Limit-State Analysis & Design of Cable-Tensioned Structures

8/13/2019 Limit-State Analysis & Design of Cable-Tensioned Structures

1/35

Limit-State Analysis and Design of Cable-Tensioned

Structures

J. Y. Richard Liew1, N. M. Punniyakotty2& N. E. Shanmugam3

ABSTRACT

This paper deals with application of nonlinear analysis to study the system's limit

state behaviour of cable-tensioned steel structures. The cable tendon is modelled as

an equivalent truss element with initial pretensioned force applied either as self-

equilibrating axial load or as an equivalent thermal load. The modulus of elasticity

of the cable material can be modified to account for the constructional stretch and

sagging effects in the cables. Pin-jointed space truss systems are modelled using a

plastic-hinge nonlinear formulation, which implicitly satisfies the design

specifications for ultimate strength of axially loaded members. Rigid space frame

systems are modelled using an elasto-plastic nonlinear frame analysis program. The

effectiveness of providing pretensioned cables in improving the limit state behaviour

of pin- and rigid-connected space frames is demonstrated through several examples.

Keywords: Barrel vault, cable-strut structures, limit state design, nonlinear analysis,

space structures, tensioned structures.

1Assoc. Prof.,

3Prof., Dept. of Civ. Engrg., National Univ. of Singapore, Department of Civil Engineering

1 Engineering Drive 2, Singapore 117576. Tel: 65-8742154, Fax: 65-7791635

2Sr. Struct. Engr., Sembawang Marine and Offshore Engineering, 60 Admiralty Road West, #01-02, Singapore

759947


2/35

2

NOTATION

A = Area of cross-section

E = Modulus of elasticity of material

Eeff= Effective modulus of elasticity of cable memberEeq= Equivalent modulus of elasticity of cable member

H = Horizontal projected length of cable

L = Length / Chord length of member

P = External load

Pb= Inelastic buckling load

P0= Cable pretensioned force

r = Radius of gyrationT = Cable tension

w = Unit weight of cable

t = Change in temperature

= Coefficient of linear expansion

y= Design strength of material


3/35

3

1 INTRODUCTION

Advanced analysis has been shown to be suitable for designing complex

structures that are slender and flexible [1-3]. Design of steel structural systems based

on direct advanced analysis has become simpler as it only requires the system to be

stable and capable of resisting the loads with sufficient factor of safety. This is in linewith the modern limit-state design codes which prefer global analysis of systems

behaviour to gain "direct" insights to their strength and stability compared to the

conventional approaches involving the use of semi-empirical formulae for member

stability checks [4-7].

For aesthetic reason, some skylight structures require members to be sleek so

that they occupy less physical area to allow passage of natural light. In other

structural systems like telecommunication masts, which carry predominantly self-

weight and wind loads, small member sizes and hence slender members are essential

to achieve an economical design. Since slender members are susceptible to buckling,

their effects need to be included in the limit analysis of the overall structural system.

Advanced analysis, which can capture both members' and system's instability, wouldhelp in identifying the most critical component members governing the limiting

strength of the system [1].

The limiting strength of slender structural systems can be enhanced by any one

of the following three approaches. The first approach is to apply prestressing forces to

the structural system by inducing initial stresses opposing those caused by the design

load. For a double-layer grid system, Hanaor and Levy [8] and Levy et. al. [9] carried

out experiments to study the effect of prestressing the critical strut members having

brittle type buckling characteristics by imposing lack of fit. They found 40%

increase in the load carrying capacity of the prestressed configuration compared with

the non-prestressed configuration.In the second approach, pretensioned cables are added to the structural system

to enhance the buckling strength of the most critical members. The pretensioned force

in the cables induces initial stresses in the critical members to counteract the design

forces experienced by them so that their failure can be delayed. Belenya [10]

reviewed various investigations carried out in this area and presented design and

erection concepts for prestressed steel trusses, beams, bridges, masts and towers, and

other special-purpose structures. Liew et al [11] proposed the use of nonlinear analysis

to study the self-erection of framework using cable tensioning technique. The stability

conditions of the structural frameworks during and after erection were investigated.

The third approach is to adopt an altogether different structural system which

uses only high-strength cables and steel struts to resist tension and compressionrespectively. This form of structural system is referred to as cable-strut structure or

tensegrity system [12-16].

In the present work, the effectiveness of using prestressed cables in improving

the limit-state behaviour of steel space frame system is studied using the advanced

plastic hinge method [1]. Cable elements are introduced in the space frame system to:

(i) reduce the load acting on the critical members,

(ii) produce counteracting prestressing force in the most critical members,

and/or

(iii) reduce the effective unbraced length of critical members by generating

lateral restraining forces.


4/35

4

Case studies are presented to demonstrate how one or more of the above will affect

the maximum strength of space frame systems by the provision of additional cables

and strut members.

2 MODELLING OF PRETENSIONED CABLE

When the lateral load effect is negligibly small, the cable element may bemodelled as an equivalent truss element [11] whose length is equal to the chord length

of the cable as shown in Fig. 1. The initial pretensioned force in the cable, P 0, can be

specified either as self-equilibrating axial load or as an equivalent thermal load. In the

latter case, the pretensioned force, P0, can be converted to an equivalent change in

temperature, t, by using the following equation [11]:

t = P0/ (E A) (1)

where, A is the cross sectional area, is the coefficient of thermal expansion and E is

the modulus of elasticity of the cable material.

When the lateral load effect is significant, the geometric change in cable

length must be included in the analysis of cable structures.The total apparent change

in the length of a cable is the result of the sum of the three distinct actions: (i) theelastic strain in the cable material which is linear and governed by the modulus of

elasticity; (ii) change in the sag of the cable which is strictly a geometric effect,

independent of material stress and varies in a nonlinear manner with the axial tensile

force in the cable; and (iii) the relative movement of individual strands in the cable to

rearrange themselves into a more consolidated cross-section under load. This

rearrangement is known as constructional stretch.

The constructional stretch is permanent and occurs below a specified

tensioned force. This permanent deformation is usually removed in the manufacturing

process by prestretching the cable to a load larger than the working load. The

deformations which are non-permanent can be compensated for by using a reducedeffective modulus of elasticity of the cable, Eeff, which is independent of tension force

in the cable. Since the variation of the sag with the axial force in the cable is

nonlinear, the axial stiffness of the cable will vary with the increase in axial force.

To account for the effects of material deformation, constructional stretch and

the change in sag in the cable members, the actual modulus of elasticity of the cable

material, E, is replaced with an equivalent modulus of elasticity, Eeq, proposed by

Buchholdt [17] as:

EE

wH AE

T

eq

eff

eff

=

+1

12

2

3

( ) (2)

where, w = unit weight of the cable, H = horizontal projected length of the cable, A=

cross-sectional area, and T = tensile force in the cable. When modelling the cable

element as equivalent truss element, the elastic, geometric and higher-order stiffness

matrices that are essential for nonlinear analysis are computed using the equivalent

modulus of elasticity of the cable given by Eqn. (2).

3 MODELLING OF INELASTIC BEAM-COLUMN ELEMENT

Analysis of rigid-jointed space frames is based on an advanced plastic hinge

analysis program [1]. The main feature of the advanced analysis formulation is to use

one element per member to model each structural component and to obtain a realistic

representation of material and geometric nonlinear effects. The analysis operates on


5/35

5

element stress resultants, i.e., forces, bi-moments and torsion. The beam-column is

subject to end forces acting on three transitional and three rotation degrees of freedom

at each end node. The effects of large displacements and coupling between lateral

deflection and axial strain are included by using nonlinear strain relations. The elastic

tangent stiffness matrices are calculated from closed form expressions, with no

numerical integration over the element cross section or over the element length. Theycontain the influence of axial force acting on lateral deformations of the member (P-

effect). The detailed formulation of the three-dimensional inelastic beam-column is

reported in Ref. [18] and will not be repeated here.

For the tie members, the axial load-elongation relationship is obtained based

on bilinear elastic-plastic stress-strain curve of the material. The axial load

deformation relationships obtained for the strut and tie elements model the large

displacement inelastic behaviour of an axially loaded member. The ultimate strength

of axially loaded member is calculated directly based on the design code requirement,

and hence no separate check is required for member stability and strength. A detailed

description on the strut and tie model for advanced analysis of space structures can befound in Ref. [19].

4 ANALITICAL PROCEDURE

Analysis of cable-tensioned structures may be performed in two stages. In the

first stage, only cable tensioning forces are applied, and incremental nonlinear analysis

is carried out to obtain the load-displacement behaviour of the structure. Each

increment of pretensioned forces is transformed to the global coordinate system as

internal resistance vector. By solving the incremental-iterative equilibrium equation

for the unbalanced forces, the new equilibrium configuration of the system, which

satisfies the force equilibrium at each node, can be found. The next increment ofpretensioned force is then applied and the same iterative process is repeated. This

procedure is continued till the desired magnitude of pretensioned forces is applied to

all cable members [11].

In the second stage, external loads are applied on the prestressed structure.

Again, incremental nonlinear analysis is carried out until the factored design load

level is reached. The structure is said to satisfy the ultimate design limit state if the

load factor associated with the limit of resistance obtained from the advanced analysis

is higher than the design load factor.

The following criteria are assumed as premature failure conditions for the

pretensioned system:

(i) cable slackening caused by compressive force before the service load isreached,

(ii) tensile force in the cable reaching the Minimum Breaking Load (MBL)

before the full design loads are applied, or

(iii) system's limiting capacity is reached before the full design loads are

applied.

The slackening or compressive failure of a cable is a gradual process and impairs

the serviceability of the structural system. On the other hand, tensile failure of a cable

is an explosive event involving release of strain energy and ought to be classified as

an ultimate limit state for all intents and purposes. Hence, the structural system is

considered to reach its limit states of design when any of the cables in the systemreaches either compression or tension failure in their respective limit states.


6/35

6

5 VERIFICATION STUDIES

Two numerical examples, (i) a two-dimensional cable truss and (ii) a three-

dimensional saddle net, are considered to verify the cable element formulation. The

inelastic beam-column formulations have been verified elsewhere [1, 18-20] and willnot be repeated herein.

5.1 Two Dimensional Cable Truss

The two-dimensional cable truss as shown in Fig. 2 consists of an upper and a

lower cable, and 14 vertical hangers [20]. The span of the structure is 3.03m, and the

height at the supports is 0.81m. Vertical hangers are equally spaced along the span.

All nodes are prevented from lateral displacement in the out-of-plane direction. A

single point vertical load of 115.4 N is applied at the lower node of the fifth hanger

from the left support.

In Fig. 3, the vertical and the horizontal displacements of upper and lower

chords obtained by the present analysis are compared with those obtained byBroughton and Ndumbaro [20] using a geometric nonlinear analysis program. Close

agreement between the results is observed.

5.2 Three Dimensional Saddle Net

The three dimensional saddle net [21] of plan dimension 50 m 40 m consists

of 142 pretensioned cable elements spaced at 5 m 5 m grid as shown in Fig. 4(a).

The modulus of elasticity and area of cross-section of all cables are 147 kN/mm2and

306 mm2, respectively. A pretensioned force of Po = 60 kN is applied to all the

cables. The external loading consists of 1 kN force indicated as P along the positive

X and Z directions at all the free nodes on one-half of the net as shown in Fig. 4(a).

The displacements obtained from the present method are compared in Table 1with those obtained by Lewis [21] using Dynamic Relaxation Method. The results for

displacements and cable forces predicted by the present nonlinear analysis method are

very close to those obtained by Lewis [21]. The maximum errors in the computation

of displacements are within 2%.

To study the effect of cable pretensioned force on the system's limit load, load-

displacement analyses are carried out on the cable net system by varying the cable

pretensioned force viz. Po= 10, 20, 30 and 40kN. The results are shown in Fig. 4(b).

External loads [denoted by P in Fig. 4(a)] are applied incrementally until failure is

detected in any one of the cables represented by cable slackening or the cable reaching

the minimum breaking load (MBL). The resulting limit loads, P, for the four load

cases are, 1.23, 3.07, 2.98 and 2.88kN respectively. In the case of Po = 10kN,

slackening of cables is detected at P= 1.23kN. In all the other three cases, the cable

joining the nodes 2 and 12 attained its MBL at the system's limit load. The analyses

show that Po= 20kN is the optimum pretensioned force that can be applied to achieve

the maximum load-carrying capacity for this particular structure. From Fig. 4(b), it

can be observed that the limit load values decrease if the cable tensioned forces are

increased beyond the optimum value of 20kN. When the pretensioned force is very

high, the cable reaches the MBL at an early stage of loading.

The centre node deflection due to initial prestressing force is in the upward

direction as indicated by the negative displacement values when the applied force is

zero (i.e., P = 0). The initial upward displacement increases with the increase inpretensioning force in the cables. Considering the displacement pattern due to live


7/35


8/35

8

rigid-jointed dome under single- and multiple-load points are shown in Figs. 8, 9 and

10. The corresponding limit loads obtained from the analysis are sumerised in Table

2.

If the cables are not prestressed, slackening occurs in all the cables when

multiple point loads are applied. Hence, this condition is not considered for this

particular load case. With the provision of the cable-strut system, there is asubstantial increase in the limit load of the system and a marginal decrease in vertical

displacement for single concentrated loading case. However, such beneficial effect is

not observed in the case of multiple-point load case [Figs. 7 and 10]. The reason is

that in single concentrated load case, a portion of the concentrated load at the crown is

transferred to the cables through the central strut resulting in a reduction of

compressive forces on the top six critical members. However, in multiple point loads

case, the bottom twelve members are the critical members and the provision of cables

and strut does not reduce the loads at the bottom members. It should be noted that

prentensioned cables provide cambering effect against deflection under gravity load.

They also increase the overall stiffness of the structure.6.2 Single-Layer Barrel Vault System

The span length, depth (in the longitudinal direction) and central rise of the

barrel vault are 29.97m, 21m and 1.973m respectively. It consists of 212 tubular

members, with E = 205 kN/mm2and y= 275 N/ mm2, arranged as shown in Figure

11. The boundary nodes along the two straight edges are constrained to move in any

directions but free to rotate. All members are rigidly connected to each other.

The structure is subject to a uniformly distributed dead load (DL) of 0.50 kN/

m2and live load (LL) of 0.75 kN/m2per plan area. Wind load (WL) computed using

BS: 6399 Part 2 [24] with basic wind speed of 30 m/s is considered. The wind load

may act in the longitudinal (= 90) or transverse direction (= 0) as shown in Figs.

12 a & 12b. Considering the two external wind pressure coefficients 0.2 for zone D

and wind acting in transverse (= 0) and longitudinal (= 90) directions, there are

four wind load cases. The net wind pressures are indicated as Zones A, B, C and D in

Fig. 12. A notional load (NL) of 0.5% of (1.4DL + 1.6LL) is considered [25] to

account for the initial imperfection effects at the system level. The loads are applied

as nodal loads.

Nonlinear analyses are carried out for the following load combinations [26]:

1. 1.4DL + 1.6LL + NL

2. 1.2[DL + LL + WL(= 0; D = 0.2)]

3. 1.2[DL + LL + WL(= 0; D = +0.2)] (5)

4. 1.2[DL + LL + WL(= 90; D = 0.2)]5. 1.2[DL + LL + WL(= 90; D = +0.2)]

In the nonlinear analysis, load factor of 1.0 means that the applied loads correspond to

the particular factored load combination, whereas load factor greater than 1.0

represents the safety margin of which the systems limit load is larger than the

required design load.

6.2.1 Barrel Vault with Arch Edges Unsupported

Nonlinear inelastic analysis is carried out for the barrel vault in which the arch

edges are free to translate. CHS 273mm x 12.5 mm is selected for arch members and

CHS 193.7mm x 12.5 mm for all other members. The limit load factors for the system

under various load combinations are shown in Table 3. The most critical loadcombination is Load Case 3, in which the central arch members placed are subject to


9/35

9

the maximum force and they become the most critical members which govern the

failure of the system. Figure 13a shows the deformed shape of the structure at the

limit load under Load Case 3. Figure 13b shows the global load-displacement curve

for the central node (denoted as "C"). The member axial load-displacement curves for

the arch members are shown in Fig. 14. The limit load of the barrel vault system is

governed by inelastic buckling of arch members (labelled as 79, 80, 89 and 90) asshown in Fig. 14. The minimum steel weight for the barrel vault of which the arch

edges are free to translate is 41.3 tons.

6.2.2 Barrel Vault with Arch Edges Stiffened by Tensioned Cables

A set of pre-tensioned radial cables are provided along the two arch edge, as

shown in Figure 15, to enhance the buckling resistance of the arch members. The

cable support point is located at the eaves level and is anchored to the adjacent

structure to prevent in-plane movement. The cables provide planar restraints to the

arch members so as to increase their load carrying capacities. In the process of

prestressing, the unbalanced force components in the cable would displace the system

in a direction opposite to that due to wind uplift resulting in an overall reduction offinal deflections due to service wind loads. Figure 16a shows an application of radial

tensioned cables for stiffening a barrel vault skylight system used in actual

construction. Figure 16b shows the detailed design of the cable-support point.

Considering a pretensioned force of 80kN in each cable and various tubular

sections for the members, nonlinear analyses were performed for the barrel vault

system with all possible load combinations. A minimum proportional load factor of

1.08 is obtained for the most critical load combination: 1.2[DL + LL + WL] when

CHS 168.3 x 8 mm section is chosen for all the members. The limiting load is

reached when the cables slacken which triggers the collapse of the overall system. The

displaced configuration of the structure at the limit of resistance under load case 3 is

shown in Figure 17a. The global load-displacement curve for the central node C andaxial load-displacement curves for the critical arch and cable members are presented

in Figs. 18 and 19a-c for the load combination 3. The total steel weight of the pre-

tensioned system is only 22.5 tons, which is 45% lighter than the structure with

unsupported arch edges.

From the cable axial load-displacement plots shown in Figs. 19b, it is

observed that the application of external loads on the system induces additional

tension force on the left side cables (denoted as member 213 and 222 in Fig. 17).

However, it induces compressive force on the right side cables (members 219 and

228) causing release of pretensioned force as shown in Fig. 19c. Thus, the load

carrying capacity of the system is controlled by the cable slackening leading to theloss of stiffness of the arched members.

Figure 19a shows that arch members 80 and 90 with a size of CHS 168.3 8

mm can provide an axial resistance of 390 kN compared to CHS 273 12.5 mm with

an axial resistance of 295 kN under unsupported arch edge condition. Thus, the

pretensioned cables act as effective restraints to the arch members and enable the use

of smaller size member to carry more axial compressive load than the case in which

the arch members are unsupported.

Larger pretensioned forces may be required to prevent cable slackening so as

to enhance the load carrying capacity. For example, instead of applying 80 kN

pretensioned force in the cables, a 100 kN pretensioned force is applied, the resulting

system's limit load is found to be increased by 7%. Since the applied initialpretensioned force cannot exceed the maximum breaking load of the cable, the load


10/35


11/35

11

because the cables with a pretensioned force of 1.2 kN is not sufficient to provide

adequate lateral restraints to the imperfect column. Subsequently, the nonlinear

analyses were carried out with increased pretensioned forces. A limit load of 39 kN

was achieved with a pretensioned force of 10 kN. The deformed configuration and

the load-displacement curve are shown in Figs. 23(b) and (c). The study shows that

the geometrical imperfections have significant effects on the limit load of the stiffenedcolumn. Numerous studies in the past tend to focus on buckling analysis of structures

without considering the effect of structural initial imperfection. The present

investigation shows that the ultimate behaviour of a prestressed column is very much

affected by the structural initial imperfection. Higher pretensioning forces may be

required to provide adequate restraints to members of imperfect geometry if their

compression resistance is to be fully realised. It should also be noted that the

magnitude of pretensioned force in the cables lying in same plane should be the same

in order to avoid initial imperfections that would otherwise affect the ultimate

resistance of the column.

7 CONCLUSIONS

The examples presented in this paper illustrate that the proposed nonlinear

analysis tools can be used for limit-load analysis of cable-tensioned structures. With

careful consideration of member and system imperfection effects, it is possible to

determine system capacity with good accuracy. This is in line with the modern design

codes which allow the use of advanced analysis for designing steel structures.

Investigations have been carried out on the use of prestressing in various space

structures, such as cable-net, dome, barrel vault and 3-D column. Their design limit-

state behaviours are studied considering various structural arrangements.Computation procedure was developed and the effect of the prestressed value was

analysed. The following observations are drawn from the case studies presented in

this paper:

(1) The assumed cable and strut system is found to be effective in increasing

the limit load of the pin- and rigid-jointed spherical domes by 47% and

37%, respectively. However, the proposed cable-strut system is designed to

resist the single-point load applied at the crown joint and may need to be

modified for other load cases.

(2) In the case of barrel vault system, a set of pretensioned radial cables act as

lateral restraints to the arch members and lead to a steel weight reduction of

45% under the same loading condition.(3) A pretensioned stiffening system is effective in providing lateral restraints

to slender columns. The presence of physical imperfections in the column

reduces the ultimate resistance quite substantially and hence their

consideration in the design of such structures is essential.

For the shallow dome, the provision of pretensioned cable-strut system is to

reduce the forces acting on the critical members by altering the load path. In the case

of the barrel vault and slender column, the force in the cable creates a stress opposite

in the direction to that from the load in the most stressed members of the system.

Pretensioning is an effective means to reduce steel consumption and cost of

structures and to enhance their strength and rigidity. Effective use of pretensioning inslender space frame design requires the development of innovative system, ones


12/35

12

different from conventional non-prestensioned structures. In general pretensioned

structures are of more complicated arrangement whose behaviour is to a great extent

affect by nonlinearity of deformation and stresses, initial imperfections, fabrication

technique and erection sequence. It is good practice to allow for these factors in

analysis and design.

ACKNOWLEDGEMENTS

The investigation presented in this paper is part of the research programs on computer

aided second-order inelastic analysis for frame design being carried out in the

Department of Civil Engineering, National University of Singapore. The work is funded

by research grants (RP920651) made available by the National University of Singapore.


13/35

13

Table 1 Comparison of displacements in saddle net

(1) (2)

Node By Lewis[27] (mm) By present analysis (mm)

No. X Y Z X Y Z

11 15.5 4.5 82.0 15.5 4.5 81.7

15 4.1 2.9 11.2 4.1 2.8 11.1

35 6.2 1.2 19.8 6.3 1.2 20.2

44 10.6 0.0 88.7 10.6 0.0 88.7

48 4.5 0.0 46.7 4.5 0.0 45.9

52 0.9 0.0 6.0 0.9 0.0 5.9

72 3.9 0.7 30.2 3.9 0.7 30.1

81 4.0 2.9 11.0 4.1 2.8 11.1

85 5.5 1.9 32.6 5.4 1.9 32.2

Maximum error = [(2) (1)]100/(1)% = 2%

Table 2 Limit load capacity of shallow spherical dome

Type of

joints

Loading details Limit load capacity (kN) of dome with

No cables Non-pretensioned

cables

Pretensioned

cables

Pin-jointed 1.0P @ crown 52.7 70.6 77.4

1.0P @ all joints 293.3 293.3

Rigid-

jointed

1.0P @ crown 64.7 82.6 89.1

1.0P @ all joints 415.1 415.8

Table 3 Limit load factors for barrel vault system

Arch

BCs.

Member size,

mm (CHS)

Weight

(Tons)

Limit load factors for load combination

1 2 3 4 5

Free

edge27312.5 &

193.712.5

41.3 1.37 1.48 1.10 1.82 1.46

Cables 168.38 22.5 1.14 1.15 1.01 1.15 1.15


14/35

14

REFERENCES

1. Liew J.Y.R. and Tang, L.K., Advanced Plastic Hinge Analysis for the Design of

Tubular Space Frames, Engineering Structures, Elsevier Science, 22, 2000, 769-

783.

2. Kitipornchai, S., Advances in nonlinear analysis of spatial and thin-walled

structures,Int Num Meth Eng., 1995, 38(5).

3. Akio Hori and A Sasagawa, Large Deformation of Inelastic Large Space Frame II:

Application,J. Structural Engineering, ASCE, 126(5), 2000, 589-595.

4. Liew J Y R, Chen W.F. and Chen, H., Advanced inelastic analysis of frame

structures,Journal of Constructional Steel Research, UK, 55:(1-3), July 2000,

267-288.

5. White, D. W., Liew, J. Y. R. and Chen, W. F., Toward Advanced Analysis in

LRFD,Plastic Hinge Based Methods for Advanced Analysis and Design of Steel

Frames - An Assessment of The State-Of-The-Art, Structural Stability Research

Council, Lehigh Univ., Bethlehem, PA., March 1993, 95-173.

6. Ziemian R.D., McGuire, W., and Deierlein, G.G. Inelastic Limit States Design

Part II: - three Dimensional Frame Study, J. Structural Engineering, ASCE,

118(9), 1992.

7. Chan, S.L. and Zhou, Z. H., On the Development of a Robust element for Second-

order NnliinearIntegrated Design and Analysis (NIDA), J Constructional SteelResearch, Elsevier, 47(1/2), 1998, 169-190,.

8. Hanaor, A. and Levy, R., Imposed lack of fit as a means of enhancing space truss

design, Space Structures, Elsevier App. Science, 1, 1985, 147-154.

9. Levy, R., Hanaor, A. and Rizzuto, N., Experimental investigation of prestressing

in double-layer grids,J. Space Structures, 9(1), 1994, 21-26.

10. Belenya, E., Prestressed load-bearing metal structures, MIR publishers, 1977,

463pp.

11. Punniyakotty, N M , Liew J.Y.R. and Shanmugam, N.M., Erection of Steelworks

by Cable-Tensioning Technique, J Structural Engineering, ASCE, Volume 126,

Issue 3, 2000, 361-370.

12. Eekhout, M., Advanced glass space structures, Space Structures 4, Thomas

Telford, London, 1993, 2016-2024.

13. McClleland, N.C. and Perry, J.C., Glass support structure interaction, analysis

and design, The Third Int. Kerensky Conf. on Global Trends in Structural

Engineering, Singapore, 1994, 413-420.


15/35

15

14. Takeuchi, T., et. al., A practical design and construction of tension rod supported

glazing,Proc. of the IASS-ASCE Int. Symposium on Spatial, Lattice and Tension

structures, Georgia, 1994, 684-693.

15. Pellegrino, S., A class of tensegrity domes, J. of Space Structures, 7(2), 1992,

127-142.16. Campbell, D. M., Chen, D., Gossen, P.A. and Hamilton, K. P., Effects of spatial

triangulation on the behaviour of Tensegrity domes,Proc. of the IASS-ASCE Int.

Symposium on Spatial, Lattice and Tension Structures, Georgia, 1994, 652-663.

17. Buchholdt, H. A., An Introduction to Cable Roof Structures, Cambridge Univ.

Press, Cambridge, New York, 1985, 257pp.

18. Liew, R J Y, Chen, H, Shanmugam, N E and Chen W F, Spatial instability and

second-order plastic hinge analysis of space frame structures, Research Report,

CE029/99. Singapore: National University of Singapore, April 1999, 50 pp.

19. Liew, J. Y. R., Punniyakotty, N. M. and Shanmugam, N. E., Advanced analysis

and design of spatial structures, J. Constr. Steel Res., Elsevier Science, 42(1),

1997,21-48.

20. Broughton, P. and Ndumbaro, P., The Analysis of Cable & Catenary Structures,

Thomas Telford, London, 1994, 88pp.

21. Lewis, W. J, A comparative study of numerical methods for the solution of

pretensioned cable networks, Proc. Int. Conf. On Non-Conventional Structures,

Vol. 2, Civil Comp. Press, Edinburgh, 1987, 27-33.

22. Yang, Y. B. and Kuo, S. R., Theory & Analysis of Nonlinear Framed Structures,

Prentice Hall, Singapore, 1994, 579 pp.

23. Yamada, S. and Taguchi, T., Nonlinear buckling response of single layer latticed

barrel vaults, Proc. of the IASS-ASCE Int. Symposium on Spatial, Lattice and

Tension Structures, Georgia, 1994, 519-528.

24. BS6399: Part2, Loading for buildings Part 2: Code of Practice for Wind Loads,

British Standards Institution, London, 1995.

25. BS5950 Part1, Structural use of steelwork in building Part 1: Code of Practice for

Design in Simple and Continuous Construction: Hot Rolled Section, British

Standards Institution, London, 1990.


16/35

List of Figures

Figure 1 Axial cable element

Figure 2 Two-dimensional cable truss

Figure 3 Comparison of results for cable truss

Figure 3 (a) Vertical displacement at lower chord locations

Figure 3 (b) Horizontal displacement at upper and lower chord locations

Figure 4 Three-dimensional saddle net

Figure 4 (a) Structure and loading details

Figure 4 (b) Effect of cable pretension on system limit load

Figure 5 Shallow spherical dome structural configurations

Figure 5 (a) Without cable and strut system

Figure 5 (b) With cable and strut system

Figure 6 Pin-jointed dome under vertical load at crown

Figure 7 Pin-jointed dome under uniform loads at free nodes

Figure 8 Load-displacement curves for rigid-jointed dome without cables and

strut

Figure 9 Load-displacement curve for rigid-jointed dome with non-pretensioned

cables and strut for vertical load at crown

Figure 10 Load-displacement curves for rigid-jointed dome with pretensioned

cables and strut

Figure 11 Single layer barrel vault system

Figure 12 Wind loads on barrel vault system

Figure 12 (a) Wind in longitudinal (= 90) direction

Figure 12 (b) Wind in transverse (= 90) direction

Figure 13 Barrel vault with unsupported arch edges

Figure 13 (a) Displaced configuration at limit load condition

Figure 13 (b) Global load-displacement curve for central node C

Figure 14 Axial load-displacement curves for barrel vault with unsupported edges

for 1.2 [DL+LL+WL (= 0; D = +0.2)] loads

Figure 15 Barrel vault with radial cables on arch edges

Figure 15 (a) Isometric view

Figure 15 (b) Side elevation


17/35

Figure 16 (a) General arrangement of arch and radial cables

Figure 16 (b) Details for radial cables support point

Figure 17 Displace configuration at limit load

Figure 18 Global load-displacement curve at central node C

Figure 19 Axial load-displacement curves for barrel vault with radial cables on

arch edges for 1.2 [DL+LL+WL (= 0; D = +0.2)] loadsFigure 19 (a) For members 80 and 90

Figure 19 (b) For cable members 213 and 222

Figure 19 (c) For cable members 219 and 228

Figure 20 Cable-strut stiffened column

Figure 21 Application of cable-strut stiffened members for supporting an

entrance canopy

Figure 22 Effect of pretension in cables of stiffened column without any member

imperfection

Figure 23 Geometrically imperfect cable-strut stiffened column with P0= 10 kN

Figure 23 (a) Initial configurationFigure 23 (b) Displaced configuration at limit load

Figure 23 (c) Axial load-displacement curve


18/35

Figure 1 Axial cable element

Figure 2 Two-dimensional cable truss


19/35

Figure 3 (a) Vertical displacement at lower chord locations

Figure 3 (b) Horizontal displacement at upper and lower chord locations

Figure 3 Comparison of results for cable truss


20/35

Figure 4 (a) Structure and loading details

Figure 4 (b) Effect of cable pretension on system limit load

Figure 4 Three-dimensional saddle net


21/35

Figure 5 (a) Without cable and strut system

Figure 5 (b) With cable and strut system

Figure 5 Shallow spherical dome structural configurations


22/35

Figure 6 Pin-jointed dome under vertical load at crown

Figure 7 Pin-jointed dome under uniform loads at free nodes


23/35

Figure 8 Load-displacement curves for rigid-jointed dome without cables and

strut

Figure 9 Load-displacement curve for rigid-jointed dome with non-pretensioned

cables and strut for vertical load at crown


24/35

Figure 10 Load-displacement curves for rigid-jointed dome with pretensioned

cables and strut


25/35

Figure 11 Single layer barrel vault system


26/35

Figure 12 (a) Wind in longitudinal (= 90) direction

Figure 12 (b) Wind in transverse (= 90) direction

Figure 12 Wind loads on barrel vault system


27/35

Figure 13 (a) Displaced configuration at limit load condition

Figure 13 (b) Global load-displacement curve for central node C

Figure 13 Barrel vault with unsupported arch edges


28/35

Figure 14 Axial load-displacement curves for barrel vault with unsupported edges

for 1.2 [DL+LL+WL (= 0; D = +0.2)] loads


29/35

Figure 15 (a) Isometric view

Figure 15 (b) Side elevation

Figure 15 Barrel vault with radial cables on arch edges


30/35

Figure 16 (a) General arrangement of arch and radial cables

Figure 16 (b) Details for radial cables support point


31/35

Figure 17 Displace configuration at limit load

Figure 18 Global load-displacement curve at central node C


32/35

(a) For members 80 and 90 (b) For cable members 213 and 222

(c) For cable members 219 and 228

Figure 19 Axial load-displacement curves for barrel vault with radial cables on

arch edges for 1.2 [DL+LL+WL (= 0; D = +0.2)] loads


33/35

Figure 20 Cable-strut stiffened column


34/35

Figure 21 Application of cable-strut stiffened members for supporting an

entrance canopy

Figure 22 Effect of pretension in cables of stiffened column without any member

imperfection


35/35

(a) Initial configuration (b) Displaced configuration at limit load

(c) Axial load-displacement curve

Figure 23 Geometrically imperfect cable-strut stiffened column with P0 = 10 kN

Documents

Limit-State Analysis & Design of Cable-Tensioned Structures