horizontal position and connected to waler beams at both

ends. Loads were applied horizontally from the ends of the struts through the waler beams using

three hydraulic jacks of maximum capacity of 800 tons each (Figure 2). The loading system

utilizes high tensile strands running along the sides of the strut and mounted onto the walers at the

ends applying a compressive loading on the struts (see Figure 3). A third party contractor, VSL

Singapore Pte Ltd, was engaged to supply and operate the hydraulic jacks. The jacks are linked to

share equal hydraulic pressure during load application using a hydraulic pump. Each hydraulic

jack was connected to 31 numbers of 0.6" diameter super low relaxation strands with the following

properties:

• Nominal Diameter of the strand: 15.7mm

• Nominal Area: 150mm

• Yield Strength: 1500 MPa

• Min. Breaking Load: 265 kN

5

The load was controlled by using a digital pressure gauge which was calibrated to ISO 17025. The

certificate of calibration is attached in Appendix A. Total applied load was manually

communicated to the data acquisition system at predetermined loading intervals listed in Table 1.

The two ends of the strutting system were bolted to waler beams which were supported by short

columns. The column bases were welded to end-plates. One end of the column base was seated

on a smooth concrete pad allowing free translation in the longitudinal direction of the strut as shown

in Figure 4. The other end of the column base (where the hydraulic jacks were mounted) was bolted

down to the concrete pad preventing any lateral movement (see Figure 5). The bolt connection to

the concrete pad offered very little resisting against overturning moment. The two end boundary

conditions of the strutting system simulate a pinned support and a roller support condition.

Before loading, the initial vertical deflection of the struts was measured and the results are shown in

Table 2. The strut has initial out-of-straightness with maximum vertical deflection of about 19 mm

at the spliced joint. This is slightly less than the maximum out-of-straightness tolerance of span

length/1000 (or 19.6mm) for column design as in BS5950:Part1:2000 [Ref. 1]. The initial

out-of-straightness in the lateral direction of the strut was found to be very small. This was due to

the present of lateral bracing members which controlled the straightness of the two struts in the

lateral direction.

4 Instrumentation

The test specimen was instrumented with strain gauges and displacement transducers to determine

the stresses in the strut and the lacing members and the lateral and vertical displacements. The

instrumentation layout plan is shown in Figure 1. A summary of the sensor locations and their

sensing direction is given in Table 3.

4.1 Displacement measurements

Displacements were measured using spring mounted strain gauge based displacement transducers.

The transducers have the following maximum travel distances (see Figure 1):

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Displacement Transducers Maximum Travel Distance

D1 and D2 50 mm

D3, D4, D5 and D6 200 mm

D7 and D8 100 mm

The measurement accuracy of the displacement transducers is ±0.02mm. The instruments were

connected electrically to a data logger of resolution 1 micro-strain and with measurement accuracy

of ±0.05% of reading.

The axial displacement was measured by taking the average readings from the displacement

transducers mounted at mid-height of the strut at positions D1, D2, D3, and D4 (see Figure 6). The

vertical deflections at the mid-span of the strut were measured using strain gauge based

displacement transducers mounted at positions D7, and D8. Additional vertical deflections were

measured at the splice joints of the laced strut at 3.8m from both ends of the test specimen as shown

in Fig. 7.

Lateral displacements were measured at the mid-length of the strut. The transducers were mounted

at positions D11, D12, D13, and D14 in Figure 1 measuring the lateral displacements of the top and

bottom flanges of the struts at mid-length.

4.2 Stress measurements

− Strain gauges were attached at the mid-length section of the lacing members along one-half of

the strut. They are indicated as L1 to L16, comprising 8 top and 8 bottom laces. Each lace

was instrumented with two strain gauges mounted longitudinally on each leg of the angle lace.

The first 4 laces nearest to the end were instrumented with 4 strain gauges with two gauges at

each leg, labelled as -1 to -4, to monitor their bending stresses.

− Strain gauges were attached to the mid-length of the strut to measure the compressive and

bending stresses at the top and bottom flanges of the strut. These comprise two strain gauges

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mounted on the top and bottom flanges at the mid-length section of each strut member, labelled

as S1 to S4.

− Strains gauges were attached to the channel tie sections located at the front end of the strut and at

the splice joints location, indicated as C1 to C6. Each channel section was instrumented with

three strain gauges to measure the average stresses acting on the channel section.

Data collection was triggered manually when the applied load reached the predetermined values.

The scanning rate of the data logger is approximately 0.08 second per channels.

5 Test Procedure

The load procedure was divided in 3 stages:

1 Preload cycling from 0 to 500 tons

− Repeated loading up to 500 tons and unloading without recording data. The bolts at the

splice joints were tighten at preload of 500 tons. This was necessary to remove any lack of fit

in the test specimen.

2 Load up to service load of 700 tons

− The service load of the test specimen is about 700 tons (design load capacity is about 1000

tons with factor of safety of 1.4). The service load indicated in Yongnam technical brochure

for this laced strut is about 750 tons. A quasi-static load was applied at an incremental load

of 100 tons up to 700 tons. At every load intervals, deflection and strain gauge readings were

taken.

3 Loading from 700 tons to failure

− Without unloading, the load was monotonically increased at intervals of 100 tons up to 1000

tons and thereafter at 50 tons increment till failure. At each load increment, deflection and

strain gauge readings were taken. Observations were made of the strut behaviour and failure

mode.

6 Mechanical Properties of Used Steel

Mechanical properties of the steel strut components were determined from coupon specimens

extracted from the used steel similar those in the test specimens. Details of the coupons and

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sampling location are shown in Figure 8. Coupons were cut longitudinal to the axis of the member

and machined to dimensions. In total, 8 coupons were extracted from the twin struts, 4 coupons

from the angle laces and 2 coupons from the channel tie sections.

The coupons were axially loaded in tension using universal testing machine with load cell

measurement accuracy of ±1%. Strains in the coupon were measured using extensometer of

measurement accuracy ±1%. Coupon test results are shown in Appendix B, Table B.1. The yield

strengths of the steel components are summarised in the table shown below:

Strut Section

UB 610x324x195 kg

12m strut segment

(6-year old)

3.8m strut segment

(4-year old)

Min. yield strength from tests 397 N/mm2 389 N/mm2

Design strength for S355 steel in BS5950

345 N/mm2

Lacing Members

Angle 80x80x9.66kg/m



275N/mm2

Channel tie members

250x90x25.5kg/m 254x76x28.29 kg/m



275N/mm2

The yield strengths of the steel components are not affected by the age, and their actual yield

strengths are higher than the nominal strength specified in the BS standards. The dimensions of the

structural sections were measured and compared with the nominal values specified in the section

table as reported in Table B2 in Appendix B. There is no evidence to suggest that the cross-section

areas of the re-used sections were reduced due to repeated use of the steel strutting system.

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7 Test Results

7.1 Axial load-displacement relationship

The axial load displacement relationship obtained from the test data is almost linear up to about

1000 tons as shown in Figure 9. The axial load displacement at service load of 700 tons is about 13

mm. Thereafter, axial displacement of the left strut increased faster than the right strut with an

average axial displacement of about 35mm at 1400 tons. Thereafter, axial deflection increased

rapidly and the strut failed at 1438 tons. Failure was characterised by the buckling of the main strut

members bending about their major axis (x-x axis) causing large deflection in the downward

direction.

7.2 Applied load- vertical displacement relationship

Figure 10 shows the applied load versus the vertical displacement curves taken at the mid-length

section and at the splice joint positions of the strut. The mid-length vertical deflection is about

14mm at the service load of 700 tons. When the applied load exceeded 1000 tons, the lateral

deflection increased in a nonlinear manner; the maximum measured vertical deflection is about 78

mm at applied load of 1400 tons occurred at the mid-length of the strut. The vertical deflection

increased rapidly when the load approached the maximum capacity of 1438 tons. The strut buckled

in the downward direction until the mid-length sections of the strut touched the ground. The

deflection profile of the strut was measured at various load stages and the deflected curves are

plotted in Figure 11. There is no slope discontinuity due to the present of splice joints along the

strut length. No opening up of splice joints was observed up to the load of 1400 tons.

7.3 Applied load- lateral displacement relationship

Figure 12 shows the applied load versus the lateral displacements measured at the mid-length section

of the strut. The lateral deflection of the strut was very small at the service load level (less than

2mm). This increases to about 8.4 mm just before failure at 1400 tons applied load. The bottom

flange of the Universal beam section defected more than the top flange under the increased load.

The maximum difference in lateral deflection is about 4mm at 1400 tons of applied. The lateral

deflection is considered to be very small as compared to the vertical displacement, indicating that the

lacing members were effective in preventing buckling in the lateral direction (i.e, y-y axis).

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7.4 Stresses in the main struts

Figure 13 shows the applied load versus the average stresses taken at the top and bottom flanges of

the main strut sections at the mid-length. The compressive stresses at the top flanges are higher

than those at the bottom flanges because of the combined axial and bending stresses at the

mid-length of the strut. It is noted that at 1400 tons of applied load, the strut sections at the mid

length are fully in compression, indicating that the moment was not large enough to induce tensile

stress in the strut. In other words, the strut remained in compression up to 1400 tons of applied

load. Slight yielding was observed at the top flange fibres at 1400 tons of applied load.

Significant yielding is expected beyond 1400 tons and up to failure load of 1438 tons since large

displacement occurred suddenly and cross section distortion occurred as shown in Figs. 17 and 18.

7.5 Force distribution in the ties and lacing members

The horizontal ties (channel members) experienced very small axial force of about 5 tons at the

applied load of 1400 tons as shown in Figure 14. Larger axial force was observed at the top

channel member near the supported end of the strut than those at the splice joints.

Figure 15 shows the axial force distribution in the lacing members along the half length of the laced

strut. Again the axial forces in the lacing members are very small. When the applied load is 700

tons (service load), the maximum lacing force is 4.4 tons which is about 0.63% the applied strut load.

When the applied load is 1400 tons, the maximum lacing force is about 7.5 tons, which is about 0.54

% the applied strut load.

The axial forces in the ties and lacing members are considered to be small as compared to the

requirement in BS5950:Part1:2000 of 2.5% of the axial force in the member, divided amongst the

transverse lacing systems in parallel planes. Detailed comparison with code’s requirement is

discussed in Section 8.

7.6 Test Observations and failure modes

Figures 16 to 18 show the deformed modes of the laced strut after collapse. The maximum load

capacity of the laced strut is 1438 tons. The failure is due to the buckling of the two main struts

buckled about their major axis (x-x direction). The large deflection caused yielding and distortion

of the universal beam section nears the mid-length of the strut as shown in Figures 16-18. All the

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bolted connections (in the splice joints, the ties and the laces) remained intact without any sign of

failure. The lacing members and their connections were adequate and effective in preventing

lateral buckling of the struts (i.e, y-y axis direction).

8 Comparison with Codes’ Design Capacity

The design of axially loaded laced struts, compared against that of conventional axially loaded struts

with web plates, should includes strength, stiffness and overall stability verifications, and

furthermore, the verification of local stability of single component should also be carried out and the

design check for all bracings (lacings) is necessary. The design of laced strut is provided in

BS5950:Part1:2000 Clause 4.7.8 [Ref. 1] and in Eurocode 3-1-1:2005 Clause 6.4 for built up

compression member [Ref. 2]. The capacity of the laced strut is controlled by (1) global buckling

of the two main struts about the major axis bending (X-X global), (2) global buckling about the y-y

axis of the compound strut (Y-Y global), and (3) local overall buckling of I-beam between the two

laced points, and (4) buckling of lacing or failure of connection. The comparison of axial capacity

based on codes’ predicted values and test result are shown in Table 4. Detailed calculations of

buckling capacity of laced strut using BS5950:Part1:2000 and EC3 (2005) are given in Appendix C.

The maximum load predicted by EC3-1-1:2005 is 984 tons, 1147 tons and 1314 tons assuming

effective length of 1.0L, 0.85L and 0.7L, respectively. The capacity is controlled by global

buckling about the X-X axis. This is consistent with the predicted failure mode and the predicted

buckling capacity is conservative compared to the test failure load of 1438 tons.

The maximum load predicted by BS5950:Part1:2000 is 995 tons, 1168 tons and 1320 tons assuming

effective length of 1.0L, 0.85L and 0.7L, respectively. If a shear force of 2.5% axial load is

assumed, the capacity of the strut is limited by the buckling capacity of lacing member which gives a

value of 1131 tons. However, failure of lacing member was not observed in the test before

buckling of the main struts. The BS5950:Part1:2000 approach is conservative as compared to the

actual failure load of the strutting system.

Clause 4.7.8 (i) of BS5950 Part 1:2000 states that “The lacings and their connections should be

designed to carry the forces induced by a transverse shear at any point in the length of the member

equal to 2.5% of the axial force in the member, divided equally amongst all the transverse lacing

systems in parallel planes”. At the applied load of 1400 tons, 2.5% of this load would indicate 18

tons of shear force. However, the measured maximum axial forces in the channel and angle section

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are only 5 and 7.5 tons, respectively. Therefore BS5950 recommendation is found to be too

conservative when compared to the measured forces in the lacing members in the test.

Eurocode 3-1-1:2005, on the other hand, provides a more reasonable interpretation of the transverse

shear force acting on the lacing members. The shear force is depending on the maximum bending

moment (i.e, axial force and lateral deflection) at the mid-length and the length of the strut.

Appendix C.3 provides the derivation of the design shear force formula in Eurocode 3-1-1:2005

based on second-order analysis of built-up compression. The predicted test result is compared with

those obtained from tests in Figure 19. EC3:2005 approach predicts a maximum axial force in the

lacing member as 8.5 tons compared to the test result of 7.5 tons. The comparison is found to be

reasonable.

In summary, the strut capacity predicted by EC3-1-1 and BS5950:Part1 are conservative compared

to the test result because:

(1) Boundary conditions may be partial restrained against rotation rather than pin-ended as

assumed in the design calculation. However, it should be noted that the bolts connecting to

the column base to the concrete pad offered very little resistance against overturning

moment. It is therefore reasonable to assume pin-ended boundary condition.

(2) The actual measured yield strength of grade S355 steel strut section is about 400 MPa which

is greater than the nominal yield strength of 345MPa in BS5950 (16mm<t<40mm) and

355MPa in EC3 (t<40mm);

(3) The lacing members are assumed to resist the total shear force in design (bending about Y-Y

axis). Actually, part of shear force was resisted by the I-beam sections. Therefore, the lacing

force is much smaller than that predicted by the codes. The actual lateral deflection of the

strut was very small and therefore the induced second-order moment and the corresponding

shear forces are smaller than those predicted by the codes.

9 Conclusions

The following conclusions may be derived from the full-scale testing of the laced strut system:

1) The predicted failure load of the strut based on BS5950:Part1:2000 is 995 tons. Based on

the design safety factor of 1.4, the working load is 710 tons. The actual collapse load of the

test specimen is 1438 tons. The factor of safety against the design working load is about

2.0. The load capacity predicted by the codes is found to be on the conservative side.

2) The ultimate load was not affected by the age of the strutting modules. Coupon tests show

that old and reused struts do not diminish in strength over the years (it means old struts can

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continue to be reused, if their thicknesses are not eroded due to sand blasting and

re-painting).

3) All the connections were robust and adequate as the failure was due to the overall buckling

of the main strut about the major axis (X-X axis) with plastic hinge formed at the mid-length

of the members. The load-carrying capacity and the load-displacement relationship of the

modular strutting system was not affected by the splice joint details.

4) Maximum axial force in the lacing members was approximately 0.54% of the applied strut

load. The shear force of 2.5% of axial force assumed in BS5950:Part1:2000 is too high.

Eurocode 3 provides a better estimation of the shear forces for designing the lacing members.

The laced members and their connections to the main struts were found to be adequate.

Failure was due to the buckling of the main struts and was not governed by the buckling of

the lacing member.

References 1. BS5950:Part 1 (2000), Structural use of steelwork in building, Part1: Code of practice for

design – rolled and welded sections, British Standards Institute.

2. Eurocode 3 Part 1-1 (2005), Design of steel structures: Part 1-1 General rules and rules for

building, British Standards Institute.

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Table 1: Loading intervals and observations

Total Applied Loads (ton) Observations 100 200 300 400 500 Maximum loading for preloading cycles 600 700 Design load of struts (750ton), no major deformation

noted 800 900

1000 1050 1100 Visible deflection at mid-span 1150 1200 1250 Adjustment of hydraulic actuators, unitisation of actuator

stroke 1300 observed reduction in strains and displacements 1350 1400 1438 Sudden buckling and collapse of strut, end of test

Table 2: Initial out-of-straightness deflection (downwards deflection) of struts before loading

Distance from the front end 3.8 m 9.8 m 15.8 m

Top flange deflection

2 mm 9 mm 21 mm

Bottom flange deflection

4 mm 8 mm 16 mm

Average deflection

3 mm 8.5 mm 19 mm

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Table 3: Locations, alignment and direction of sensors Measuring Element Location Position Direction Ref in

Fig. Ref in

Data fileAxial Front Waler Right of strut Centre line of load pts Outwards, +ve=Comp strut D1 0

// Left of strut Centre line of load pts Outwards, +ve=Comp strut D2 1 Rear Waler Right of strut Centre line of load pts Outwards, +ve=Comp strut D3 2 // Left of strut Centre line of load pts Outwards, +ve=Comp strut D4 3

Vertical Strut Right Joint nearer Front

Top channel of side strut Downward, +ve=Defl down D5 4

Strut Left // Top channel of side strut Downward, +ve=Defl down D6 5 Strut Right Mid-span Top flange of main strut Downward, +ve=Defl down D7 6 Strut Left // Top flange of main strut Downward, +ve=Defl down D8 7 Strut Right Joint nearer

Rear Top channel of side strut Downward, +ve=Defl down D9 8

Strut Left // Top channel of side strut Downward, +ve=Defl down D10 9 Lateral Strut Right Mid-span Top Flange, 100mm ext Towards left, +ve=Sway left D11 10

// // Bottom Flange, 100mm ext Towards left, +ve=Sway left D12 11 Strut Left Mid-span Top Flange, 100mm ext Towards right, +ve=Sway right D13 12 // // Bottom Flange, 100mm ext Towards right, +ve=Sway right D14 13

Strain Strut Right Mid-span Top Flange, top surface Middle of right outstand S1-1 14 // // Top Flange, top surface Middle of left outstand S1-2 15 // // Bottom Flange, bottom surface Middle of right outstand S2-1 16 // // Bottom Flange, bottom surface Middle of left outstand S2-2 17 Strut Left Mid-span Top Flange, top surface Middle of right outstand S3-1 18 // // Top Flange, top surface Middle of left outstand S3-2 19 // // Bottom Flange, bottom surface Middle of right outstand S4-1 20 // // Bottom Flange, bottom surface Middle of left outstand S4-2 21

Strain Channel #1 Mid section Flange nearer front Top channel C1-1 22 // // Middle of web // C1-2 23 // // Flange nearer rear // C1-3 24 Channel #2 Mid section Flange nearer front Bottom channel C2-1 25 // // Middle of web // C2-2 26 // // Flange nearer rear // C2-3 27 Channel #3 Mid section Flange nearer front Top channel C3-1 28 // // Middle of web // C3-2 29 // // Flange nearer rear // C3-3 30 Channel #4 Mid section Flange nearer front Bottom channel C4-1 31 // // Middle of web // C4-2 32 // // Flange nearer rear // C4-3 33 Channel #5 Mid section Flange nearer front Top channel C5-1 34 // // Middle of web // C5-2 35 // // Flange nearer rear // C5-3 36 Channel #6 Mid section Flange nearer front Bottom channel C6-1 37 // // Middle of web // C6-2 38 // // Flange nearer rear // C6-3 39

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Table 3 (continue): Locations, alignment and direction of sensors Measuring Element Location Position Direction Ref in

Fig. Ref in

Data fileStrain Lacing #1 Bolted flange 12mm from edge Top lacing L1-1 40

// // 12mm from other flange // L1-2 41 // Vertical flange 12mm from other flange // L1-3 42 // // 12mm from edge // L1-4 43 Lacing #2 Bolted flange 12mm from edge Bottom lacing L2-1 44 // // 12mm from other flange // L2-2 45 // Vertical flange 12mm from other flange // L2-3 46 // // 12mm from edge // L2-4 47 Lacing #3 Bolted flange 12mm from edge Top lacing L3-1 48 // // 12mm from other flange // L3-2 49

Strain Lacing #3 Vertical flange 12mm from other flange Top lacing L3-3 50 // // 12mm from edge // L3-4 51 Lacing #4 Bolted flange 12mm from edge Bottom lacing L4-1 52 // // 12mm from other flange // L4-2 53 // Vertical flange 12mm from other flange // L4-3 54 // // 12mm from edge // L4-4 55 Lacing #5 Bolted flange Middle of flange Top lacing L5-1 56 // Vertical flange // // L5-2 57 Lacing #6 Bolted flange Middle of flange Bottom lacing L6-1 58 // Vertical flange // // L6-2 59 Lacing #7 Bolted flange Middle of flange Top lacing L7-1 60 // Vertical flange // // L7-2 61 Lacing #8 Bolted flange Middle of flange Bottom lacing L8-1 62 // Vertical flange // // L8-2 63 Lacing #9 Bolted flange Middle of flange Top lacing L9-1 64 // Vertical flange // // L9-2 65 Lacing #10 Bolted flange Middle of flange Bottom lacing L10-1 66 // Vertical flange // // L10-2 67 Lacing #11 Bolted flange Middle of flange Top lacing L11-1 68 // Vertical flange // // L11-2 69 Lacing #12 Bolted flange Middle of flange Bottom lacing L12-1 70 // Vertical flange // // L12-2 71 Lacing #13 Bolted flange Middle of flange Top lacing L13-1 72 // Vertical flange // // L13-2 73 Lacing #14 Bolted flange Middle of flange Bottom lacing L14-1 74 // Vertical flange // // L14-2 75 Lacing #15 Bolted flange Middle of flange Top lacing L15-1 76 // Vertical flange // // L15-2 77 Lacing #16 Bolted flange Middle of flange Bottom lacing L16-1 78 // Vertical flange // // L16-2 79

Sign convention: Displacement transducers (D1 to D14) + is extension, -ve is retraction Strain Gauges (S1 to S4, C1 to C6, L1 to L16) +ve is tension, -ve is compression Note: Strain gauges on channels and lacing installed on inner surface, as shown in figure

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Table 4: Axial load capacity of laced strut -comparison of predicted results with test result

A fy L I Max. Load (tons) Failure mode (mm2) (MPa) (mm) (mm4) EC3 BS 5950 Test

X-X Global 49800 S355 19600 3.346E+09 984 / 1147 / 1314 *

995 / 1168 / 1320 * Laced

Struts Y-Y Global 49800 S355 19600 1.245E+10

1506 /1582 /1656*

1498 /1569 /1685*

I-beam y-y Local 24900 S355 2000 1.416E+08 1533**

1726** x-x/y-y 1230 S355 1414.2 7.24E+05

u-u 1230 S355 1414.2 1.15E+06Lacing v-v 1230 S355 1414.2 3.00E+05

2467 1131

1438

Notes: * Different values with different effective lengths assumed LEX=1.0L/0.85L/ 0.70L;

** Value obtained based on effective length LEY =1.0L.

18

Figure 1: Test and instrument layout

19.6m total length consisting of 3.8m + 12m + 3.8m segments

6 m 3.8 m

19

Figure 2 Load application using hydraulic jacks and high-strength strands

20

Figure 3: Strut with the loading strands in position

21

Figure 4 Base support allowing horizontal movement

22

Figure 5 Base support preventing lateral translations.

Figure 6: Transducer D3 measuring axial displacement at the real end of the strut.

23

Figure 7: Vertical displacement transducers D5 and D6 at the splice joint of strut.

24

Figure 8: Details of coupon specimens and extracted location

25

Axial displacement at

0

200

400

600

800

1000

1200

1400

1600

0 5 10 15 20 25 30 35 40 45 50Axial Displacement (mm)

Tot

al A

pplie

d A

xial

Loa

d (t

ons)

Right StrutLeft Strut

Figure 9: Applied load versus axial displacements

26

Vertical deflection at

0

200

400

600

800

1000

1200

1400

1600

0 10 20 30 40 50 60 70 80 90 100Vertical Deflection (mm)

Tot

al A

pplie

d A

xial

Loa

d (t

ons)

1st splice joint from front endmid-length1st splice joint from rear end

Figure 10: Applied load versus vertical deflection

27

Total applied axial load

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Distance from Front to Rear (m)

Ver

tical

Def

lect

ion

(mm

)

700 tons1000 tons1200 tons1400 tons

Figure 11: Vertical deflection profile of the strut

Lateral deflection at

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4 5 6 7 8 9 10Lateral Displacement (mm)

Tot

al A

pplie

d A

xial

Loa

d (t

ons)

Top flange Right strutBottom flange Right strutTop flange Left strutBottom flange Left strut

Figure12: Load versus lateral displacement at mid-length

28

Stresses measured at

0

200

400

600

800

1000

1200

1400

1600

0 50 100 150 200 250 300 350 400Stress at mid-length section of Struts (N/mm2)

Tot

al A

pplie

d A

xial

Loa

d (t

ons)

Top flange Right strutBottom flange Right strutTop flange Left strutBottom flange Left strut

+ve indicating compressive stresses

Figure 13: Stresses on top and bottom flanges of the strut sections at mid-length

Forces measured at

0

200

400

600

800

1000

1200

1400

1600

-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16Axial Force on Channels (ton)

Tot

al A

pplie

d A

xial

Loa

d (t

on)

Channel #1Channel #2Channel #3Channel #4Channel #5Channel #6

+ve indicating compressive forces

Figure 14: Axial forces in the Channel Sections

29

Forces measured at

0

200

400

600

800

1000

1200

1400

1600

-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16

Axial Force on Lacings (ton)

Tot

al A

pplie

d A

xial

Loa

d (t

on)

Lacing #1Lacing #2Lacing #3Lacing #4Lacing #5Lacing #6Lacing #7Lacing #8Lacing #9Lacing #10Lacing #11Lacing #12Lacing #13Lacing #14Lacing #15Lacing #16

+ve indicating compressive forces

Figure 15: Applied load versus axial forces in the lacing members

30

Figure 16: Buckling of the main struts and lacing members after collapse

31

Figure 17: Buckling of the mid-length strut section

32

Figure 18: Another view showing the bucking of the laced strut

33

0

200

400

600

800

1000

1200

1400

1600

-6 -4 -2 0 2 4 6 8 10

Predicted by EC3

Lacing #1

Lacing #2

Lacing #3

Lacing #4

Lacing #5

Lacing #6

Lacing #7

Lacing #8

Lacing #9

Lacing #10

Lacing #11

Lacing #12

Lacing #13

Lacing #14

Lacing #15

Lacing #16

Figure 19 Applied force versus lacing forces – comparison with EC3 approach

34

Appendix A: Certificate of Calibration for Digital Pressure Gauge

35

Appendix B Coupon Test Results Table B.1 Mechanical properties of steel sections from coupon tests

12m strut segment (4 year-old) 3.8m strut segment (6 year-old)Strut Section UB 610x324x195 kg Flange Web Flange Web Coupon Sample Reference 5F1 5F2 5W3 5W4 10F1 10F2 10W3 10W4Measured Width (mm) 12.60 12.61 12.72 12.67 12.55 12.72 12.57 12.65Measured Thickness (mm) 23.32 23.24 14.69 14.68 23.06 22.93 15.11 14.78Cross-sectional Area (mm2) 293.83 293.06 186.86 186.00 289.40 291.67 189.93 186.97Yield Load (kN) 116.5 132.6 76.7 76.5 115.7 113.5 78.3 79.6 Yield Strength (N/mm2) 397 453 411 411 400 389 412 426 Maximum Load (kN) 168.8 164.1 108.1 107.2 146.9 144.2 98.4 97.0 Max. Tensile Strength (N/mm2) 575 560 579 576 508 494 518 519 Elastic Modulus (kN/mm2) 209.0 211.5 199.8 197.0 214.6 202.9 199.1 202.0 Lacing Angle 80x80x8 Coupon Sample Reference 5L1 5L2 10L1 10L2 Measured Width (mm) 12.79 12.50 13.03 12.63 Measured Thickness (mm) 9.60 9.53 8.20 7.70 Cross-sectional Area (mm2) 122.78 119.13 106.85 97.25 Yield Load (kN) 38.4 37.2 36.4 37.8 Yield Strength (N/mm2) 313 312 341 389 Maximum Load (kN) 55.1 54.7 55.1 57.0 Max. Tensile Strength (N/mm2) 449 459 516 586 Elastic Modulus (kN/mm2) 190.7 193.3 168.0** 182.7 Channels

254x76x28.29 kg/m

250x90x25.5kg/m

Coupon Sample Reference 5C 10C Measured Width (mm) 12.66 12.68 Measured Thickness (mm) 8.91 6.68 Cross-sectional Area (mm2) 112.80 84.70 Yield Load (kN) 38.5 30.4 Yield Stress (N/mm2) 341 358 Maximum Load (kN) 56.4 42.3 Tensile Strength (N/mm2) 500 499 Elastic Modulus (kN/mm2) 201.4 195.3

Note: ** Low value, this result is ignored Table B.2 Section Dimensions of Lacing members and Channels D (mm) B (mm) t (mm) T (mm) Area

(cm2)

36

Lacing members Measured dimensions 81.0 81.0 8.1 8.1 12.50 From section table - 80x80x9.66kg/m

80.0 80.0 8.0 8.0 12.30

Channels Measured dimensions for channel at 3.8m strut segment

262.0 76.5 7.9 13.1 38.78

From section table 254x76x28.29kg/m

254.0 76.2 8.1 10.9 36.03

Measured dimensions for channel at 12m strut segment

251.0 90.2 8.9 14.3 45.67

From section table - 250x90x25.5kg/m

250.0 90.0 8.0 15.0 45.20

37

Appendix C: Design Approaches for Calculating Buckling Resistance of Build-up members

C.1 BS5950:Part1:2000 Approach

The cross-section UB610×324×195 ( 9 4 8 41.673 10 , 1.416 10 ,x yi mm i mm= × = × 259 , 75.5x yr mm r mm= = ,

2249chA cm= ) is used for chords and section L80×80×8 ( 5 47.24 10x yi i mm= = × , 24.3x yr r mm= = ,

6 4 5 41.15 10 , 3.0 10u vi mm i mm= × = × , 30.6 , 15.6u vr mm r mm= = , 212.3dA cm= ) for lacing members;

2. 0 1000 , 2000 , 1000 2h mm a mm d mm= = = ;

d

h

a

0

Ach

Ad

1000

x

L80×80×8

UB

610×

324×

195

y

NEd NEd

L=19600mm

Fig. C1 Dimension of laced strut

3. Structural steel grade: S355;

4. Calculation of the overall buckling resistance based on BS 5950-1:2000:

(1) Check overall buckling resistance of struts about X-X axis

a) LE=1.0L

/ / 19600 / 259 76X E X xL R L rλ = = = = (1)

2196( / ) ( , )cp N mm rolled I section buckling curve c= − (2)

, ,9760.824900 2 196 9760.8( ) ( ) 995( )

9.81b Rd XN kN ton ton= × × = = = (3)

b) LE=0.85L

/ 0.85 / 0.85 19600 / 259 64X E X xL R L rλ = = = × = (4)


NEd/2 NEd/2

38

, ,1145424900 2 230 11454( ) ( ) 1168( )9.81b Rd XN kN ton ton= × × = = = (6)

c) LE=0.70L

/ 0.70 / 0.70 19600 / 259 53X E X xL R L rλ = = = × = (7)


, ,1294824900 2 260 12948( ) ( ) 1320( )9.81b Rd XN kN ton ton= × × = = = (9)

(2) Check buckling resistance about Y-Y axis

i) Global (check struts member)

a) 1.0 19600EL L mm= =

2 8 2 10 40 10002 2 ( ) 2 1.416 10 2 24900 ( ) 1.273 10 ( )2 2Y y chhI i A mm= + = × × + × × = × (10)

/ 2 505( )Y Y chR I A mm= = (11)

/ 19600 / 505 39Y E YL Rλ = = = (12)


, , ( ) 24900 2 295 14691( ) 1498( )b Rd Y globalN kN ton= × × = = (14)

b) 0.85EL L=

2 8 2 10 40 10002 2 ( ) 2 1.416 10 2 24900 ( ) 1.273 10 ( )2 2Y y chhI i A mm= + = × × + × × = × (15)

/ 2 505( )Y Y chR I A mm= = (16)

/ 0.85 19600 / 505 33Y E YL Rλ = = × = (17)



c) 0.70EL L=

2 8 2 10 40 10002 2 ( ) 2 1.416 10 2 24900 ( ) 1.273 10 ( )2 2Y y chhI i A mm= + = × × + × × = × (20)

/ 2 505( )Y Y chR I A mm= = (21)

/ 0.70 19600 / 505 27Y E YL Rλ = = × = (22)



39

ii) Local ( 2000 ,chL mm check single chord= ):

/ 2000 / 75.5 26.5ch yL rλ = = = (25)

2340( / ) ( , )cp N mm rolled I section buckling curve b= − (26)

, , 24900 340 8466( ) 863( )b Rd chN kN ton= × = = (27)

, ,2 1692( ) 1726( )Ed b Rd chN N kN ton≤ = = (28)

(3) Check lacing member

/ 58x y xd rλ λ= = = , / 46u ud rλ = = , / 91v vd rλ = = (29)

2, ,

2,

2,

252 /286 / ( , )160 /

c x c y

c u

c v

p p N mmp N mm rolled angle buckling curve cp N mm

⎧ = =⎪ =⎨⎪ =⎩

(30)

, , ( ) , , ( ) ,

, , ( ) ,

, , ( ) ,

310( ) 32( )352( ) 36( )197( ) 20( )

b Rd x lacing b Rd y lacing c x d

b Rd u lacing c u d

b Rd v lacing c v d

N N p A kN tonN p A kN tonN p A kN ton

⎧ = = = =⎪ = = =⎨⎪ = = =⎩

(31)

, , ( )2 / 21131( )

2.5% 2.5%b Rd v lacingEd

Ed

NVN ton×

= ≤ = (32)

40

C.2 BS EN1993-1-1:2005 Approach

5. Calculation of the overall buckling resistance based on BS EN1993-1-1:2005:

(1) Check overall buckling resistance of struts about X-X axis

a) 1.0 19600EL L mm= =

The plastic resistance of the cross-section to compression:

, 24900 355 2 17679( )pl Rk yN Af kN= = × × = (33)

The Euler buckling load:

2 2 5 9

, 2 2

2.1 10 2 1.673 10 18052( )19600cr X

E

EIN kNL

π π × × × × ×= = = (34)

The relative slenderness:

, ,/ 0.990X pl Rk cr XN Nλ = = (35)

The slenderness reduction factor: 2

0.5[1 ( 0.2) ] 1.183 ( )X XX buckling curve cϕ α λ λ= + − + = (36)

22

1 0.5460X

XX X

χϕ ϕ λ

= =+ −

(37)

The overall buckling resistance of the struts about X-X axis:

, , ,96539653( ) ( ) 984( )9.81b Rd X X pl RdN N kN ton tonχ= = = = (38)

b) 0.85EL L=

2 2 5 9

, 2 2

2.1 10 2 1.673 10 24986( )(0.85 19600)cr X

E

EIN kNL

π π × × × × ×= = =

× (39)

, ,/ 0.841X pl Rk cr XN Nλ = = (40)


22

1 0.6363X

XX X

χϕ ϕ λ

= =+ −

(42)

, , , 11250( ) 1147( )b Rd X X pl RdN N kN tonχ= = = (43)

c) 0.70EL L=

2 2 5 9

, 2 2

2.1 10 2 1.673 10 36841( )(0.7 19600)cr X

E

EIN kNL

π π × × × × ×= = =

× (44)

, ,/ 0.693X pl Rk cr XN Nλ = = (45)


41

22

1 0.7292X

XX X

χϕ ϕ λ

= =+ −

(47)

, , , 12891( ) 1314( )b Rd X X pl RdN N kN tonχ= = = (48)

(2) Check buckling resistance about Y-Y axis

i) Global

a) 1.0 19600EL L mm= =

The Euler buckling load: 2 2 10 400.5 0.5 1000 24900 1.245 10 ( )eff chI h A mm= = × × = × (49)

(Note: EC3 uses above conservative formula; more accurate formula should be 2 2 8 10 400.5 2 0.5 1000 24900 2 1.416 10 1.273 10 ( )eff ch yI h A i mm= + = × × + × × = × )

2 2 5 10

, 2 2

2.1 10 1.245 10 67170( )19600

effcr Y

E

EIN kN

Lπ π × × × ×

= = = (50)


, ,/ 0.513Y pl Rk cr YN Nλ = = (51)


0.5[1 ( 0.2) ] 0.708 ( )Y YY buckling curve cϕ α λ λ= + − + = (52)

22

1 0.8357Y

YY Y

χϕ ϕ λ

= =+ −

(53)

The overall buckling resistance of the struts:

, , ( ) , 14774 1506( )b Rd Y global Y pl RdN N kN tonχ= = = (54)

b) 0.85EL L=

2 2 5 10

, 2 2

2.1 10 1.245 10 92969( )(0.85 19600)

effcr Y

E

EIN kN

Lπ π × × × ×

= = =×

(55)

, ,/ 0.436Y pl Rk cr YN Nλ = = (56)


22

1 0.8781Y

YY Y

χϕ ϕ λ

= =+ −

(58)


c) 0.70EL L=

42

2 2 5 10

, 2 2

2.1 10 1.245 10 137082( )(0.70 19600)

effcr Y

E

EIN kN

Lπ π × × × ×

= = =×

(60)

, ,/ 0.359Y pl Rk cr YN Nλ = = (61)


22

1 0.9187Y

YY Y

χϕ ϕ λ

= =+ −

(63)


ii) Local ( 2000 ,chL mm check single chord= ):

The plastic resistance of the cross-section to compression:

, , 24900 355 8839500 8839.5pl Rk ch ch yN A f N kN= = × = = (65)

The Euler buckling load: 2 2 5 8

, 2 2

2.1 10 1.416 10 73371( )2000cr ch

ch

EIN kNLπ π × × × ×

= = = (66)


, ,

,

0.347pl Rk chch

cr ch

NN

λ = = (67)


0.5[1 ( 0.2) ] 0.585 ( )ch chch buckling curve bϕ α λ λ= + − + = (68)

22

1 0.9466ch

chch ch

χϕ ϕ λ

= =+ −

(69)

The local buckling resistance of single chord:

, , , , 8367 853( )b Rd ch pl Rd chN N kN tonχ= = = (70)

The shear stiffness of the lacings:

2 5 20

3 3

2 2.1 10 1230 2000 1000 182646( )2 2 (1000 2)

dv

nEA ahS kNd

× × × × ×= = =

× (71)

The design value of the maximum moment in the middle of the struts considering second order effects

(MIEd=0):

0

,

1

IEd Ed

EdEd Ed

cr Y v

N e MM N NN S

+=

− − (72)

The design force at the mid-height of single chord should fulfill

0, , , 853( )

2 2Ed Ed ch

ch Ed b Rd cheff

N M h AN N tonI

= + ≤ = (73)

Then the design axial force NEd should fulfill

43

15035( ) 1533( )EdN kN ton≤ = (74)

(3) Check lacing member

Similarly, the buckling resistance of lacing member is calculated:

, ( / )

, ( )

, ( )

326( ) 33( )

364( ) 37( )

212( ) 22( )

b Rd x x y y

b Rd u u

b Rd v v

N kN ton

N kN ton

N kN ton

− −

−

−

⎧ = =⎪

= =⎨⎪ = =⎩

(75)

The design force NEd should fulfill

, ( )

0

,

2 / 2 300( )

1

Ed b Rd v v

IEd Ed Ed

EdEd Ed

cr Y v

V N kN

M N e MV N NL LN S

ππ

−⎧ ≤ =⎪⎪ +⎨ = =⎪ − −⎪⎩

(76)

24200( ) 2467( )EdN kN ton≤ = (77)

44

Table C1: Summary on the buckling resistance of laced strut system

A fy L I Max. Load NEd (ton) Failure mode (mm2) (MPa) (mm) (mm4) EC3 BS 5950

X-X Global 49800 S355 19600 3.346E+09 984 /1147/1314* 995 / 1168 / 1320* Laced

Struts Y-Y Global 49800 S355 19600 1.245E+10 1506 /1582 /1656 1498 / 1569 / 1685

I-beam y-y Local 24900 S355 2000 1.416E+08 1533** 1726 x-x/y-y 1230 S355 1414.2 7.24E+05 u-u 1230 S355 1414.2 1.15E+06 Lacing v-v 1230 S355 1414.2 3.00E+05

2467** 1131

Notes: * Different values under different effective lengths LE=1.0L, 0.85L or 0.70L;

** Value under effective length LE=1.0L.

If the built-up member is bent about Y-Y plane, the relationship between the shear force VEd and the design

compression force NEd to the built-up member is shown in following Fig. C2 by assuming is the initial bow

imperfection e0 as L/500.

e0=L/500

0.005

0.006

0.007

0.008

0.009

0.01

1000 3000 5000 7000 9000 11000 13000 15000

Fig. C2 The relationship between shear force VEd and compression force NEd

Design chart for laced struts showing the relationship between the design capacity and the effective length is shown in

Fig. C3. If BS5950:Part1:2000 approach is adopted the design capacity is limited by the buckling capacity of the

lacing member assuming a maximum shear force of 2.5% axial force. The capacity of the lacing member will

govern the design when the strut length id less than 17 m. However, such limitation does not exist if

BSEN1993:EC3:2005 approach is adopted. This is explained in the following sections.

NEd (kN)

VE

d/NE

d

45

0

2

4

6

8

10

12

14

16

10 12 14 16 18 20 22 24

EN 1993BS 5950Shear resistance control line

Effective length, Lex (m)

Fig. C3 Design chart for laced struts using 2UB610×324×195 Grade S355 section

Stru

t res

ista

nce

(103

kN)

46

C.3 EC 3 approach to evaluate the shear force of the axially loaded laced struts

An axially loaded column, pinned at the two ends, is showed in Fig C42.

Fig. C4 The shear force of axially loaded column

Assuming the deflection curve is

sin xy vlπ

=

(1)

Then the moment is

sin xM Ny Nvlπ

= = (2)

The shear force is

cosdM N v xVdx l l

π π= = (3)

Therefore, the maximum shear force at the two ends is

maxN vV

lπ

= (4)

The maximum moment is (at middle height)

maxM Nv= (5)

Thus, Equation (4) can be expressed as

maxmax

MVl

π= (6)

Equation (6) is the formula adopted in BSEN1993:EC3:2005 The maximum shear force in the laced strut is

depending on the lateral deflection, the applied axial force (i.e, Mmax) and the strut length.

47

C.4 Example

The cross-section UB610×324×195 ( 9 4 8 41.673 10 , 1.416 10 ,x yi mm i mm= × = × 259 , 75.5x yr mm r mm= = ,

2249chA cm= ) is used for chords and section L80×80×8 ( 5 47.24 10x yi i mm= = × , 24.3x yr r mm= = ,

6 4 5 41.15 10 , 3.0 10u vi mm i mm= × = × , 30.6 , 15.6u vr mm r mm= = , 212.3dA cm= ) for lacing members;

0 1000 , 2000 , 1000 2h mm a mm d mm= = = ;

d

h

a

0

Ach

Ad

1000

x

L80×80×8

UB

610×

324×

195

y

NEd NEd

L=19600mm

Fig. C5 Dimension

Structural steel grade: S355;

Calculation of lacing force according to EC3 (Y-Y axis):

The maximum shear force in struts is

EdEd

E

MVL

π= (1)

where LE is the effective length and MEd is maximum moment in the middle of the struts considering second order

effects

0

,

1

EdEd

Ed Ed

cr Y v

N eM N NN S

=− −

(2)

where Sv is the shear stiffness of the lacings

NEd/2 NEd/2

48

2 5 20

3 3

2 2.1 10 1230 2000 10002 2 (1000 2)

182646( ) 18618( )

dv

nEA ahSd

kN tons

× × × × ×= =

×= =

(3)

and Ncr,Y is the effective critical force about Y-Y axis of the struts 2

, 2 67170( ) 6847( ) ( 1.00 )effcr Y E

E

EIN kN tons L L

Lπ

= = = = (4)

Therefore, the maximum axial force in one lacing member is

0

,

2 22 2 1

Edlacing Ed

Ed EdE

cr Y v

N eN V N NLN S

π= =

− − (5)

Taking e0=LE/500 according to EC3, it obtains

,

21000 1

Edlacing

Ed Ed

cr Y v

NN N NN S

π=

− − (6)

It can be observed that the maximum axial force in the lacing member is depending on the applied axial load, NEd, the

shear stiffness, Sv, and the elastic critical load of the laced strut bending about the y-y direction, Ncr,y.

full-scale load testing of steel strutting system for ... · pdf filefull-scale load testing...

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