School of Civil Engineering Sydney NSW 2006 AUSTRALIA http

School of Civil Engineering

Sydney NSW 2006

AUSTRALIA

http://www.civil.usyd.edu.au/

Centre for Advanced Structural Engineering

Structural Modelling of Support Scaffold

Systems

Research Report No R896

Tayakorn Chandrangsu BSc MSc

Kim JR Rasmussen MScEng PhD

June 2009

ISSN 1833-2781


Centre for Advanced Structural Engineering

http://www.civil.usyd.edu.au/

Structural Modelling of Support Scaffold Systems

Research Report No R896

Tayakorn Chandrangsu, BSc, MSc

Kim JR Rasmussen, MScEng, PhD

June 2009

Abstract:

In this report, accurate three-dimensional advanced analysis models are developed to capture

the behaviour of support scaffold systems, as observed in full-scale subassembly tests

consisting of three-by-three bay scaffold systems with combinations of various lift heights,

number of lifts and jack extensions. The paper proposes methods for modelling spigot joints,

semi-rigid upright-to-beam connections and base plate eccentricities. Material nonlinearity is

taken into account in the models based on the Ramberg-Osgood expression fitted to available

experimental data. Actual initial geometric imperfections including member out-of-

straightness and storey out-of-plumb are also incorporated in the models. The ultimate loads

from the nonlinear analyses were calibrated against failure loads and load-deflection

responses obtained from full-scale subassembly tests. The numerical results show very good

agreement with tests, indicating that it is possible to accurately predict the behaviour and

strength of highly complex support scaffold systems using material and geometric nonlinear

analysis. The report is a milestone in the ongoing development of a design methodology for

support scaffold systems based on advanced analysis currently undertaken at the University

of Sydney.

Keywords: Advanced analysis, Formwork subassemblies, Support scaffold systems, Steel scaffolds,

Falsework, Subassembly tests, Structural models, Calibrations

Structural Modelling of Support Scaffold Systems June 2009

School of Civil Engineering Research Report No R896

2

Copyright Notice

School of Civil Engineering, Research Report R896

Structural Modelling of Support Scaffold Systems

© 2009 Tayakorn Chandrangsu and Kim JR Rasmussen

[email protected] and [email protected]

ISSN 1833-2781

This publication may be redistributed freely in its entirety and in its original

form without the consent of the copyright owner.

Use of material contained in this publication in any other published works must

be appropriately referenced, and, if necessary, permission sought from the

author.

Published by:


The University of Sydney

Sydney NSW 2006

AUSTRALIA

June 2009

This report and other Research Reports published by the School of Civil

Engineering are available on the Internet:

http://www.civil.usyd.edu.au



3

Table of Contents

1. Introduction.......................................................................................................5

1.1 Scaffold Systems.........................................................................................5

1.2 Advanced Analysis .....................................................................................6

1.3 Previous Scaffold Models ...........................................................................7

2. Full-Scale Subassembly Tests.........................................................................10

2.1 Test Setup and Procedures ........................................................................10

2.2 Test Configurations...................................................................................12

2.3 Test Results ...............................................................................................15

3. Finite Element Models ....................................................................................17

3.1 Spigot Joints..............................................................................................17

3.2 Semi-Rigid Standard-to-Ledger Connections...........................................18

3.3 Brace Connections ....................................................................................19

3.4 Base Plate Eccentricity .............................................................................20

3.5 Load Eccentricity ......................................................................................20

3.6 Geometric Imperfections ..........................................................................20

3.7 Geometric and Material Nonlinearities.....................................................21

3.8 Calibrations ...............................................................................................25

4. Discussion .......................................................................................................35

5. Conclusions.....................................................................................................36

Acknowledgement ..............................................................................................36

References ...........................................................................................................36



4



5

1. Introduction

1.1 Scaffold Systems

Scaffolds are temporary structures commonly used in construction to support various types of

loads. The vertical loads on scaffold can be from labourers, construction equipment,

formworks, and construction materials. Commonly, scaffolds must also be designed to

withstand lateral loads, including wind loads, impact loads, and earthquake loads. Depending

on their use, scaffolds may be categorised as access scaffolds or support scaffolds. Access

scaffolds are used to support light to moderate loads from labourers, small construction

material and equipment for safe working space. They are usually attached to buildings with

ties and only one bay wide. Support scaffolds, also sometimes called falsework, are subjected

to heavy loads, for example, concrete weight in the formwork. Support scaffolds are the main

focus in this research. An example of a support scaffold system is shown in Figure 1. Support

scaffolds normally consist of standards (vertical members), ledgers (horizontal members),

and braces. The scaffold standards are connected to each other to create a lift via couplers,

also known as spigot joints (Figure 2). In order to connect ledgers to standards, wedge-type

or Cuplok joints (Figure 3) are usually preferred for the connection because no bolting or

welding is required; though, in some systems manually adjusted pin-jointed couplers are still

being used. The connections for diagonal brace members are usually made of hooks for easy

assembling. The base of scaffolds consists of threaded adjustable jacks, which can be

extended up to typically 600 mm by a wing nut to accommodate irregularity of the ground.

The top of scaffolds consists of threaded adjustable jacks with U-heads which support timber

bearers and ensure the levelling of the formwork.

Figure 1: Typical support scaffold



6

Figure 2: Schematic of spigot joint

Top cup

Bottom cup

Standard

Ledger

Ledger blade

3

1

2

Locking pin

Figure 3: Schematic of Cuplok joint

1.2 Advanced Analysis

With the ready availability of powerful computers and sophisticated structural analysis

software packages, geometric and material nonlinear structural analysis has become feasible

and practical. Nonlinear analysis allows researchers and practitioners to more accurately

predict the failure load and deformation of scaffold systems. Advanced analysis involves the

modelling of changes of the geometry of structures as a result of loading and inelastic

material behaviour. In the research by Gylltoft and Mroz [1], a three-dimensional geometric

and material nonlinear finite element model was verified against the results of a full scale test

scaffold. The model was further applied to determine the ultimate load of a typical access

scaffold considering various configurations and load combinations.

However, in many cases research on scaffold systems has focused on elastic nonlinear

geometric modelling associated with second-order effects. For example, elastic geometric

nonlinear analyses were reported by Peng et al. [2], Prabhakaran et al. [3], Yu et al. [4], Chu

et al. [5], and Weesner and Jones [6]. Geometric nonlinear analysis is also a common practice

in design offices, whereas the use of inelastic analysis is still rare. Nevertheless, with accurate

finite element model, advanced analysis method can usually fulfil the design requirement

with no tedious separate member capacity checks.

Top Standard

Bottom Standard

Spigot Insert



7

AS4100 [7] allows the application of advanced analysis for the design of steel frames in

which the members are of compact cross-section with full lateral restraint, thus preventing

local buckling and flexural-torsional buckling. Advanced analysis models should include

related material properties, residual stresses, instability effects, initial geometric

imperfections, actual connection behaviour, construction methods, and interaction with the

foundations [8]. In the research described herein, three-dimensional advanced structural

analysis models are proposed in order to develop a new design methodology for support

scaffold systems.

1.3 Previous Scaffold Models

By means of available commercial finite element softwares such as ANSYS [9], LUSAS

[10], and NIDA [11], many new studies on scaffold behaviour were carried out through three-

dimensional models such as those presented by Prabhakaran et al. [3], Milojkovic et al. [12],

and Godley and Beale [13]. Three-dimensional structural analysis is beneficial in describing

complex failure modes such as those observed when the combined effects of in-plane and

out-of-plane bending are present. Some past models proposed by Huang et al. [14], and Peng

et al. [15] were created in two dimensions for simplicity and computational efficiency.

Two types of geometrical imperfections are typically required to be considered in an

advanced analysis for steel framed systems to capture the second-order effects: the initial

member out-of-straightness of the standard and the initial story out-of-plumb of the frame.

There are many ways of taking geometric imperfection effects into account. Three methods

of modelling imperfections were trialled in [16], including the scaling of eigenbuckling

modes (EBM), the application of notional horizontal forces (NHF), and the direct modelling

of initial geometric imperfections (IGI). EBM was performed by carrying out an

eigenbuckling analysis on the structural model, and then scaling and superimposing the

lowest eigenmode onto the perfect geometry to create an initial imperfect structural frame for

the second-order structural analysis. In the NHF approach, additional lateral point loads were

applied at the top of each column in one direction of the frame and initial member out-of-

straightness could be represented by lateral distributed forces along each member. The IGI

method consisted of applying an initial sway of the frame and an out-of-straightness to each

column in the frame.

For scaffold systems, these same approaches can be applied to model the effects of initial

imperfections in the analysis. For example, Yu et al. [4] and Chu et al. [5] integrated EBM

with the magnitude of the column out-of-straightness of 0.001 of the height of the scaffold

units into the model. Moreover, Yu and Chung [17] investigated a method called critical load

approach where initial imperfections were integrated directly into a Perry-Robertson

interaction formula to determine the failure loads of the scaffolds in the analysis. In other

research on scaffold systems by Peng et al. [2], the NHF approach was incorporated in the

model by applying a horizontal notional force of 0.1% to 0.5% of the vertical loads at mid-

height of the scaffold lift. Godley and Beale [18] adopted an IGI approach by imposing a

sinusoidal bow to the members and angular out-of-plumb to the frame. In each of these

approaches, careful calibration against test results or numerical reference values is required.

Scaffold joints are complex in nature due to need for rapid assembly and reassembly in

construction. The Cuplok connections behave as semi-rigid joints, and show looseness with

small rotational stiffness at the beginning of loading. Once the joints lock into place under

applied load, the joints become stiffer [13]. Wedge-type joints are generally more flexible

and closer to pinned connections. They also often display substantial looseness at small

rotations [18]. Figure 4 shows typical moment-rotation curves for cuplock [13] and wedge-

type [18] joints. As to spigot joints, the spigot can create out-of-straightness of the standards,



8

and the possibility of the joint to open up due to the gap between the standard and the spigot

can produce complexity in modelling [19]. Moreover, the modelling of boundary conditions

of scaffold systems is crucial because the top and bottom restraints can significantly influence

the stability and strength of the system [20].

In recent research by Peng et al. [2], analysis models of wedge-type jointed, 3-storey, 3-bay,

and 5-row scaffold system were presented. Experimental tests on scaffold joints showed that

the joint stiffness varied between 4.903 kNm/rad (50 ton cm/rad) and 8.826 kNm/rad (90 ton

cm/rad) with the average of 6.865 kNm/rad (70 ton cm/rad) being adopted for all joints into

their model.

Godley and Beale [18] found that scaffold connections are frequently made of wedge-type

joints, for which the joint stiffness exhibits different response under clockwise and counter-

clockwise rotations, and occasionally exhibits looseness in connections with low stiffness.

Consequently, Prabhakaran et al. [3] modified the stiffness matrix for the end points of the

beam to include connection flexibility, using a piecewise linear curve to model the moment-

rotation response.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.00 0.05 0.10 0.15 0.20

Rotation (radian)

Mo

men

t (k

Nm

)

Cuplok joint

Wedge-type joint

Figure 4: Typical moment-rotation curves for Cuplok and wedge-type joints

Yu [20] studied the effects of boundary conditions of scaffold systems, and categorised them

into four cases, i.e. Pinned-Fixed, Pinned-Pinned, Free-Fixed, and Free-Pinned, with the first

term being the translational restraint at the top of the scaffold, and the second term being the

rotational restraint at the base of the scaffold. In all analyses, the rotation at the top was

assumed to be free. These conditions were incorporated into the models of one bay of one-

storey modular steel scaffolds (MSS1), and two-storey modular steel scaffolds (MSS2). Yu

found that for MSS1 the failure loads for Free-Fixed and Pinned-Pinned conditions are

reasonably close to test results; however, for MSS2 the model results are considerably higher

than the test results. Subsequently, Yu suggested that since the top of the scaffolds normally

has lateral restraints then joints at the top can be modelled as translational springs, and for the

bottom rotational spring can be applied. A stiffness of 100 kN/m for the top translational

spring and stiffness of 100 kNm/rad for the bottom rotational spring gave comparable results

to the tests.



9

Chu et al. [5] studied single storey double bay scaffolds. In the presence of restraints on the

loading beam and the jack bases, the top and base were modelled with various boundary

conditions, and the scaffold connections were assumed to be rigid. The researchers found that

both Pinned-Pinned and Pinned-Fixed conditions gave higher load carrying capacities than

the experimental results; on the other hand, the Free-Fixed condition gave satisfactory result

compared to the tests. Research on the stability of single storey scaffold systems by Vaux et

al. [21] found that when Cuplok connections are represented by pin joints, and the

connections of the top and bottom jacks to the standards are assumed as rigid with the top-

bottom boundary conditions taken as Pinned-Pinned, good agreement can be achieved

between numerical and experimental failure loads.

Weesner and Jones [6] studied the load carrying capacity of three-storey scaffolds assuming

rigid joints between the stories, and pin joints for the top and the bottom boundary conditions.

The results of their elastic buckling analysis were higher than the test values with the

percentage differences ranging from 6% to 17%. In the analysis of large access scaffold

systems by Godley and Beale [18], cantilever arm tests were carried out on scaffold wedge-

type joints. The nonlinear moment-rotation curve from the tests showed joint looseness and

different values of rotational stiffness under positive (counter-clockwise) rotation and

negative (clockwise) rotation. The authors suggested the use of a multi-linear or nonlinear

moment-rotation curve for scaffold joint modelling.

In the work by Enright et al. [19], the modelling of spigot joints was studied for the stability

analysis of scaffold systems. The spigot insert (Figure 2) was considered to have bending

resistance, but not to transmit axial load; therefore, the model adopted two vertical members

connected by pin joints representing the standards, and on the side, the entirely rigid spigot

member was connected at the top, centre, and bottom to the standard via short and axially

stiff members capable of transferring only lateral forces, as shown in Figure 5. Due to the

axial load in the standards, the spigot would be in bending, and the amount of bending would

depend on the amount of axial load and the degree of out of straightness. From research of

Harung et al. [22], it was found that if the spigot joints are modelled as fully continuous

joints, the analysis would overestimate the load carrying capacity of the system.

Figure 5: Spigot joint model

Milojkovic et al. [23] studied eccentricity in the modelling of scaffold connections. Given

that the neutral axes of the connections were offset by 50 mm, the authors modelled the

eccentric joint with a finite spring of length equal to the eccentricity of 50 mm. The spring

Axial load

Standards Spigot

Pin joint



10

had specific rotational stiffness, and was assumed to be axially stiff. The authors concluded

that for large frames, unless torsion failure occurs, then the effects of joint eccentricity are

insignificant. In the scaffold study by Gylltoft and Mroz [1] the braces were represented as

truss members with pinned joints connected to the standards, and the connections between

other members were modelled as short finite elements with nonlinear stiffness in all

directions. To model the shores of the scaffold system, Peng et al. [15] applied rigid links

with pinned supports at both ends, given that actual shores were connected loosely by nails at

the top and bottom.

2. Full-Scale Subassembly Tests

2.1 Test Setup and Procedures

A total of 18 support scaffold subassembly tests were conducted at the University of Sydney

in 2006 [24] to study the behaviour and ultimate load-carrying capacities of such systems. In

all tests, the formwork subassembly, also known as Cuplok scaffold system, was constructed

as a grid frame of three-by-three bays with a constant nominal bay width of 1829 mm in both

directions. The first fourteen tests were systems of three lifts with equal nominal lift height of

1.5 m. The systems featured different bracing arrangements (full, none, perimeter, core, and

North-South direction only) and different jack extension heights (300 mm or 600 mm) at both

top and bottom. In the last four subassembly tests, systems with 1 m and 2 m lift heights with

full bracing were tested with the variation in the number of lifts from 2 to 4 and jack

extension heights of 300 mm or 600 mm.

All testing components were taken from stocks of used material. As a result, the testing

materials showed some geometric imperfections representing those encountered in practice,

particularly in regard to the out-of-straightness of the standards. Besides, the Cuplok joints

showed signs of wear from frequent use and were therefore representative of joints used in

practice in terms of joint stiffness and strength [24].

The standards, attached with Cuplok joints, were made from cold-formed circular steel tube

grade 450 MPa with nominal outside diameter of 48.3 mm and thickness of 4 mm. The grade

350 MPa ledgers with end blades were of nominal outside diameter of 48.3 mm and thickness

of 3.2 mm. The telescopic braces with hook ends were made of 48.3 mm x 4.0 mm outer tube

and 38.2 mm x 3.2 mm inner tube with nominal yield stress of 400 MPa. The adjustable jacks

were made of 36 mm diameter threaded steel rod of grade 430 MPa. The base plates were

180 mm x 180 mm x 10 mm in dimension with nominal yield stress of 250 MPa [24].

A test frame was constructed specially for the subassembly tests consisting of four loading

beams at both the top and bottom running in the North-South direction. A total of sixteen

hydraulic jacks attached to the top loading beams (four hydraulic jacks per loading beam)

were used to load the (150 mm x 77 mm) timber bearers running in the East-West direction

that applied loading to the top of each standard via (210 mm clear width) U-heads. Four sets

of cross-bracing were installed to prevent sway of the top loading beams. Ball bearings were

inserted between the jacks and timber bearers in the first test. However, this condition

produced excessive lateral displacements and rotations of the adjustable jacks and was

deemed non-representative of construction practice, where the bearers support a series of

closely spaced secondary bearers running orthogonally to the main bearers. These secondary

bearers elastically restrain displacements and rotations of the primary bearers. Consequently,

the results of Test No. 1 were discarded and in subsequent tests, secondary bearers spaced

approximately at 600 mm were attached at the top of primary bearers. Figure 6 illustrates a

typical test frame showing primary and secondary bearers and bracings. The results of Test



11

No. 7 were also discarded since the hydraulic jacks accidentally moved out of positions

during the test.

Figure 6: Typical test frame from top view



12

In all tests except Test No. 6, the loads were applied at an eccentricity of 25 mm in the North-

South direction to the top adjustable jacks (Figure 7(a)) along the second row in the East-

West direction while for the rest of the standards the loads were applied concentrically. In

addition, the base plates in the row of eccentrically loaded standards were placed on 3 mm

diameter circular steel rods at a nominal eccentricity of 15 mm, as shown in Figure 7(b), as

per AS3610 [25].

The load eccentricities applied at the top and bottom of the system were arranged such that

the standards were bent in single curvature. The loads were applied equally by hydraulic

jacks on each standard through primary bearers, except in Test No. 14 where the loads

applied to the corner, perimeter, and centre jacks were in the ratio of 1:2:4 respectively. The

applied loads were recorded at each increment of loading until failure occurred, and

theodolites were employed to measure initial geometric imperfections of all the standards

before the test began and the displacements of six selected standards during loading [24].

Hydraulic jack

Primary bearer

U-head

Unit: mm

S N

Base plate

(a)

(b)

3 mm steel rod

Figure 7: Enlarged view of (a) top eccentricity and (b) bottom eccentricity

2.2 Test Configurations

A summary of the test configurations which includes test number, test date, lift height,

number of lifts, top and bottom jack extension length, position of spigot, bracing

arrangement, type of loading, and loading eccentricity is presented in Table 1.



13

Table 1: Summary of test configurations

Test Date Lift

height

No.

of

lifts

Jack

extension

Spigot

(lifts) Bracing Loading

Load

eccentricity in

2nd

row

standards

1 17/1/06 1.5 m 3 600 mm 2

nd &

3rd

full uniform

25 mm top &

15 mm bottom

2 31/1/06 1.5 m 3 600 mm 2

nd &

3rd

full uniform

25 mm top &

15 mm bottom

3 8/2/06 1.5 m 3 600 mm 2

nd &

3rd

full uniform

25 mm top &

15 mm bottom

4 13/2/06 1.5 m 3 600 mm 2

nd &

3rd

none uniform

25 mm top &

15 mm bottom

5 16/2/06 1.5 m 3 600 mm 2

nd &

3rd

perimeter uniform

25 mm top &

15 mm bottom

6 22/2/06 1.5 m 3 600 mm 2

nd &

3rd

perimeter uniform 15 mm bottom

7 3/3/06 1.5 m 3 300 mm 2

nd &

3rd

full uniform

25 mm top &

15 mm bottom

8 10/3/06 1.5 m 3 300 mm 2

nd &

3rd

full uniform

25 mm top &

15 mm bottom

9 17/3/06 1.5 m 3 300 mm 2

nd &

3rd

none uniform

25 mm top &

15 mm bottom

10 24/3/06 1.5 m 3 300 mm 2

nd &

3rd

core uniform

25 mm top &

15 mm bottom

11 30/3/06 1.5 m 3 300 mm 2

nd &

3rd

full uniform

25 mm top &

15 mm bottom

12 7/4/06 1.5 m 3 300 mm 2nd

full uniform 25 mm top &

15 mm bottom

13 13/4/06 1.5 m 3 300 mm 2

nd &

3rd

N-S only uniform

25 mm top &

15 mm bottom

14 3/5/06 1.5 m 3 300 mm 2

nd &

3rd

core 1:2:4

25 mm top &

15 mm bottom

15 15/5/06 2 m 2 300 mm 2nd


15 mm bottom

16 19/5/06 1 m 3 600 mm 3rd


15 mm bottom

17 7/6/06 1 m 4 300 mm 3rd


15 mm bottom

18 30/6/06 1 m 4 300 mm 3rd


15 mm bottom

A schematic of a typical test configuration is shown in Figure 8. The figure shows a typical 3-

lift support scaffold system with a lift height of 1.5 m in a full bracing arrangement being

loaded by hydraulic jacks attached to the test frame. The figure also shows a temporary

support deck for access to the test frame. The bracing arrangement is according to the

labelling in the figure showing core and perimeter braces. Full bracing arrangement includes

both core and perimeter braces. N-S bracing arrangement consists of braces running in the



14

North-South direction. As an example, Figure 9 shows the actual Test No. 8 setup consisting

of a 3-lift, 1.5 m lift height and 300 mm jack extension subassembly test with full bracing

arrangement including top and bottom eccentricities in 2nd

row.

Figure 8: Schematic of typical test configuration in plan and elevation view



15

Figure 9: Test No. 8 setup

2.3 Test Results

A summary of the test results consisting of test number, ultimate load from hydraulic jacks at

3 different locations (corner, perimeter, and centre), and observed failure mode is shown in

Table 2. As noted earlier, the results of Tests No. 1 and 7 are unrepresentative, and thus not

shown in the summary.



16

Table 2: Summary of test results

Test

Ultimate

load at

corner

jacks

(kN)

Ultimate

load at

perimeter

jacks

(kN)

Ultimate

load at

centre

jacks

(kN)

Observed failure mode

2 87 86 89 N-S sway mode, final failure of top and

bottom jacks

3 91 90 91 N-S sway mode, failure of top and bottom

jacks, and spigot

4 50 50 50 N-S sway mode, final failure of top and

bottom jacks

5 60 60 60 N-S sway of centre bay, final failure of top

jacks

6 60 60 60 N-S sway of centre bay, final failure of top

jacks and spigot

8 130 130 130 Some N-S sway, failure of standards and

spigot at top lift

9 65 65 65 N-S sway mode, final failure of top jacks and

top standards

10 70 70 70 N-S sway mode, failure of corner standards

and spigots

11 120 120 120 Some N-S sway, final failure of top spigots

and standards

12 119 120 120 Some N-S sway, failure of top spigots and

corner standards

13 70 70 70 Some E-W sway, final failure of perimeter

spigots in 2nd

lift

14 40 80 160 Some N-S sway, failure of top spigots and

centre standards

15 105 105 105 Failure of corner spigot and top standard

16 100 100 100 N-S sway mode, failure of jacks

17 140 140 140 Bearer broke off before final failure of top

jacks

18 150 150 150 Some N-S sway, final failure of corner

standard at top lift

The test results suggest that the failure modes are controlled by the jack extension length

since when 600 mm top and bottom extensions are used the failure mode is North-South

sway with final failure at the jacks. On the contrary, when 300 mm extensions are used,

failure occurs mainly in the standards and spigots with only small sway displacements.

Noticeably, the ultimate load decreases as the jack extension increases. The test results show

that the bracing arrangement significantly influences the ultimate load of the system. Also,

the higher lift height reduces the ultimate load. Moreover, the standards tend to fail at the top

lift and around the perimeter region, especially at the corner where there is no bracing and

only two ledgers are connected. Final failure occurred in spigots and jacks in most cases, as



17

shown in Figure 10. Complete data on initial geometric imperfections and displacements as

well as supplementary tests on components of Cuplok scaffold systems, including tensile

coupon, stub column and bending tests are available in [24].

(a) (b)

Figure 10: Failure in (a) spigot and (b) jack

3. Finite Element Models

In this research, three-dimensional finite element models have been developed for analysing

support scaffold systems. The analyses include geometric and material nonlinearities and are

performed using the commercial finite element software package Strand7 [26]. The models

present efficient and accurate methods for representing spigot joints, standard-to-ledger

connections, base plate eccentricities, and load eccentricities. Also, initial geometric

imperfections and material nonlinearity of all components of the system are incorporated in

the models. In modelling the structural elements of the scaffold system, nonlinear beam

elements, including contact, link, and connection elements, are used as described in sections

3.1 to 3.7. The models are compared with the subassembly tests [24] and calibrated against

the ultimate loads and displacement responses in section 3.8.

3.1 Spigot Joints

In the studied systems, the spigot joint consists of an insert made from a circular hollow steel

tube with 38.2 mm outside diameter, 3.2 mm in thickness, and 300 mm in total length. The

insert feeds into the abutting top and bottom standards to create a required lift height, as

shown in Figure 2. The top standard can slide over the insert, which is fastened to the bottom

standard by a fixed pin. The spigot modelling suggested by Enright et al. [19] is adopted, as

shown in Figure 11.



18

Figure 11: Schematic of spigot joint model

The top and bottom standards are modelled as nonlinear beam element connected to the

spigot via pinned connections. The spigot beam element is connected to the standards by

three pinned stiff links capable of only transferring lateral forces from the standards to the

spigot. As a result, the vertical force travels through the standards and only horizontal forces

transfer to the spigot via the pinned links. When the standard bends under vertical load, the

spigot is forced to bend because of the lateral forces acting oppositely at the top/bottom and

centre of the spigot. The degree of bending of the spigot depends on the amount of initial

geometric imperfection of the standard and vertical force. In three-dimensional analyses, the

spigot model is arranged in the direction perpendicular to the primary bearers which is in the

same direction as that of the load eccentricity. This arrangement is reasonable since it was

observed from the subassembly tests [24] that the spigot joint tends to fail in the same

direction as the load eccentricity. For simplicity, the spigot model is applied at mid height of

the lift, even though the spigot is often located at little below or above mid height in actuality.

3.2 Semi-Rigid Standard-to-Ledger Connections

The connections between standard and ledger in this research consist of a semi-rigid Cuplok-

type joint that can join up to four ledgers to the standard. The relation between the moment

and rotation of the Cuplok connections is modelled by a tri-linear curve, as illustrated in

Figure 12. The parameters that describe the tri-linear curve (k1, k2, k3, β1, β2, β3) were

obtained from laboratory tests. Three different joint configurations were tested in bending

about vertical and horizontal axes, i.e. the 4-way, 3-way and 2-way configurations, reflecting

the number of ledgers connected at the joint. It was observed that the more ledgers connected,

the less movement in the joint itself, and hence the greater stiffness. The average joint

stiffness values for k1, k2, and k3 for different joint configurations and bending axes (Figure

13) are presented in Table 3. The average joint rotation values for β1, β2 and β3 are presented

for different joint configurations and bending axes in Table 4. The connection element in

Strand7 [26] is used to model the relation between moment and rotation. It requires that a

multi-linear moment-rotation table is specified for bending about vertical and horizontal axes.

The connection element is used to supply stiffness for any of the six degrees of freedom

(axial, shear in 2 directions, and bending about 3 axes); in this case, only bending about

vertical and horizontal axes is incorporated in the multi-linear table; the rest are assumed to

be rigid.

Load

Top Standard

Spigot

Pinned link

Pinned link

Pinned link

Bottom Standard

150 mm

150 mm

0



19

Table 3: Average Cuplok joint stiffness (kNm/rad)

Bending about horizontal axis Bending about vertical axis

Joint configuration k1 k2 k3 k1 k2 k3

4-way 80 102 5.3 15 7.5 0.8

3-way 75 87 5.1 14 7 1

2-way 70 77 4.6 7.5 5 1.5

Table 4: Average rotation for Cuplok joints (rad)

Bending about horizontal axis Bending about vertical axis

Joint configuration β 1 β 2 β 3 β 1 β 2 β 3

4-way 0.014 0.036 0.16 0.02 0.04 0.1

3-way 0.012 0.036 0.16 0.02 0.04 0.1

2-way 0.007 0.036 0.16 0.02 0.04 0.1

Figure 12: Tri-linear moment-rotation for the Cuplok joints

Figure 13: Bending axes of the Cuplok joints

3.3 Brace Connections

The braces are made of telescopic members with hooks at the ends. They are modelled using

two rigidly connected elements with different cross-sections. Connection elements with only

Rotation

Moment

β1 β2 β3

k1

k2

k3



20

axial stiffness form the connection between the brace member elements and the ledgers. The

axial spring stiffness is taken as 1.8 kN/mm as obtained from test calibrations on braced

scaffold systems. The braces are offset 60 mm from the nodal points between the standards

and ledgers because in actual construction the braces are connected to ledgers at about this

distance away from the joints.

3.4 Base Plate Eccentricity

The placement of the base plate of scaffold systems on an uneven or sloped ground can create

eccentricity. The amount of base eccentricity depends largely on ground surface irregularities

as shown in Figure 14(a). AS3610 [25] specifies an expected base eccentricity of no more

than 40 mm or bp/4, whichever is less, where bp is the stiff portion of bearing of an end plate,

as shown in Figure 14(a). For example, bp/4 is 17 mm for the scaffold system in the study

which is less than 40 mm; therefore, the expected base eccentricity of the system is no more

than 17 mm. The base eccentricity model proposed is illustrated in Figure 14(b), in which the

base eccentricity is labelled as “e”. The standard and the base plate are modelled using

nonlinear beam elements with their corresponding cross-sectional and material properties. A

contact element is used to model a gap between the base plate and the ground. The contact

element is set to provide stiffness only in compression, and only when the nodes to which it is

connected come into contact, that is when the gap closes. The stiffness is specified as

“infinity,” implying that when the load transfers from the standard to the base plate causing

the far end of the base plate to rotate and touch the ground, the point of contact becomes

infinitely stiff representing solid ground or other hard surface.

Figure 14: (a) base plate on uneven ground and (b) base eccentricity model

3.5 Load Eccentricity

A load eccentricity can occur between the timber bearer and the U-Head since the bearer is

not always positioned such that its centre line coincides with the centre line of the jack, even

though in good construction practice the U-head is twisted against the bearer so as to reduce

the amount of eccentricity. In order to model the eccentricity, a rigid link with length equal to

the load eccentricity is connected to the top of the jack in the direction perpendicular to the

bearer, and the vertical point load is applied at the far end of the link. The rigid link behaves

as a short, stiff cantilever that introduces vertical force and additional moment into the jack.

3.6 Geometric Imperfections

Scaffold systems are generally slender and sensitive to stability effects; therefore, initial

geometric imperfections producing member P-δ and frame P-∆ effects (Figure 15) must be

considered in the analysis model. A common approach to incorporate geometric

Load

Standard

Base plate

Uneven ground Contact element

Base plate

Standard

(a) (b)

bp

1 1

e



21

imperfections is to scale one or more critical elastic buckling modes and apply the scaled

displacements to the perfect geometry. Nevertheless, several issues remain unanswered in

this method. For instance, how many buckling modes should be included and what scaling

factors should be applied? One alternative is to use the maximum allowable imperfection

values from available structural codes. For example, the Australian steel design standard [7]

specifies a maximum out-of-straightness of L/1000, where L is the member length.

Nonetheless, this method often produces conservative predictions of the strength of systems.

Another approach is to apply notional horizontal forces, but some doubt remains as to the

magnitude of force to use.

Alternatively, for the purpose of calibrating the analysis model, in this research the

magnitudes of the member out-of-straightness and the frame out-of-plumb are implemented

directly at the nodes of the finite element models from acquired initial imperfection

measurements taken as part of the subassembly tests [24]. The member out-of-straightness (δ)

is applied at mid height of the standard in each scaffold lift and the frame out-of-plumb (∆) is

applied at each ledger-standard connection point and at the U-head at the top of the scaffold.

From the measurements, the average out-of-straightness of the standards is Lh/820 mm for the

lifts with spigot joint and Lh/1700 mm for the lifts without spigot joint, where Lh is the lift

height, and the average out-of-plumb of the frames is H/470 mm, where H is the total height.

Full details of the initial geometric imperfections of the subassembly tests are available in

[24]. For other studies on the scaffold systems, real data on initial geometric imperfections is

procured from construction sites around the Sydney area.

Figure 15: P-δ and P-∆ effects

3.7 Geometric and Material Nonlinearities

In geometric nonlinear analysis, an accurate determination of the displacements is attained

which is particularly important in slender structures such as scaffold systems. In the present

beam element based analysis, the deformed geometry is used to establish the equilibrium

equation and the element’s local reference system is updated at each load increment to

capture the load deflection characteristics.

In material nonlinear analysis, the nonlinear relationship between stress and strain is applied.

The stress-strain relations for the scaffold components used in the models are based on the

Ramberg-Osgood expression [27, 28] fitted to experimental data obtained from

supplementary tests on components of the subassembly tests [24]. Figures 16 to 21 show the

Ramberg-Osgood stress-strain curves used in the material modelling of the experimental

standard, ledger, jack, base plate, brace, and spigot respectively. Since there is no stress-strain

data for the ledger, brace and spigot, the stress-strain relations for these components are

obtained by scaling the Ramberg-Osgood stress-strain relation used for the standards to their



22

nominal yield stress. However, the ledger, brace and spigot insert are expected to be loaded

only in elastic range, and therefore, the material nonlinearity effects of these components are

negligible. The Ramberg-Osgood parameters (E0, σ0.2, n) for each scaffold component are

summarised in Table 5. In the table, E0 is the initial Young’s modulus, σ0.2 is the 0.2% proof

stress as the equivalent yield stress, and n is a parameter which determines the sharpness of

the knee of the stress-strain curve.

Table 5: Ramberg-Osgood parameters for scaffold components

Component E0 (GPa) σ0.2 (MPa) n

Standard 200 530 38.2

Ledger 200 380 38.2

Jack 200 495 16.0

Base plate 200 260 25.0

Brace 200 430 38.2

Spigot 200 430 38.2

The Ramberg-Osgood stress-strain relations are applied to the beam elements of each

scaffold component. As the beam cross-section and length are subdivided, sampling points on

the cross-section and integration points along the length of the beam are utilised to

numerically integrate the stiffness characteristics of the beam. As a result of this section and

length-wise integration, the propagation of yielding through the cross-section and along the

beam element can be included. The axial and bending stiffness are coupled as the neutral axis

on the yielded beam shifts [26]. This method is referred to as plastic-zone analysis [8].

Figure 16: Stress-strain curve for standard

0.00E+00

1.00E+08

2.00E+08

3.00E+08

4.00E+08

5.00E+08

6.00E+08

0.0000 0.0050 0.0100 0.0150 0.0200 0.0250

Strain

Str

ess

(Pa)

Ramberg-Osgood Test result



23

Figure 17: Stress-strain curve for ledger

Figure 18: Stress-strain curve for jack

0.00E+00

1.00E+08

2.00E+08

3.00E+08

4.00E+08

5.00E+08

0.0000 0.0050 0.0100 0.0150 0.0200 0.0250

Strain

Str

ess

(Pa)

Ramberg-Osgood

0.00E+00

1.00E+08

2.00E+08

3.00E+08

4.00E+08

5.00E+08

6.00E+08

7.00E+08

0.0000 0.0050 0.0100 0.0150 0.0200 0.0250

Strain

Str

ess

(Pa)




24

Figure 19: Stress-strain curve for base plate

Figure 20: Stress-strain curve for brace

0.00E+00

1.00E+08

2.00E+08

3.00E+08

4.00E+08

0.0000 0.0050 0.0100 0.0150 0.0200 0.0250

Strain

Str

ess

(Pa)


0.00E+00

1.00E+08

2.00E+08

3.00E+08

4.00E+08

5.00E+08

0.0000 0.0050 0.0100 0.0150 0.0200 0.0250

Strain

Str

ess

(Pa)

Ramberg-Osgood



25

Figure 21: Stress-strain curve for spigot

3.8 Calibrations

The commercial software package Strand7 [26] was used to create a finite element model for

each of the full-scale subassembly tests using the actual frame dimensions and measured

values of imperfections. The mean of the measured dimensions of components were used for

cross-sectional properties in the finite element models. As an example, Figure 22 shows the

finite element model for Test No. 3 of the subassembly tests [24]. The ultimate loads and

displacements obtained from the nonlinear analyses accounting for both material and

geometric nonlinearities were calibrated against failure loads and load-deflection responses

obtained from the full-scale subassembly tests [24].

The calibrations were achieved by changing the stiffness of the elastic restraints applied at the

U-head and base plate, as well as the axial spring stiffness of the brace connections; the latter

was changed after the calibrations were performed on unbraced systems for the top and

bottom rotational stiffness. Table 6 shows the results of the stiffness parameters obtained

from the calibrations. In the table, K represents translational stiffness with subscript showing

its direction corresponding to Figure 22, and R represents rotational stiffness with subscript

showing the axis of bending according to Figure 22. It should be noted that the top rotational

stiffness about the x-axis is assumed to be rigid, corresponding to the negligible strong axis

bending of the bearer. However, the y-axis bending stiffness is taken as 40 kNm/rad since

bending about this axis occurs during failure as observed in the tests [24]. The bottom

rotational stiffness about the x and y axes is calibrated as 100 kNm/rad. The bottom rotational

stiffness is applied to all uprights except the uprights with bottom eccentricity for which base

plate modelling is applied. The translational stiffness at the base is taken as rigid in all

directions. At the top, the translational stiffness is assumed to be rigid in the x and y

directions, but 0 in the z direction. The brace end connections have an axial stiffness of 1.8

kN/mm capable of transferring only axial forces to the ledgers.

0.00E+00

1.00E+08

2.00E+08

3.00E+08

4.00E+08

5.00E+08

0.0000 0.0050 0.0100 0.0150 0.0200 0.0250

Strain

Str

ess

(Pa)

Ramberg-Osgood



26

Table 7 shows the calibration results for the failure loads and their statistics. The average of

the ratio of test failure load to ultimate load from advanced analysis is 1.014 with standard

deviation (STD) and coefficient of variation (COV) of 0.0980 and 0.0966, respectively.

Figures 23 to 37 compare the finite element analysis results with the experimental load-

deflection responses at certain point of the frame, as indicated for each test in the titles of the

figures.

Table 6: Parametric calibration results

Kx (kN/mm) Ky (kN/mm) Kz (kN/mm) Rx (kNmm/rad) Ry (kNmm/rad) Rz (kNmm/rad)

Rigid Rigid Rigid 100,000 100,000 0

Kx (kN/mm) Ky (kN/mm) Kz (kN/mm) Rx (kNmm/rad) Ry (kNmm/rad) Rz (kNmm/rad)

Rigid Rigid 0 Rigid 40,000 0

Top boundary conditions

Brace end connections

Axial stiffness (kN/mm) 1.8

Bottom boundary conditions

Table 7: Load calibration results

Test

Ultimate load

from

advanced

analysis (kN)

Test failure

load (kN)Test load / Advanced analysis result

2 96 89 0.927

3 91 91 1.000

4 45 50 1.111

5 60 60 1.000

6 66 60 0.909

8 138 130 0.942

9 50 65 1.300

10 64 70 1.094

11 127 120 0.945

12 129 120 0.930

13 68 70 1.029

14 160 160 1.000

15 105 105 1.000

16 100 100 1.000

18 147 150 1.020

Average 1.014

STD 0.0980

COV 0.0966



27

Figure 22: Finite element model of Test No. 3 showing axes

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40

Deflection (mm)

Lo

ad (

kN

)

Test result FE result

Figure 23: Calibration of load-deflection responses at mid-height of the standard in the 3rd

lift

of the 2nd

row of the frame for Test No. 2



28

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30 35 40

Deflection (mm)

Lo

ad (

kN

)



lift

of the 2nd


0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30

Deflection (mm)

Lo

ad (

kN

)



lift

of the 2nd




29

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35

Deflection (mm)

Lo

ad (

kN

)



lift

of the 2nd


0

10

20

30

40

50

60

70

0 2 4 6 8 10 12

Deflection (mm)

Lo

ad (

kN

)



lift

of the 2nd




30

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30

Deflection (mm)

Lo

ad (

kN

)



lift

of the 2nd


0

10

20

30

40

50

60

0 1 2 3 4 5 6 7 8 9

Deflection (mm)

Lo

ad (

kN

)



lift

of the 2nd




31

0

10

20

30

40

50

60

70

0 0.5 1 1.5 2 2.5 3

Deflection (mm)

Lo

ad (

kN

)


Figure 30: Calibration of load-deflection responses at mid-height of the standard of the 3rd

lift

of the 2nd


0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16

Deflection (mm)

Lo

ad (

kN

)



lift

of the 2nd




32

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

Deflection (mm)

Lo

ad (

kN

)



lift

of the 2nd


0

10

20

30

40

50

60

70

80

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Deflection (mm)

Lo

ad (

kN

)


Figure 33: Calibration of load-deflection responses at the 2nd

lift of the 1st row of the frame

for Test No. 13



33

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12 14 16 18

Deflection (mm)

Lo

ad (

kN

)



lift

of the 2nd


0

20

40

60

80

100

120

0 2 4 6 8 10 12 14 16

Deflection (mm)

Lo

ad (

kN

)


Figure 35: Calibration of load-deflection responses at mid-height of the standard in the 2nd

lift

of the 2nd




34

0

20

40

60

80

100

120

0 5 10 15 20 25 30

Deflection (mm)

Lo

ad (

kN

)



lift

of the 2nd


0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Deflection (mm)

Lo

ad (

kN

)



lift

of the 2nd




35

4. Discussion

The calibrations show that advanced analysis using geometric and material nonlinear finite

element models gives very good predictions of the ultimate loads of the systems. Most of the

predictions are within 10% of the actual failure loads. In fact, the average of the ratios

between failure test load and predicted ultimate load is very close to 1 (1.014) with a

relatively small COV of 0.0966.

In addition, advanced analysis gives good results in predicting deformation responses of

support scaffold systems. The finite element analysis results of the load-deflection responses

fit the test results [24] reasonably closely with most of the values within 20% of one another.

It can be noticed that in some tests there are no deflection values available for the failure

load. Also, Test No. 4 only provides three measured deflections during loading, and has been

ignored in the comparison.

Two distinct failure modes are observed from the advanced analysis, as one exhibiting an S-

shape member buckle (Figure 38) and the other a lateral frame buckle with large lateral

displacements at the top story (Figure 39). The failure modes are noticed to be sensitive to the

jack extension length, where 600 mm jack extension produces lateral frame buckling with

main failure in the jacks and 300 mm jack extension produces S-shape buckling of the

standards with predominant failure deformations in the spigots. These failure modes were

also observed in the tests [24] suggesting that advanced analysis is capable of accurately

predicting the behaviour and failure mode of support scaffold systems.

Figure 38: S-shape member buckling



36

Figure 39: Lateral frame buckling

5. Conclusions

In this paper, nonlinear finite element analysis models for support scaffold systems have been

developed. Models for various components of the systems including spigot joints, semi-rigid

upright-to-beam connections and base plate eccentricities are proposed. Calibrations of these

models to the full-scale subassembly tests [24] consisting of three-by-three bay formwork

systems with the combinations of different numbers of lifts, jack extension, and lift height are

achieved by adjusting the top and bottom boundary conditions as well as the brace connection

stiffness. The ultimate loads obtained from advanced analysis are in close agreement with the

failure loads of the tests; moreover, comparisons of load-deflection responses also show close

agreement, demonstrating that advanced analysis is able to accurately predict the behaviour

and strength of highly complex support scaffold systems. The development of a design

methodology for support scaffold systems based on advanced analysis is in progress at the

University of Sydney.

Acknowledgement

The authors would like to thank Boral Formwork & Scaffolding Pty Ltd for providing

subassembly test data and support of this research project.

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Documents

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