117

CHAPTER 5

CODAL COMPARISON

5.1 GENERAL

Singly symmetric angle sections may fail either by buckling about

the plane of symmetry or by a combination of twisting and bending. For open

sections like plain angles, lipped angles, channels, lipped channels the

torsional flexural buckling load can be significantly lower than the Euler load.

5.2 BUCKLING OF MONO SYMMETRIC SECTIONS

A singly symmetric section, centrally loaded tends to bend in

one of the principle planes containing the centroidal axis. If this plane also

contains the shear centre axis, bending can take place without simultaneously

inducing twist. However, if this plane of bending does not contain the shear

centre axis as in the case of a member in a panel with panelling eccentricity,

the bending is accompanied by twisting. This torsional flexural buckling

deformation is shown in Figure 5.1. The section has only one axis of

symmetry, the x-axis and the shear centre axis lies on that axis and yo = 0.

Then the torsional-flexural buckling equation is given by (Timoshenko and

Gere, 1985)

0]r

xPP)P)(PP)[(P(P

20

20

2

xy =−−−− ϕ (5.1)

This relation is satisfied either if

2

y2

yl

EIπPP == (5.2)

118

or if

0r

xPP)P)(P(P

2

0

2

0

2

x =−−− ϕ (5.3)

where P - Critical load

E - Modulus of elasticity of steel

Iy - Moment of inertia about Y – axis

l - Unbraced length of column

x

y

u

C.G

x o

Shear

Centre

Shear

Centre

y

x

i

xo

C.G

v

Figure 5.1 Torsional-flexural buckling deformation

119

2

x

2

xl

EIπP = (Euler load for Ix) (5.4)

where Ix - Moment of inertia about x-axis

)l

ECπ(GJ

r

1P

2

w

2

2

0

+=ϕ (5.5)

where ro - The polar radius of gyration

G - Shearing modulus of elasticity

J - St. Venant torsional constant

Cw - Warping constant

xo - Distance from shear centre to centroid along the x-axis

yo - Distance from shear centre to centroid along the y-axis

u - x-axis translation

v - y-axis translation

I - rotation about shear centre w.r.t x-axis

In general the mode of buckling for the mono symmetric sections

depends on the unsupported length of the column. When the slenderness ratio

is in the Euler column range or more than 120 the column will fail in flexural

buckling. When the columns are short columns with slenderness ratio less

than 50, then the column will fail by local buckling or by yielding depending

on the flat width to thickness ratio of the element. When the columns are in

the intermediate range with slenderness ratio 50 to 120 the column may fail

by interaction of torsional, torsional-flexural, flexural and local buckling.

Most of the members in latticed masts are designed as intermediate columns.

Moreover the leg members of transmission line towers are mostly designed in

the inelastic range of stresses and compact sections are usually preferred.

When a mono symmetric section buckles in the torsional mode the

120

mid-section bifurcates by rotating about the shear centre. However sectional

failure will be initiated by local buckling of the plate elements. For compact

sections, the local buckling strength is always more than or equal to the

torsional buckling strength, the effect of torsional-flexural buckling must be

considered.

In general, torsional flexural buckling may be the critical mode of

failure for short columns with slender outstands. Transmission line towers

normally consist of two types of members. Leg members which are the main

load carrying members are connected on both flanges as shown in

Figure 5.2(a) and hence they are concentrically loaded. However bracing

members which add stability to the leg members are connected on one flange

only and are eccentrically loaded as shown in Figure 5.2(b).

Bra

cing

ShearCentre

Eccentricity

x

y

C.G C.G

y

Bracing

Leg

x x

y

y

(a) Leg member (b) Bracing member

Figure 5.2 Connection details

121

When mono symmetric sections are subjected to eccentric loading,

the flexural buckling load about weak axis is lower than the torsional flexural

buckling load. On the other hand if the torsional flexural buckling load is

lower than the flexural buckling load the member tends to twist and fail by

torsional flexural. The load at which the members start twisting depends on

the restraint coefficients, eccentricity and sectional parameters.

5.3 STUDIES ON EQUIVALENT RADIUS OF GYRATION

The effect of equivalent radius of gyration on hot rolled angles

sections is studied. Variation of radius of gyration about minor axis,

equivalent radius of gyration with respect to length is compared in

Figure 5.3(a) and 5.3(b).

Based on the studies on the behaviour of radius of gyration versus

effective length behaviour shown in Figure 5.3, a non dimensional curve is

developed to determine the relation between width to thickness ratio and the

slenderness ratio upto which the equivalent radius of gyration is critical as

shown in Figure 5.4. The equivalent radius of gyration (rtf) is not critical for

the angle sections with width to thickness ratio upto 15. For sections with

width to thickness ratio in between 15 to17 the equivalent radius of gyration

is critical upto a slenderness ratio below 45 as shown in Figure 5.4.

122

10

14

18

22

26

30

34

38

42

46

50

0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000

LENGTH IN mm

RA

DIU

S O

F G

YR

AT

ION

IN

mm

rvvrtf

100x100x6 :b/t =16.67

ISA 200x200x12 rtf

150x150x10 rtf

ISA 130x130x8 rtf

ISA 100x100x6 & 100x100x7

rvv

ISA 100*100*6 rtf130x130x8 : b/t =16.25

150x150x10 rvv : b/t =15

200x200x12 rvv : b/t =16.67

b/t >14.25

100*100*7 rtf

100x100x7 :b/t =14.28

(a)

0

5

10

15

20

25

30

35

40

45

50

0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000

LENGTH IN mm

RA

DIU

S O

F G

YR

AT

ION

IN

mm

150*150*12 b/t <14

80*80*6 rtf

80*80*6 rvv

150*150*12 rtf

150*150*12 rvv

80*80*6 b/t <14

b/t <14

rtf rvv

(b)

Figure 5.3 Radius of gyration vs. Effective length behaviour

123

0

10

20

30

40

50

60

70

80

12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20

WIDTH TO THICKNESS RATIO

SL

EN

DE

RN

ES

S R

AT

IO G

OV

ER

NE

D B

Y E

QU

IVA

LE

NT

RA

DIU

S O

F

GY

RA

TIO

N (

rtf)

Figure 5.4 Slenderness ratio (governed by equivalent radius of

gyration) vs. Effective width behaviour

Generally in transmission line towers the slenderness ratio of leg

members varies from 40 to 60 and in this range the compression capacity of

the angle section is equal to the tension capacity. Mostly the leg members are

concentrically loaded and with insignificant bending. Hence leg members are

not subjected to torsional flexural buckling. The bracing members are

eccentrically loaded and subjected to bending along with axial forces may be

subjected to torsional flexural buckling. But the slenderness ratio of the

bracing members is generally greater than 60 and hence the equivalent radius

of gyration is not critical for their design.

124

5.4 LIMITATING WIDTH TO THICKNESS RATIO

5.4.1 IS -802: (Part 1 /Sec 2):1992

For effective width calculations, the distance between the edges of

fillet to free end is considered in the Indian standards. The limiting width to

thickness ratio is given by

ylim

F)210(t

b=

(5.6)

where, yF is minimum guaranteed yield stress of the material in MPa. The

maximum permissible width to thickness ratio (b/t) for any type of steel shall

not exceed 25.

5.4.2 ASCE 10-97:2000

For effective width calculations, the distance between the edges of

fillet to free end is considered in the American Standards. The limiting width

to thickness ratio is given by

ylim

F)80(t

bΨ=

(5.7)

where, Ψ = 2.62 for yF in MPa.

For sections supported on only one longitudinal edge the flat width

to thickness ratio shall not exceed 25.

125

5.4.3 British Standard (BS 8100-3:1999)

The effective width of angle is considered as the distance between

toe to toe of angles in British Standard. The limiting effective width to

thickness ratio is given by

σ=

ylim

E567.0

t

b (5.8)

where yσ is specified minimum yield stress of the material in MPa.

5.5 DESIGN OF COMPRESSION MEMBERS

Compression members are broadly classified as concentrically

loaded members subjected to flexural buckling and columns subjected to

torsional or torsional-flexural buckling. The allowable stress equations

recommended by various standards are discussed in the following sections:

5.5.1 ASCE 10-97:2000

Members with singly symmetric open cross-section shall be

checked for flexural buckling in the plane of symmetry and for torsional-

flexural buckling. The design torsional-flexural buckling stress is calculated

with the radius of gyration ry replaced by rtf computed on the gross cross

section.

The design compressive stress Fa on the gross cross-sectional area

of axially loaded compression member shall be:

y

2

ca F

C

rKL

2

11F

−= cC

r

KL≤ (5.9)

126

2

2

a

r

KL

EF

π= cC

r

KL> (5.10)

y

cF

E2C π= (5.11)

where Fy - Minimum guaranteed yield stress;

E - Modulus of Elasticity;

L - Unbraced length;

r - Radius of gyration; and

K - Effective length coefficient.

If the width to thickness ratio (w/t) exceeds (w/t)lim given by

Ψ=

ylim F

80

t

w

( ) y

limcr F

tw

tw677.0677.1F

−= (5.12)

ylim F

144

t

w

t

w Ψ≤

≤

( )2

2

crtw

E0332.0F

π=

yF

144

t

w Ψ> (5.13)

where Ψ = 2.62 for Fy in MPa

The ratio (w/t) of flat width to thickness shall not exceed 25 for

elements supported on only one longitudinal edge.

127

The common design practice is to design the redundant members

for 1 to 2.5% of the load in the supported member.

5.5.2 IS: 802 (Part 1 /Sec 2):1992

The allowable unit stress aF , in MPa on the gross cross sectional

area of the axially loaded compression members shall be:

2

a y

C

1 KL rF 1 F

2 C

= −

(5.14)

when C

KL r C≤

and ( )

2

a 2

EF

KL r

π= (5.15)

when CKL r C>

where C yC 2E F= π (5.16)

Fy = minimum guaranteed yield stress of the material, MPa.

E = modulus of elasticity of steel (2×105 MPa)

rKL = largest effective slenderness ratio of any unbraced

segment of the member,

L = unbraced length of the compression member in cm, and

r = appropriate radius of gyration in cm.

128

The formulae given above is applicable provided the largest width

thickness ratio b/t is not more than the limiting value given by

( ) ymin F/210tb = (5.17)

where b = distance from edge of fillet to the extreme fibre in mm,

and t = thickness of flange in mm.

where the width to thickness ratio exceeds the limits.

Then formulae given below shall be used substituting for Fy

the value crF given by

( )

( )cr y

lim

0.677 b tF 1.677 F

b t

= −

(5.18)

when lim y(b t) 378 F≤

and ( )tb

65550Fcr = when yF378tb ≥ (5.19)

The redundant members shall be checked individually for

2.5 percent of axial load carried by the member to which it is providing

support. For the design of the compression member six curves are given based

on the type of end fixity and eccentricity similar to the American Standard.

5.5.3 BS 8100-3 :1999

The design buckling resistance, N, of a compression member

should be taken as:

r mN jxA /= σ γ (5.20)

129

where j - 0.8 for single angle members connected by one bolt at each

end, 0.9 for single angle members connected by one bolt at

one end and continuous at the other end and 1.0 in all other

cases;

A - the cross-sectional area of the member;

χ - the reduction factor for the relevant buckling mode, given

in reduction factor.

rσ - reference stress given in calculation of reference stress.

mγ - the partial factor on strength, as given in BS 8100-1 and -4,

appropriate to the quality class of the structure, subject to

the following:

• For untested structures

mγ is 1.1 for Class A structures;

mγ is 1.2 for Class B structures;

mγ varies from about 1.3 to 1.45 for Class C structures

depending on the performance requirements.

• For angle section towers which have successfully been

subjected to full scale tests under the equivalent factored

loading or where similar configurations have been type tested:

mγ is 1.0 for Class A structures;

mγ is 1.1 for Class B structures;

mγ varies from about 1.2 to 1.35 for Class C structures

depending on the performance requirements.

130

For hot rolled steel members with the types of cross-section

commonly used for compression members, the relevant buckling mode is

general “flexural” buckling. In some cases the “torsional” or “flexural-

torsional” modes may govern.

Reduction factor χ

For constant axial compression in members of constant cross-

section, the value of χ for the appropriate effective slenderness effA should

be determined from:

0.5

2 2

eff

1x

A=

φ + φ −

(5.21)

where ϕ = ( )[ ] 5.02effeff A2.0A15.0 +−α+

α is an imperfection factor;

Λeff = KΛ (5.22)

Λ= λ/λ1 (5.23)

λ1 = slenderness ratio

[ ] 5.0/2758.85 rσλ = (5.24)

rσ = reference stress

and where χ ≤ 1.

The imperfection factor corresponding to the appropriate

buckling curve is given. Values of the reduction factor χ for the appropriate

effective slenderness Λeff are also given.

131

The reference stress ‘ rσ ’ required to derive the ultimate stress of a

member depends on the slenderness of the section. Most hot rolled sections

are at least semi-compact. Values of µ and the limiting t/B and t/D ratios

are given below, together with formulae for the reference stress rσ which is

used in place of the yield stress yσ for the design of slender sections.

For hot rolled angle sections

yr σ=σ if µ≤tB / (5.25)

)/2( tByr µσσ −= if

µµ 33.1/ << tB

(5.26)

22 )/1.5/( tBEr

πσ = if µ≥tB /

(5.27)

where yσ is the specified minimum yield stress of material,

‘B’ is the leg length of the angle. For unequal angles and compound

angles, ‘B’ is the longer length, except for single angles connected

by bolts or welding through one leg only at both ends of the

element under consideration for which ‘B’ should be taken as the

length of the connected leg;

‘t’ is the thickness of angle leg;

y0.567 E µ = σ (5.28)

‘E’ is the modulus of elasticity.

Effective slenderness factor ‘K’ for leg members is specified as 0.9

in the British Standard. For bracing members the effective slenderness factor

‘K’ varies based on end condition whether continuous or discontinuous and

the same for single bolted and double bolted connections.

132

5.5.3.1 Compound Members

For compound members built up with two angles as cruciform

section and intermittently connected and used as leg members, the possible

additional deformations due to shear should be taken into account by

modifying the slenderness ratio, ‘λ ’ in accordance with the following:

2 2 2

0 1λ = λ + λ (5.29)

where 0λ - is the slenderness ratio of the full member;

1λ - is the slenderness ratio of one component angle ( )vvrC

It is good practice to have 10 λ≥λ and 501 ≤λ

Compound members consisting of a pair of identical angles back

to back as ‘T’ section separated by a small distance and connected at intervals

by spacers and stitch bolts, may be used for bracing. They should be checked

for buckling about both rectangular axes.

• For buckling about the xx axis the two angles should be

assumed to act compositely for the purpose of calculating

stiffness and radius of gyration.

• For buckling about the yy axis the additional deformation due

to shear should be taken into account by modifying the

slenderness ratio, λ in accordance with the following:

21

20

2 λ+λ=λ taking a maximum value of 01 75.0 λ=λ

where 0λ is the slenderness ratio of the full compound member;

1λ is the slenderness ratio of one component angle ( )vvrC

C is the length of individual angle between stitch bolts

133

In order to keep the effect of this interaction to a minimum, the

spacing between stitch bolts should be limited to give a maximum value 1λ of

90. When only stitch bolts and packs are used, composite section properties

should be based on either;

• The actual space between the individual angle members, or

• A space taken as 1.5 times the thickness of one of the angle

members, whichever is smaller. If batten plates are used,

composite section properties may always be used based on the

actual space between the individual angle members.

5.6 REVIEW ON THE CODAL PROVISIONS

Design provisions given in Indian, American and British standards,

on width to thickness ratio, effective slenderness ratio and permissible

compressive stresses are compared. The Indian Standard IS:802 - Use of

Structural Steel in overhead Transmission line towers – Part 1 gives six

buckling curves for computing the buckling stress of hot rolled angles similar

to ASCE 10-97 standard based on slenderness ratio and end conditions. The

permissible stress curves are based on Euler formula in the elastic range and

Structural Stability Research Council (SSRC) formula in the inelastic range

for concentrically loaded columns. Test experience on tower members is

limited in the slenderness range of 0 to 50, but indications are that the SSRC

formula applies equally well in this range if concentric framing details are

used. The ASCE standard is suitable for steels with yield points up to 448MPa

and for width to thickness values of 25. The recommendations are intended

for both hot-rolled and cold formed members. The influence of end fixity is

assumed to have negligible effect. Using the curves, the strength of angle strut

is checked for buckling. Local buckling is accounted for by considering the

width to thickness ratio of angle sections and appropriately reducing the yield

134

stress if the ratio exceeds the prescribed limit. The strengths given in BS

8100-3:1999 are based on 95% probability values. The design strengths are

obtained by dividing the characteristic strengths by the appropriate partial

factor. The recommendations given in BS standard is valid for tubular or solid

round sections, angle sections either hot rolled or cold formed.

• The Indian and American Standards suggest six different

formulae for the design of the compression member based on

the type of loading and end restraint.

• The Indian and American Standards consider the width after

deducting the thickness and root radius of the fillet in the

angle section in effective width to thickness ratio calculations.

• The Indian Standard specifically mentions that the redundant

member shall be designed for 2.5% of the axial force in the

main member. This is a useful assumption. Tower failures

have indicated that the leg members and main bracing

members have failed due to insufficient strength of redundant

members.

• The British Standard considers an effective length factor of

0.9 for the leg members. The effective length factor for

bracing members varies depending upon the continuous or

discontinuous ends and is the same for both single bolted and

double bolted members.

• The British Standard considers the effect of shear deformation

in the compound members made from two angles in the form

of ‘T’ and star sections by modifying the slenderness ratio.

• The British Standard specifies a separate procedure for

calculating the forces in the secondary members.

135

5.7 COMPARISON OF LEG AND BRACING MEMBER

CAPACITIES

The results predicted from the experimental and analytical studies

conducted on transmission line towers are compared with the codal

predictions and given in Tables 5.1 and 5.2. The 400 kV (0-20) tangent double

circuit tower and 275 kV ‘H’ type large angle deviation tower that have failed

below 75% of their respective design loads are compared separately in

Table 5.3.

Figures 5.5 and 5.6 show the comparison of failure loads for leg

and bracing members calculated based on different standards, Finite Element

analysis and also based on experiments. It shows that the member capacity

predicted by American standard is always higher than the experimental values

for all the slenderness ratios of the members. Nonlinear FE analysis results

are 10 to 12% more than the test results.

In Figures 5.7 and 5.8 there is a wide discrepancy between code

prediction and experimental values since the premature failures in some of the

towers studied are mainly due to non triangulated hip bracing pattern and

inadequate member sizes and non compliance of codes and over estimation of

member forces.

13

6

Table 5.1 Bracing members

Tower

type

Member details Failure load in

percentage

Non Linear analysis

force in kN Member capacity

Remarks

Size L/r Fy Test

FE

Nonlinear

analysis

At test

failure

Load

At FE

failure

Load

ASCE 10-97/

IS:802

in kN

BS

in kN

(1) 220kV

D/C ‘DE' 90O

Dev

ISA

90×90×8 89 290

100 103

186 189 240 193 X- brace

top Half

ISA

90×90×8 96 290 191 196 228 183

Bottom

half

(2) 400kV D/C

‘DB'

ISA

100×100×8 133 255 95 102 148 160 185 146

K- brace

In second panel

(3)

400kV

D/C ‘DD'

ISA

130×130×10 79 350 93 106 399 450 493 426

K- brace

below

middle

Cross arm

(4)

400kV

S/C

ISA

130×130×10 89 350

99 106

404 429 454 397 X- brace

Top half

ISA

120×120×10 60 350 425 449 521 447

X- brace

Bot half

13

7

Table 5.1 (Continued)

Tower

type

Member details Failure load in

percentage

Non Linear analysis

force in kN Member capacity

Remarks

Size L/r Fy Test

FE

Nonlinear

analysis

At test

failure

Load

At FE

failure

Load

ASCE 10-97/

IS:802

in kN

BS

in kN

(5)

400kV

D/C ‘DC'

┘└

80×80×6 105 350 100 106 267 284 291 253

K brace in

second

panel

(8)

400kV

D/C ‘DE'

ISA

110×110×8 100 350 90 104 205 237 276 247

Brace in

portal

(10)

400kV D/C

(0-2o)

with ‘V’

insulator strings

ISA

70×70×5 200 255

100 105

36 37 45 39 Bracing in

2nd panel

ISA

75×75×6 163 255 65 69 79 66

Bracing in 4th panel

ISA

80×80×6 114 255 91 94 126 96

Bracing in

5th panel

(13)

220kV M/C

ISA

100×100×8 193 255

100 107

98 103 112 95 X brace in

3rd panel

ISA

100×100×8 177 255 117 124 126 107

X brace in

4th panel

13

8

Table 5.2 Leg members

Tower

type

Member details Failure load in

percentage

Non Linear analysis

force in kN Member capacity

Remarks

Size L/r Fy Test

FE

Nonlinear

analysis

At test

failure

Load

At FE

failure

Load

ASCE 10-

97/ IS:802

in kN

BS

in kN

(4)

400kV

S/C

ISA

200×200×20 45 350 99 106 1953 2056 2428 2497 Leg

(5)

400kV

D/C ‘DC'

ISA

200×200×20 50 350 100 106 1962 2091 2378 2465

Leg in second

panel from

ground

(6) 220kV

D/C ‘D9DT'

Cruciform with

two ISA

200×200×18

23 350 90 105 3466 4027 4659 4401

Leg in second

panel from ground

(7) 800kV

S/C

ISA

150×150×20 63 255 100 109 1138 1221 1249 1305

Girder Top

chord member

(10)

400kV D/C

(0-2o) with

‘V’ insulator

strings

ISA

130×130×10 50 450

100 105

872 927 896 950 Leg in third

Panel

ISA

130×130×10 60 450 798 848 826 904

Leg in fourth

panel

13

9

Table 5.2 (Continued)

Tower

type

Member details Failure load in

percentage

Non Linear analysis

force in kN Member capacity

Remarks

Size L/r Fy Test

FE

Nonlinear

analysis

At test

failure

Load

At FE

failure

Load

ASCE 10-

97/ IS:802

in kN

BS

in kN

(12)

275kV D/C

Medium dev.

ISA

150×150×18 52 410

100 101

1464 1481 1795 1883 Leg in first

panel

ISA

150×150×18 52 410 1399 1410 1795 1883

Leg in second

panel

ISA

150×150×18 62 410 1334 1361 1663 1786

Leg in third

panel

(13)

220kV M/C

(0-15O)

Cruciform with

two ISA

150×150×12

26 255 100 107 1502 1592 1726 1628

Leg in fourth

panel from ground

14

0

Table 5.3 LEG and bracing members (Failed due to instability)

Tower

type

Member details Failure load in

percentage

Non Linear analysis

force in kN Member capacity

Remarks

Size L/r Fy Test

FE

Nonlinear

analysis

At test

failure

Load

At FE

failure

Load

ASCE 10-

97/ IS:802

in kN

BS

in kN

(9)

400kV D/C (0-2o)

ISA

150×150×12 61 255

75 97

520 669 774 807 Leg in first

panel

ISA

150×150×12 58 255 505 648 785 813

Leg in second

panel

ISA

80×80×6 182 255 35 44 65 62

Bracing in

first panel

(11)

275kV D/C

‘H’ type

Large

deviation

ISA

150×150×18 36 410

62.3 94.4

1011 1504 1943 1980 Leg in first

panel

ISA

150×150×18 43 410 970 1450 1882 1939

Leg in second

panel

ISA

120×120×8 150 275 62 94 192 170

Bracing in first

panel

ISA

90×90×6 128 275 50 77 133 108

Bracing in

second panel

141

LEG MEMBERS

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

3300

3600

3900

4200

4500

4800

5100

CA

PA

CIT

Y (

kN

)FEM

TEST

ASCE and IS

BS

T TOWER NUMBER

T4 T13T12T12T12T10T10T7T6T5

Figure 5.5 Comparison of capacity of leg members

BRACING MEMBERS

0

50

100

150

200

250

300

350

400

450

500

550

CA

PA

CIT

Y (

kN

)

FEM

TEST

ASCE and IS

BS

T TOWER NUMBER

T1 T10T8T5T4T4T3T2 T10 T10 T13T13

Figure 5.6 Comparison of capacity of bracing members

142

LEG MEMBERS

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

CA

PA

CIT

Y (

kN

)

FEM

TEST

ASCE and IS

BS

T TOWER NUMBER

T9 T11T11T9

Figure 5.7 Comparison of capacity of leg members

BRACING MEMBERS

0

20

40

60

80

100

120

140

160

180

200

220

CA

PA

CIT

Y (

kN

)

FEM

TEST

ASCE and IS

BS

T 9

T TOWER NUMBER

T 11 T 11

Figure 5.8 Comparison of capacity of bracing members