pap_0583_ms-26

7th EUROMECH Solid Mechanics Conference J. Ambrósio et.al. (eds.)

Lisbon, Portugal, September 7-11, 2009

NUMERICAL MODELLING OF FULL-SCALE TUBE AND FITTING SCAFFOLD TESTS

Robert G. Beale*, Michael H.R. Godley†

*Oxford Brookes University

Gipsy Lane, Headington, Oxford, OX3 OBP, UK [email protected]

†Oxford Brookes University

Gipsy Lane, Headington, Oxford, OX3 OBP, UK [email protected]

Keywords: scaffolding, non-linear analysis, semi-rigid, buckling, elastic, steel

Abstract. The replacement of the UK design code BS for scaffold structures by the Euro-pean standard EN128112 has led to a change in UK scaffold practices. The authors have de-veloped a guidance note which implies that established scaffold designs overestimate scaffold performance. To verify the conclusions full-scale tests were conducted at the UK Building Re-search Establishment. The experimental scaffold consisted of a four bay, four lift access scaf-fold with diagonal façade and ledger bracing which was tied to a façade.

Small horizontal loads were applied to the scaffolds at points where a numerical analysis illustrated that they would have the maximum destabilizing effect followed by vertical loads until failure occurred. A numerical model of the scaffold structure was constructed using the LUSAS finite element program which showed that the behavior of the frame could be pre-dicted as long as the full non-linear joint characteristics were included including the allow-ance of vertical slip at bracing-standard joints. In common with the experiments the model showed the sensitivity of the frame to the bracing pattern – the asymmetric ledger-standard pattern put additional loads onto either the rear or the front standards which either caused early buckling or restrained the buckling. In addition small changes in the rotational stiff-nesses of the scaffold connections cause large changes in the scaffold behavior. Due to the initial large stiffnesses of the perfect frame one of the series of scaffold tests was able to have failure loads in excess of the first buckling mode but followed by immediate snap-through to the buckling load once failure was initiated. The second series of tests and the numerical model were only able to reach the buckling load.

Robert G. Beale and Michael H. Godley

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1 INTRODUCTION

Steel scaffolds are extensively used to provide access and support to permanent works dur-ing different stages of their construction. These structures are generally slender and prone to fail by elastic instability. The replacement of the UK design code for scaffold structures BS 5973 [1] by the European standard EN12811 [2] has led to a change in UK scaffold practices. The authors constructed several numerical models of tube and fitting scaffolds according to the code [3] and as a result the UK National Access and Scaffolding Confederation (NASC) issued a guidance code TG20:05 [4]. The provisions of this guide implied that established scaffold designs overestimated the performance of the structures. Hence the NASC decided to undertake full-scale tests at the UK Building Research Establishment (BRE) to see if the code predictions were correct [5]. The elastic buckling load of a scaffold is strongly influenced by the stiffnesses of the connections, which exhibit semi-rigid deformation behavior that can con-tribute substantially to the stability of the structure as well as to the distribution of member forces.

Figure 1 shows a schematic of the scaffold structures tested.

X

Y

Z

Tie

Standard

Ledger brace

Transom

Ledger

Face brace

Figure 1: Schematic of tested scaffold

The experimental scaffold consisted of a four bay, four lift access scaffold with diagonal façade and ledger bracing which was tied to the façade as shown in Figure 1. Each bay was 2 m wide and the height of each lift was 2 m except for the top lift which was only 1.8 m high. The front and rear frames were 1.215m apart. The scaffold tubes were 48.7 mm diameter with an area of 557 mm2 and second moment of area about a diameter of 1380000 mm4. Horizontal guard-rails were attached at the front in the middle of the second, third and fourth lifts and an additional guardrail 0.5 m above the third lift as shown in Figure 1. All connec-tions between ledgers and standards and transoms and ledgers were semi-rigid. The connec-tions between all bracing and standards and between guardrails and standards were pinned. Tie-bars consisting of scaffold tubes pinned to two standards and restrained from moving

Robert G. Beale and Michael H.R. Godley

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horizontally at the rear but free to move vertically were used to fix the scaffold to a rear fa-cade. Three small horizontal loads were placed on the scaffold (two parallel to the façade and one perpendicular to the façade at points where a buckling analysis indicated that they would have the most destabilizing effect) prior to loading vertically to failure. The loading mecha-nism was by means of tie rods connected to cross-frames which were then bolted to single beams placed across two standards and jacked from below the frame. When the vertical load was applied to the scaffold little deflection occurred until the scaffold failed at just over 40kN with a steep fall in load and a snap through into a buckling pattern corresponding to the first buckling mode which was calculated with standard connection and section properties to be 25 kN. In a second test of a nominally similar structure with components supplied by a dif-ferent manufacturer the scaffold failed by sway buckling in the first mode at a maximum load of 25 kN with no post buckling strength. The objective of this paper is to produce numerical models which predict the behavior.

2 CONNECTION PROPERTIES

Figure 2 shows moment rotation curves for typical right-angled connectors as used in tube and fitting scaffolds. Samples of these connectors were recently tested by the authors [6].

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-1

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0

0.5

1

-0.3 -0.2 -0.1 0 0.1

Rot at ion ( r ad)

-1

-0.5

0

0.5

1

1.5

-0.2 -0.1 0 0.1 0.2 0.3

Rotation (Rad)

Mom

ent (

kNm

)

Figure 2: Typical moment-rotation curves for tube and fitting right-angled connectors

For the purpose of design and analysis the moment rotation curve is often assumed to be bi-linear or multi-linear and the same curve is used for both sagging and hogging moments. In this case, the predicted behavior of the structure may be quite unrealistic compared to that of the actual structure. In addition, due to the slender nature of scaffold structures, geometric non-linear interactions between the axial load and lateral deformations increase the complex-ity of the analysis.

The majority of previous experimental and theoretical research [7-13] into scaffold struc-tures has primarily concentrated on modelling the joints as elastic semi-rigid connections as-suming a linear behavior with the same clockwise and anti-clockwise rotational stiffnesses. However, as can be seen from Figure 2 the assumption of linear behavior is considerably in error even for common scaffold connections. The authors [6] used EN12810 Part 3 [14] to derive properties of the scaffold connections. The code enables the curves in Figure 2 to be represented by bi-linear expressions as shown in Figure 3(a). If, as occurred in the connec-tions used in the test, the rotational stiffnesses differ by less than 10% the same values can be used for clockwise and anti-clockwise rotations. However, many computer programs are un-able to correctly handle multi-linear curves and hence the authors, using a procedure devel-


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oped in pallet rack design codes [15] where the bi-linear line is represented by a single line with equal work above and below the experimental curve (Figure 3(b)).

This procedure was found in experiments by Abdel-Jaber et al [16] to give theoretical re-sults which agreed with the experimental joint moments and which conservatively overesti-mated deflections.

All translational stiffnesses for connections were taken to be 1.0*1012 kN/m. The bracing elements were allowed to slip vertically after achieving a maximum shear load of 10 kN. The rotational stiffnesses about the non-principal axes were taken as 0.001 kNm/rad. Table 1 shows the rotational stiffnesses used in the analyses. The adjusted stiffness is the single stiff-ness described in Figure 3(b).

rotation

Moment Design maximum moment

Experimental curve

Bi-linear design line

rotation

Moment Design maximum moment

Equal areas

Design line

CC

EEF

F

(a) Eurocode bi-linear representation (b) Equal area single design line

Figure 3: Design method to determine the connection properties .

connection Initial stiff-ness

(kNm/rad)

Moment at

point E (kNm)

Post E stiffness

(kNm/rad)

Maximum moment (kNm)

Adjusted stiffness

(kNm/rad)

Ledger-standard (axis paral-lel to transom)

14.27 0.404 3.79 0.666 9.993

Ledger-transom (axis paral-lel to standard)

3.13 0.056 1.14 0.092 2.470

Bracing-standard 0.001

Table 1: Rotational stiffness of connections

3 THEORETICAL MODEL

3.1 Introduction

Figure 4 shows the initial theoretical model of the scaffold structure showing the loading

positions. As the first buckling mode was a sway mode parallel to the façade of the rear frame initial small horizontal loads were applied experimentally by hanging weights at positions S1,


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S2 and S3 of values 45 kg, 50 kg and 30 kg respectively. Once these weights had been at-tached the frame was loaded vertically through the cross braces shown in the figure. The ex-perimental frame was erected onto base-plates spanning between the front and rear frames and was considered to be pinned. The ties to the façade caused the rear frame to buckle between tie positions so that there was a full sine wave between the ground and the top frame. The first three buckling modes are shown in Figure 5. In the first and third modes the front face did not buckle and there was no buckling normal to the façade and hence these modes are drawn in elevation. The second mode consists of buckles normal to the facade.

X

Y

Z

S 1

S 2

S 3

V VV

VV V

V VV V

Figure 4: Numerical model showing loading positions

All standards, ledgers and braces were modelled using beam elements (BS3) from the LUSAS program library which have three rotational and the three translational degrees of freedom at each end and at mid element the incremental change in the three translational dis-placements. The elements were formulated according to the Kirchoff procedure [17]. Each standard had 20 elements per lift as previous research by the authors [3] had shown that this gave converged results. There were 10 elements per bay for the ledgers and bracing elements and 7 elements for each transom ensuring that each element was approximately the same size and that the bracing could buckle. The joint elements used to model the semi-rigid connec-tions were the JSH4 element which has three rotational and three translational degrees of freedom at each end. All connections between steel tubes were made by the joint elements. Eccentricities (of about 50mm) between overlapping steel tubes were ignored as earlier re-search by the authors [11] had shown negligible effects on scaffold structural performance when these imperfections were included. The LUSAS joint elements were capable of handling bi-linear curves with different tensile/compressive lines (or the equivalent rotational charac-teristics).

The symbol ‘Z’ in the figures shows the positions of the joint elements used to model the semi-rigid connections. The buckling load factors for the first three modes were 24.8 kN, 36.5 kN and 42.5 kN.

Early buckling analyses of the frame failed to produce any results as the cross-brace load-ing frame seen in Figure 4 had a horizontal sine wave buckling mode of below 1 kN. To get an estimate of the buckling mode the cross frames were removed from the model and the ver-tical loads applied directly on the top of the standards.


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X

Y

Z

X

Y

Z

(a) First buckle mode shape (b) Second buckle mode shape

X

Y

Z

(c) Third buckle mode shape

Figure 5:First three buckle modes of frame

The side loads were also removed so that only vertical loads were considered. Under these conditions a buckling load of 26kN per standard was achieved. However, the experiment (re-peated three times) gave failure loads of 42 kN (twice and 36 kN once when slip of the stan-dard-bracing connection was observed) followed by snap thorough failure with the load reducing to about 20 kN. The snap through could not be followed by the loading frame. The final displacement profile was that of a buckle in the mode shown in Figure 5. A second series of experiments was conducted using components supplied by a second manufacturer with the difference that the ledger-bracing was applied in the opposite direction (i.e. with the zigzag starting at the rear element closest to the ground and with a slightly different face brace pat-tern). These frames only took a load of 25 kN and the side-sway buckle then occurred with the frame unable to take any load in excess of the buckling load.

Previous research by the authors [18] had shown that pallet rack frames which structurally have the same behavior as scaffold frames and which rest on flat base-plates, similar to the base-plates of the scaffold, often have initial buckling modes corresponding to fixed based structures before displacements cause the structure to change the mode from a fixed base to a pinned base. Using fixed bases the lowest buckling mode changed to 36 kN, below the ob-served experimental load and hence this could not be used as the reason for the high failure load.


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3.2 Non-linear analyses

In order to attempt to simulate the behavior observed non-linear geometric (including overall P − Δ imperfections) were conducted. The shape of the overall imperfection was that of a sine wave in the buckling mode (amplitude 0.005* buckle length) and an out-of-plumb in the side-sway direction of also 0.005*height of frame. Both these imperfections gave only marginal differences to the frame behavior when no imperfections were included. The itera-tion scheme used was a Total Lagrangian Formulation (LUSAS is unable to undertake an Up-dated Lagrangian formulation for the elements used in this analysis but investigations by the authors have shown that the system is able to converge to the correct results as long as the load increments are sufficiently small). It was noted that in all investigations that it was im-portant to apply the load at either the ends of the cross-beams or at the middle of the loading beam. Applying loads at the top of the standards as was undertaken to obtain buckling loads gave an incorrect force distribution within the standards due to the asymmetry of the ledger-bracing.

To investigate the behavior of the frame the following analyses were conducted:

• A non-linear analysis was performed using LUSAS of the frame using load increments with the rotational properties of the joint taken to be linear and with joint stiffnesses taken to be the initial stiffness given in Table 1. The program showed changes in the slope of the load deflection curve at the first buckling mode but increased to approxi-mately 45 kN where there was significant horizontal deflection and the failure calcu-lated was a combination of the first and third buckling modes. Figure 6 shows a load-deflection curve for a point at the top of the rear column at the right hand end.

05

101520253035404550

0 100 200 300 400 500

Horizontal Deflection (mm)

Load

Fac

tor (

kN)

Figure 6: Load-deflection curve for a point at right-hand rear

It was felt that there were various difficulties associated with this model. Firstly, the use of a single initial rotation stiffness did not allow for the reduced rotational stiffness as the scaffold deflected. Secondly that the use of load increments meant that the load shedding part of the curve would not be properly followed using arc length control. In addition an investigation of the loading-cross beam showed that the rotational instabili-ties due to having two loads applied at each end could be removed without detriment to the model by replacing it with a load at the centre of each loading beam.


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• The same model was analyzed under displacement control when using simple bi-linear rotational joint properties as determined from the connection tests. This produced a maximum load of 45 kN and again predicted failure in the shape of the third buckling mode. Note that an investigation of the reactions at the base of each standard showed that until the first buckling mode was reached that there was very little difference in the reactions between front and rear faces. However, above the first buckling mode differ-ences in reactions for braced pairs of uprights magnified so that the front column had over twice the reaction of that in the rear column.

• As it was noted that the maximum moments predicted by the use of the bi-linear joint

curves were above those allowed by the code a revised joint model was constructed which had the same area under the curve as the code values but was able to hold a maxi-mum moment (See section 3.1). This gave slightly improved results where the maxi-mum load was also 45 kN but following this maximum there was a small drop in load before excessive horizontal deflections were predicted. To account for the slip observed in the third test where the bracing elements were incorrectly tightened the model was modified so that the bracing elements had a maximum vertical shear of 10 kN, a com-mon value found in tests. This had no effect on the model results.

• As the experiments clearly showed that failure occurred elastically the joint rotation

curves were investigated. Figure 7 shows the results of a test on a transom-ledger con-nection

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0

0.1

0.2

0.3

0.4

-0.2 -0.1 0 0.1 0.2 0.3 0.4

Rotation (Rad)

Mom

ent (

kNm

)

Initial Stiffness

Bi-linear curve

Figure 7: Experimental joint-rotation curve

The bi-linear curves used in the analyses are taken from the third cycle of a connection test so that connection is assumed to have bedded in and all initial plasticity has taken place. However, as can be clearly seen from Figure 7, the initial stiffness on the first cycle is signifi-cantly higher than either of the two stiffnesses obtained from the code. The maximum hori-zontal displacement before failure of the scaffold showed that for most connections the rotation was of the order 0.01 radians which would imply that the stiffnesses of the connec-


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tions should be higher than those used in Table 1. When a stiffness of approximately three times that from Table 1 was used the first buckling load was raised to 42 kN per standard, the result observed in the tests. However once initial buckling has taken place then joint stiff-nesses change to those on the bi-linear curve hence causing an immediate fall to the buckling mode found earlier.

3.3 Second frames

Compounding the problem of predicting the behavior of the frame three nominally identi-cal frames were supplied by a second manufacturer and erected by staff at the BRE. The dif-ferences between the frames from the second manufacturer and the first three were that the ledger-bracing was installed with the diagonal members orientated in the opposite direction to the first set, a different front brace pattern was used and the top lift was 2.0 m instead of 1.8 m. A schematic is given in Figure 8.

X

Y

Z

Figure 8: Schematic of the second frame

A similar model to the first frame was constructed including the effects of imperfections. The buckling loads and modes were nearly the same as the former model. The results of the final numerical model assuming bi-linear joint behavior, slip and geometric nonlinearity showed quite a different load deflection characteristic curve, although the final displaced shape was the same as shown in Figure 9.


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X

Y

Z

Figure 9: Displaced shape of second frame

A plot of the mean reaction against the displacement at the rear of the frame, top of the second column from the right, is given in Figure 10.

-505

1015202530354045

0 20 40 60 80 100 120 140

Horizontal deflection (mm)

Mea

n re

actio

n (k

N)

Figure 10: Load-deflection curve for a point at right-hand rear

The load-deflection curve shown in Figure 10 shows a different behavior from that displa-yed in Figure 6 for the original frame. An investigation of the reactions at the base of the frame showed that there was a significant difference between the reactions in the front and rear frame which caused the frame to buckle earlier. To further prove this conjecture the final model for the second frame was only changed to have the ledger bracing elements arranged so that they corresponded with that for the original frame. The resulting load-deflection curve for the same point on the frame is given in Figure 11.

The difference in behavior between this curve and that of Figure 6 can be attributed to the different façade bracing pattern and the additional height of the top lift. All other parameters were identical. This shows the sensitivity of the analysis procedure to small changes.

Further work is continuing in order to be able to predict the load-descending part of the first model. An investigation into the true joint characteristics of the second frame is also be-


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ing undertaken as it thought that although nominally of the same specification that in reality the second frame’s connections are less rotationally stiff. This would have the effect of accen-tuating the initial buckling takes place.

-505

101520253035404550

-0.5 0 0.5 1 1.5 2Horizontal deflection (mm)

mea

n re

actio

n

Figure 10: Load-deflection curve for a point at right-hand rear on the modified original frame

3 CONCLUSIONS

This paper has investigated two series of tests undertaken by the UK Building Research Station where apparently similar scaffold structures exhibited significantly different behavior. Both frames had the same buckling load but the first frame was able to carry loads in excess of the buckling load before a snap-through failure occurred. The second frame was only able to achieve the buckling load before failure.

The investigation has shown that the prime cause of the different behavior is the load dis-tribution in the standards due to the different bracing patterns with a secondary difference due to the different joint characteristics of the two frames.

REFERENCES

[1] BS 5973, Code of Practice for Access and Working Scaffold and Special Scaffold Struc-tures. British Standards Institution, London, 1994.

[2] EN 12811-1, Temporary works equipment, Part 1: Scaffolds-Performance requirements and general design. European Committee for Standardisation, Brussels, 2003.

[3] R.G. Beale and M.H.R. Godley, Numerical Modelling of Tube and Fitting Access Scaf-fold Systems, Advanced Steel Construction, 2, 199-223, 2006.

[4] NASC, TG20:05, Guide to Good Practice for Scaffolding with Tubes and Fittings. Na-tional Access and Scaffolding Confederation, London, 2005.

[5] BRE, Tests on a Full-scale Tube Scaffold with fittings – Test 1, BRE, 2008. [6] M.T. Abdel-Jaber, R.G. Beale, M. Godley and M. Abdel-Jaber, Rotational resistances of

tube and fitting scaffold connectors, to appear in Proc. ICE, Structures and Buildings, 2009.


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[7] R. Beale and M. Godley, The analysis of scaffold structures using LUSAS, Proceedings of LUSAS 95, FEA Ltd, London, United Kingdom, 9-16, 1995.

[8] S.L. Chan, Z.H. Zhou, W.F. Chen, J.L. Peng and A.D. Pan, Stability analysis of semi-rigid steel scaffolding, Engineering Structures, 17, 568-574, 1995.

[9] M.H.R. Godley and R.G. Beale, Sway stiffness of scaffold structures, The Structural En-gineer, 75, 4 -12, 1997.

[10] Y.L. Huang, Y.G. Kao and D.V. Rosowsky, Load carrying capacities and failure modes of scaffold shoring systems, Part II: An analytical model and its closed form solution, Structural Engineering and Mechanics, 10, 67-79, 2000.

[11] B. Milojkovic, R.G. Beale and M.H.R. Godley, Modelling Scaffold Connections, Pro-ceedings of the Fourth ACME UK Annual Conference, Glasgow, 85-88, 1996.

[12] J.L. Peng, A.D. Pan, D.V. Rosowsky, W.F. Chen, T. Yen and S.L. Chan, High clearance scaffold systems during construction-I. Structural modelling and modes of failure, Engi-neering Structures, 18, 247-257, 1996.

[13] L.B. Weesner and H.L. Jones, Experimental and analytical capacity of frame scaffolding, Engineering Structures, 23, 592-599, 2001.

[14]British Standards Institute. EN 12811-3, Temporary works equipment, Part 3: Load Test-ing, London, 2002.

[15] British Standards Institution, Draft BS EN15512, Steel static storage systems – Adjust-able pallet racking systems – principles for structural design, London, 2006.

[16] M.S. Abdel-Jaber, R.G. Beale and M.H.R. Godley, A theoretical and experimental inves-tigation of pallet rack structures under sway, Journal of Constructional Steel Research, 62, 68-80, 2006.

[17] FEA Ltd, LUSAS 13 Theory manual, London, 2000. [18] H.H. Lau, R.G. Beale, M.H.R. Godley, The Effects of Column Base Connectivity on the

stability of Slender Frame Structures, Progress in Steel Building Structures, 9, 33-40, 2007.

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