Analysis and Design of Tubular and Angular Steel Trusses By ...

Journal of Engineering, Computers & Applied Sciences (JEC&AS) ISSN No: 2319-5606 Volume 2, No.8, August 2013 _________________________________________________________________________________

www.borjournals.com Blue Ocean Research Journals 30

Analysis and Design of Tubular and Angular Steel Trusses

By Post-Tensioning Method Jyoti .P. Sawant, P.G. Student, Civil Engineering Department, Government Engineering College, Haveri,

Karnataka, India

Prof. Vinayak Vijapur, Prof. Civil Engineering Department, Government Engineering College, Haveri, Karnataka,

India

ABSTRACT Now a day there is pronounced application of Post-tensioning to steel trusses. The bridges which were earlier

designed for lighter loads has to bear the increased load due to rapid urbanization and increased population and

thus to replace the earlier bridge is uneconomical and also disrupts the transportation. So, these bridges are

strengthened by the application of post-tensioning. Now post tensioning is most widely accepted all over since

trusses consume a lot of less material compared to beams to span the same length and transfer moderate to heavy

loads.

In countries like India where labour cost is less post-tensioning can be utilized to the fullest extent. In the current

study post tensioning has been applied to both angular and tubular trusses for 30m span Mansard and Pratt trusses

with single and double drape tendons using SAP2000v15 software it has been found that with the application of Post

tensioning with single and double drape tendons at the eccentricity of 0.9 m and 1.2 m the pre-stressing force in the

members have been reduced. External Post-tensioning is considered in the present study since the tendons are

outside the trusses. Here the trusses are examined for member forces, pre-stressing forces at zero deflection at the

mid span of the truss, the reduction in the cross sections and weight of the members of trusses

Key words: Post-tensioning method, steel structures, post-tensioned trusses, truss strengthening, design parameters,

load carrying capacity.

Introduction

Post-tensioning is one of the best methods of

rehabilitation of structures. The application of

Post-tensioning using tendons is a simple and

economical method of increasing the load carrying

capacity of the truss. In this application, some of

the tension is removed from the bottom chord of

older timber and steel bridges.

If additional rehabilitation is required, load-

carrying capacity cannot be obtained by arranging

tendons in a straight line, and therefore the

efficiency of the Pre-stressing force may have to be

increased using draped tendons.

The cross section of a concrete member is

usually susceptible to a tensile stress. The cross

section of a steel member, however, does not require

specific consideration of stress distribution. In

addition, the tendon in a steel structure does not

cause a large friction loss.

Objectives a) To calculate the reduction in forces of the truss

members due to the external Post-tensioning.

b) To find the reduction in weight of the truss after

Post-tensioning.

c) To compare the cross-section members of the

trusses without Post-tensioning and with Post-

tensioning.

Present Investigation A roof truss is basically a framed structure formed by

connecting various members at their ends to form a

system of triangles, arranged in pre-decided pattern

depending upon the span, type of loading and

functional requirements. In industrial buildings, steel

trusses are commonly used.

Truss Configuration Considered

A-Type Configuration truss of 30 meter span trusses

are considered for the research work. The height of

the truss is 3 meters. The dead load, live load and

wind load applied at each joint at the top chord of the

truss.



The trusses are as follows:

1. Angular and tubular Mansard truss

2. Angular and tubular Pratt truss

Post Tensioned Tendon Layouts Considered

External post tensioned tendon layouts are considered

in the present study. In this layout, the tendons are

placed outside the truss system. Single drape and

double draped tendon profiles are considered in case

of external tendon layouts as shown in below Fig.

The tendon is placed between the two end joints of

the truss. The tendon connected between two end

joints and passes over one or two more new

additional joints depending on either one draped or

two draped. These new joints are constructed below

the bottom chord of the truss by using additional

members, which need to be attached to the existing

truss joints at the bottom.

Tendon Profiles:

a) Single drape tendon.

b) Double drape tendon.

Fig. 1 Types of Post Tensioning Tendon Layout

Analysis Of Post Tensioned Steel Trusses The following are the steps involved in the Analysis

of the Steel truss.

a) Selection of Truss Configuration.

b) Analysis of post-tensioned steel truss using

Sap2000v15 software.

c) Modeling of the Truss for Different Tendon

profile and Eccentricity.

d) Selection of Member Cross sections.

e) Applications of Loads.

f) Analysis for the Load Combinations.

g) Comparison of Member forces and weight of

members

Type of

truss

Span in

meter

Height

in meter

Wind

Pressure

in kG/sq.

Spacing

of

trusses

in

meters

Mansard 30 3 150 6

Pratt 30 3 150 6

Table 1. Configuration of 2 types of steel roof

truss

Application of Loads The trusses have to be analyzed for dead load, live

load and wind load according to IS: 875-1987. The

basic wind pressure has been considered as specified

in IS: 875-1987. The forces in the truss members due

to the combination of dead load and live load are

compared with that due to dead load and wind load in

order to determine the governing design forces. The

member design forces for all the trusses and their

support reactions referred as per SP38-1987

handbook.

Analysis of Steel Trusses The steel trusses have been analyzed as simply

supported at ends. It is assumed that the members are

prevented from out of plane buckling the support at

both end is assumed to be hinged for the purpose of

analysis. The analysis has been made using

Sap2000v15 Software. After the analysis on

Sap2000v15, member forces are computed for DL +

LL, DL + LL+ PSF, DL + WL+ PSF load

combinations. The member properties required for

the analysis have been referred from SP38-1987

handbook, and half portion of the trusses results is

taken



Results and Discussion

Table 2 Comparison between member forces of angular Mansard and Pratt trusses with and without single drape and

double drape tendon

Fig. 2 Variation of top rafter member forces of Mansard and Pratt trusses with and without Single drape and Double drape

tendons



Table 3 Percentage of reduction in member forces of Angular Mansard and Pratt trusses with single drape and

double drape tendons as compared to normal trusses

Percentage of reduction in member forces of Angular Mansard and Pratt trusses with single drape and double

drape tendons as compared to normal trusses

Group Truss type Single Drape Double Drape

0.9 m 1.2 m 0.9 m 1.2 m

C T C T C T C T

Top Rafter Mansard 34.76 30.67 35.19 34.63

Pratt 30.68 32.65 31 31.03

Web member Mansard 6.75 16.81 11.91 5.92 32.16 50.1 30.95 46.86

Pratt 0.3 54.36 2.23 51.13 34.05 51.25 32.98 46.33

Bottom Chord Mansard 10.12 2.45 9.48 23.57 38.68 20.08 33.27 13.18

Pratt 6.75 2.32 1.08 10.1 28.66 9.56 29.49 6.78

Fig. 3 Variation of web member forces of Mansard and Pratt trusses with and without Single drape and Double

Drape tendons



Fig. 4 Variation of bottom member forces 0f Mansard and Pratt trusses with and without Single drape and Double

drape tendons

Table 4 Comparison between member forces of tubular Mansard and Pratt trusses with and without single drape and

double drape tendons

Comparison between Member Forces of Tubular Mansard and Pratt trusses with and without Single drape and

Double drape tendon

Group

Truss type

Normal Single Drape Double Drape

0.9m 1.2m 0.9m 1.2m

C T C T C T C T C T

kN kN kN kN kN kN kN kN kN kN

Top Rafter

Mansard 653.20 420.64 -543.06 475.47 481.05

Pratt 684.55 512.74 512.57 523.44 525.25

Web

member

Mansard 74.69 74.51 84.25 77.49 -70.838 66.447 58.94 51.41 54.68 47.03

Pratt 72.64 76.54 70.51 61.52 72.12 62.71 53.58 66.53 53.63 42.78

Bottom

chord

Mansard 178.88 79.59 156.93 74.50 -172.45 27.691 129.53 39.85 109.48 44.22

Pratt 132.12 93.34 145.98 75.42 155.91 63.95 122.23 60.86 136.81 50.55



Table 5 Percentage of reduction in Member Forces of Tubular Mansard and Pratt trusses with Single drape and

Double drape tendons as compared to normal trusses

Percentage of reduction in Member Forces of Tubular Mansard and Pratt trusses with Single drape and

Double drape tendons as compared to normal trusses

Group

Truss type

Single Drape Double Drape

0.9 m 1.2 m 0.9 m 1.2 m

C T C T C T C T

Top Rafter

Mansard 35.60 16.86 27.21 26.35

Pratt 25.10 25.12 23.53 23.27

Web member

Mansard 12.81 4.00 5.15 10.82 21.08 31.01 26.79 36.88

Pratt 2.93 19.63 0.72 18.07 26.24 13.09 26.17 44.11

Bottom

Chord

Mansard 12.27 6.40 3.60 65.21 27.59 49.94 38.80 44.45

Pratt 10.49 19.20 18.01 31.49 7.48 34.80 3.55 45.85

Fig. 5 Variation of top rafter member forces of tubular Mansard and Pratt trusses with and without Single drape and

Double drape tendons



Table 6 Comparison between weight of angular Mansard and Pratt trusses with and without single drape and double

drape tendons

Comparison between weight of angular Mansard and Pratt trusses with and without

single drape and double drape tendons


0.9m 1.2m 0.9m 1.2m

N N N N N

Mansard 46849.79 39767.37 24388.52 29423.75 26512.37

Pratt 29795.61 28408.38 23314.72 28893.71 29065.81

Fig. 6 Variation of web member forces of tubular Mansard and Pratt trusses with and without Single drape and




Table 7 Percentage weights of angular Mansard and Pratt trusses with and without single drape and double drape

tendons

Percentage weight of angular Mansard and Pratt trusses with

and without single drape and double drape tendons

Truss type Single Drape Double Drape

0.9 m 1.2 m 0.9 m 1.2 m

Mansard 15.12 47.94 37.2 43.41

Pratt 4.66 21.75 3.03 2.45

Fig 7 Variation of bottom member forces of tubular Mansard and Pratt trusses with and without single drape

and double drape tendons



Table 8 Comparison between weight of tubular Mansard and Pratt trusses with and without Single drape and Double

drape tendons

Comparison between weight of tubular Mansard and Pratt trusses with

and without Single drape and Double drape tendons

Truss type


0.9 m 1.2 m 0.9 m 1.2 m

kN kN kN kN kN

Mansard 12703.14 11287.01 9288.84 9124.1 8060.29

Pratt 13976.86 10870.83 10165.73 9732.62 9963.34

Fig. 8 Variation in weight of Mansard and Pratt trusses with and without single drape and double drape tendons



Table 9 Percentage weights of tubular Mansard and Pratt trusses with and without Single drape and double drape tendons

Percentage weight of tubular Mansard and Pratt trusses with

and without Single drape and double drape tendons

Truss type Single Drape Double Drape

0.9 m 1.2 m 0.9 m 1.2 m

Mansard 11.15 26.88 28.17 36.55

Pratt 22.22 27.27 30.37 28.72

Fig. 9 Variation in weight of tubular Mansard and Pratt trusses with and without Single drape and double drape

tendons



Table 10 Comparison between Pre-stressing force of Angular Mansard and Pratt trusses with Single drape and


Comparison between Pre-stressing force of Mansard and Pratt trusses with Single

drape and Double drape tendons

Truss type


0.9m 1.2m 0.9m 1.2m

kN kN kN kN

Mansard 905.00 620.00 515.00 390.00

Pratt 760.00 575.00 505.00 380.00

Fig. 10 Variation of pre-stressing forces of Mansard and Pratt trusses with and without Single drape and Double

drape tendons



Table 11 Comparison between Pre-stressing force of Tubular Mansard, Howe and Pratt trusses

Comparison between Pre-stressing force of tubular Mansard and Pratt trusses with

Single drape and Double drape tendons

Truss type


0.9 m 1.2 m 0.9 m 1.2 m

kN kN kN kN

Mansard 725.00 200.00 150.00 120.00

Pratt 515.00 390.00 315.00 240.00

Fig. 11 Variation of pre-stressing forces of tubular Mansard and Pratt trusses with and without Single drape and

Double drape tendon

The forces for angular and tubular Mansard and Pratt

trusses configuration with 30m span and different

eccentricity, post tensioned with external tendon

layouts are tabulated in Table 2 and Table 4. As all

the trusses considered are symmetrical, results of

only left half portion of the trusses are taken.

In Mansard and Pratt trusses bottom chords are in

tension and few are in compression all the top chords

are in compression, whereas in web members some

members are in tension and some members are in

compression as shown in Table

2 and Table 4

Post Tensioned Trusses Results of angular and tubular Mansard and Pratt

trusses after external Post Tensioning by single drape

& double drape tendon layout are explained

below.

Single Drape tendon layout Angular

The reduction of forces for top members as observed

from the table 3 is 34.76% and 30.67% in Mansard

trusses, 30.68% and 32.65% in case of Pratt trusses in

single drape.



From the above table it is observe that, in web

members percentage of reduction in forces is

5.92% to 16.1% in Mansard trusses and 51.13% to

54.36% in Pratt truss in tension and there is no

reduction of forces in compression in mansard and

Pratt truss in case of single drape tendon. From the

above table it is observe that in bottom chord

percentage of reduction in forces is 2.45%

Double Drape tendon layout Angular

As in case of double drape tendon in bottom chord

percentage of reduction in forces is 33.27% to

38.68% in compression 13.18% to 20.08% in

tension in case of mansard trusses, and 28% to 29%

in compression and 6.78% to to 23.57% in tension

and there is no reduction in compression in case of

Mansard truss. Further there is no reduction of forces

in case of Pratt trusses in single drape tendon

Tubular

Table 5 shows the percentage of reduction in member

forces in between Mansard and Pratt trusses. From

the above table it is observe that in bottom chord

percentage of reduction in forces is 3% to 12%

in compression 6% to 65.21% in tension in case

mansard trusses and 19% to 31% in tension only in

case of Pratt trusses in single drape tendon .

The reduction of forces in top members as observed

from the table 5 is 35.60% and 16.86% in Mansard

trusses, 25.10% and 25.12% in case of Pratt trusses in

single drape.

From the above table it is observe that, in web

members percentage of reduction in forces is

18.07% to 19.63% in tension, 0.72% to 2.93% in

compression in case of Pratt trusses and in Mansard

trusses there is no reduction in forces in case of

single drape tendon 9.56% in tension in case of Pratt

trusses. In web members percentage of reduction

in forces is30.95% to 32.16% in compression,

46.86% to 50.10% in tension in case of mansard

trusses, 32.98% to 34.05% in compression and

46.33% to 51.25% in tension. In top members

percentage of reduction in forces is 35.19% and

34.63% in Mansard trusses, 31% and 31.03% in

case of Pratt trusses.

Tubular

As in case of double drape tendon in bottom chord

percentage of reduction in forces is 27% to 38% in

compression 44% to 50% in tension in case mansard

trusses and 34% to 45% in tension only in case of

Pratt trusses. In top members percentage of

reduction in forces is 27.21% and 26.35% in

Mansard trusses and 23.53% and 23.27% in case of

Pratt trusses. In web members percentage of

reduction in forces is 21% to 26% in compression,

31% to 36% in tension in case of mansard trusses,

13% to 44% in tension and 26.17% to 26.24% in

compression in case of Pratt trusses.

Weight of the Truss Angular

From the table 6 In case of Mansard truss the overall

weight of the truss is 46849N before Post-

tensioning, whereas after Post-tensioning by single

drape tendons the weight of the truss reduced to

39767.37N and 24388.52N. On other hand Post-

tensioning by double drape tendon the weight is

reduced to 29423.75Nand 26512.37N. From table 7

percentage of reduction in weight is 15.12% and

47.94% after Post- tensioning by single drape

tendons and 37.29% and 43.41% after Post-

tensioning by double drape tendons.

In case of Pratt truss percentage of reduction in

weight is 4.66% and 21.75% after Post- tensioning by

single drape tendons and 3.03% and 2.45% after

Post-tensioning by double drape tendons.

From the table 6 it is observe that Pratt trusses have

lesser weight as compare to Mansard trusses.

Tubular

From the table 8 in case of Mansard truss the overall

weight of the truss is 12703N before Post-

tensioning, whereas after Post-tensioning by single

drape tendons the weight of the truss reduced to

11287N and 9288N. On other hand Post-tensioning

by double drape tendon the weight is reduced to

9124N and 8060N.

From table 9 percentage of reduction in weight is

11.15% and 26.88% after Post-tensioning by single

drape tendons and 28.17% and 36.55% after Post-

tensioning by double drape tendons.

In case of Pratt truss percentage of reduction in

weight is 22.22% to 27.27% after Post- tensioning by

single drape tendons and 28.72% to 30.37% after

Post-tensioning by double drape tendons.

From the table 8 it is observed that Pratt trusses have

lesser weight as compared to Mansard trusses.



Pre-stressing force

Angular

The Post-tensioning force is applied to bottom chords

it is effect on top chords, bottom chords and web

members, from table 10 it is observed that as the

eccentricity of the cable increases the pre-stressing

force which is applied to truss decreases. From the

table 10 is observed that Pratt trusses are having

lesser pre-stressing force when compared to Mansard

trusses

Tubular

From the table 5.11 it is observed that Pratt trusses

are having lesser pre-stressing force when compared

to the Mansard truss.

6. CONCLUSION

Post tensioning by external tendon layout are

suggested to strengthen and to increase useful life of

steel truss. The trusses configuration with different

tendon profile for post tensioning the truss with

different eccentricities are considered and the effect

of post tensioning on member forces, cross section of

members and weight of truss is studied in this

analytical work.

a) In case of truss post tensioned with single drape

tendon layout.

b) There is significant reduction in member forces

and cross section members of all the bottom

chord as well as top chord and web members.

c) In case of truss post tensioned with Double drape

tendon layout.

d) There is significant reduction in member forces

and cross section members of all the bottom

chord as well as top chord members and web

members. The reduction in cross sections and

member forces is more significant in case of

double drape tendon layout as compared to

single drape tendon layout.

e) In case of Pratt trusses the reduction in cross

sections, member forces, pre-stressing forces and

weights of the trusses is more significant as

compare to Mansard trusses.

f) As the eccentricity increases the amount of pre-

stressing force which is applied to post

tensioning of the truss is decreases.

g) From economical point of view tubular trusses

costs less when compared to the angular trusses.

h) Tubular trusses consume a lot of less material

when compared to the angular trusses.

i) Tubular trusses has good aesthetic view when

compared to the angular trusses

j) Angular trusses are labour intensive when

compared to the tubular trusses.

k) Tubular trusses have lesser pre-stressing force

when compared to the tubular

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Analysis and Design of Tubular and Angular Steel Trusses By ...

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