Analysis and Design of Tubular and Angular Steel Trusses By Post-Tensioning Method

Transcription

1 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, loadcarrying 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 Posttensioning. 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. Blue Ocean Research Journals 30

2 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 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. Mansard Pratt Table 1. Configuration of 2 types of steel roof truss Spacing of trusses in meters Application of Loads The trusses have to be analyzed for dead load, live load and wind load according to IS: The basic wind pressure has been considered as specified in IS: 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 SP 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 SP handbook, and half portion of the trusses results is taken 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. Blue Ocean Research Journals 31

3 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 Blue Ocean Research Journals 32

4 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 Pratt Web member Mansard Pratt Bottom Chord Mansard Pratt Fig. 3 Variation of web member forces of Mansard and Pratt trusses with and without Single drape and Double Drape tendons Blue Ocean Research Journals 33

5 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 Top Rafter Normal Single Drape Double Drape Truss type 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 Mansard Pratt Web member Mansard Pratt Bottom chord Mansard Pratt Blue Ocean Research Journals 34

6 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 Pratt Web member Mansard Pratt Bottom Chord Mansard Pratt Fig. 5 Variation of top rafter member forces of tubular Mansard and Pratt trusses with and without Single drape and Double drape tendons Blue Ocean Research Journals 35

7 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 Normal Single Drape Double Drape 0.9m 1.2m 0.9m 1.2m N N N N N Mansard Pratt Fig. 6 Variation of web member forces of tubular Mansard and Pratt trusses with and without Single drape and Double drape tendons Blue Ocean Research Journals 36

8 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 Pratt Fig 7 Variation of bottom member forces of tubular Mansard and Pratt trusses with and without single drape and double drape tendons Blue Ocean Research Journals 37

9 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 Normal Single Drape Double Drape 0.9 m 1.2 m 0.9 m 1.2 m kn kn kn kn kn Mansard Pratt Fig. 8 Variation in weight of Mansard and Pratt trusses with and without single drape and double drape tendons Blue Ocean Research Journals 38

10 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 Pratt Fig. 9 Variation in weight of tubular Mansard and Pratt trusses with and without Single drape and double drape tendons Blue Ocean Research Journals 39

11 Table 10 Comparison between Pre-stressing force of Angular Mansard and Pratt trusses with Single drape and Double drape tendons Comparison between Pre-stressing force of Mansard and Pratt trusses with Single drape and Double drape tendons Single Drape Double Drape Truss type 0.9m 1.2m 0.9m 1.2m kn kn kn kn Mansard Pratt Fig. 10 Variation of pre-stressing forces of Mansard and Pratt trusses with and without Single drape and Double drape tendons Blue Ocean Research Journals 40

12 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 Single Drape Double Drape Truss type 0.9 m 1.2 m 0.9 m 1.2 m kn kn kn kn Mansard Pratt 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. Blue Ocean Research Journals 41

13 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 Posttensioning, whereas after Post-tensioning by single drape tendons the weight of the truss reduced to N and N. On other hand Posttensioning by double drape tendon the weight is reduced to Nand N. 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 Posttensioning 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 Posttensioning, 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 Posttensioning 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. Blue Ocean Research Journals 42

14 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 prestressing 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 References [1] 2007 Nova Award Nomination 22-entitled Posttensioned Steel Trusses for Long Span Roofs [2] A.Masullo and V.Nunziata, Napoli, Italy. In their paper entitled Pre-stressed steel structures: historical and technological analysis. [3] Akgül, F. and Frangopol, D. (2004). In their journal entitled Lifetime Performance Analysis of Existing Pre-stressed Concrete Bridge Superstructures. J. Struct. Eng., 130(12), [4] Albrecht, P. and Lenwari, A. (2008). in their journal entitled Design of Pre-stressing Tendons for Strengthening Steel Truss Bridges. J. Bridge Eng., 13(5), [5] Ayyub, B. and Ibrahim, A. (1990). in their paper entitled Post-tensioned Trusses: Reliability and Redundancy. J. Struct. Eng., 116(6), [6] Ayyub, B., Ibrahim, A., and Schelling, D. (1990). in their paper entitled Post-tensioned Trusses: Analysis and Design. J. Struct. Eng., 116(6), [7] Daly.A.F and Witarnwan.W (1997) in their paper entitled Strengthening of bridges using external Post-tensioning [8] Dr.S.K. Dubey, Prakash Sangamnerkar, Prabhat Soni in International Journal of Advanced Engineering Research and Studies entitled Analysis of steel roof truss under normal permeability condition IJAERS/Vol. I/ Issue IV/July-Sept., 2012/08-12 [9] Durfee, R. (1986) in his paper entitled Review of Triangular Cross Section Truss Systems. J. Struct. Eng., 112(5), [10] Durfee, R. (1987) in his paper entitled Design of a Triangular Cross Section Bridge Truss. J. Struct. Eng., 113(12), [11] F. Wayne Klaiber, P.E. In the paper entitled Evaluation of Post-tension strengthened Steel Girder Bridge using frp bars November 2003 [12] Frater, G. and Packer, J. (1992). in their paper Weldment Design for RHS Truss Connections. II. Experimentation. J. Struct. Eng., 118(10), [13] Frater, G. and Packer, J. (1992). in their paper entitled Weldment Design for RHS Truss Blue Ocean Research Journals 43

15 Connections. I: Applications. J. Struct. Eng., 118(10), [14] Kyoung-Bong Han, Sun-Kyu Park in the journal entitled Parametric study of truss bridges by the Post-tensioning method Canadian Journal of Civil Engineering, 2005, 32(2): , [15] Nihal Ariyawardena and Amin Ghali. (2002).in their paper entitled Pre-stressing with Unbounded Internal or External Tendons: Analysis and Computer Model. J. Struct. Eng., 128(12), [16] Packer, J. and Cassidy, C. (1995). in their paper Effective Weld Length for HSS T, Y, and X Connections. J. Struct. Eng., 121(10), [17] Wu, X. and Lu, X. (2003). in their journal entitled Tendon Model for Nonlinear Analysis of Externally Pre-stressed Concrete Structures. J. Struct. Eng., 129(1), [18] Yadava, and Gurujee, (1997). In their journal entitled Optimal Design of Trusses Using Available Sections. J. Struct. Eng., 123(5), Blue Ocean Research Journals 44