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Experimental analysis of prestressed thin-walled structures stability
ARTICLE IN PRESS
Thin-Walled Structures 45 (2007) 834–839 www.elsevier.com/locate/tws
Experimental analysis of prestressed thin-walled structures stability A. Bluma,, D. Chodorowskab a
AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krako´w, Poland The State Higher School of Vocational Education in Krosno, ul. Wyspian´skiego 20, 38-400 Krosno, Poland
b
Available online 17 October 2007
Abstract In this paper the results of experimental investigations and numerical calculations of thin-walled plate girders are presented. The objective of this investigation was to determine the effect of prestressing technology based on weld shrinkage of fillet welds joining additional overlay plates welded in the area of the structure tension on their stability. r 2007 Published by Elsevier Ltd. Keywords: Technological prestressing; Structure stability
1. Introduction The process of permanent deflection accumulation in structures has been taking place with different rates as the result of multiyear operation of mechanical facilities and road and railway bridges, where main bodies are thinwalled plates and box girders. The progress of permanent deflection increment is as a rule the prelude to the next stage of the structure failure, i.e. cracks in girders. These problems are actually of serious significance as the process of permanent deflection accumulation of thin-walled under-crane girders is more and more frequently observed in industrial plants. Fig. 1 presents the isometric diagram of permanent deflection of under-crane roadway beam in a heavy industry plant. The reasons for permanent deflections are complex: they are loaded over the rated capacity or the process of lamellar cracks propagation develops with operational time. The lamellar cracks formed as the result of joining nonmetallic inclusions decrease the structure capacity. At present the permanent deflection phenomenon is a significant problem for users of load-bearing structures with plate girders. As a matter of fact the increase of Corresponding author. Tel.: +48 126173088.
E-mail address: [email protected] (A. Blum). 0263-8231/$ - see front matter r 2007 Published by Elsevier Ltd. doi:10.1016/j.tws.2007.08.040
permanent deflection results in the structure strength exhaustion and at the same time it influences the improper operation of overhead cranes due to the increase of motion resistance on deformed road. Present market trend is aimed at minimization of investment costs which means limitations in purchase of new devices and machines. It is the reason for more and more common use of temporary levelling of the truck by application of graduated pads put between the rail and the upper flange as it is presented in Fig. 2. This method improves traction conditions, however it does not affect the removal of the strength effects resulting from permanent deformation. What is more, strength effects are additionally worsened by applying the weight of pad plates to the permanently deformed girders. The method, which has been successfully examined in box girders, is technological prestressing [3]. The method of technological prestressing engages the phenomenon of shrinkage of fillet welds connecting additional overlay plates put in the tension area due to their own weight and operational load of the sheet girders. Welding stresses cause tension of the compressed area of the structure and compression of the tension area resulting in bending of the girder with convexity directed upwards [4]. Anyway the essential and up to now not examined matter is the estimation of the effect of prestressing on the stability of sheet girders in comparison with the stability of not prestressed girders.
ARTICLE IN PRESS A. Blum, D. Chodorowska / Thin-Walled Structures 45 (2007) 834–839
60 50 40 30 20 10 0
26 32.5
84.5
13 19.5
6.5
0
39 45.5 ] 52 [m ay w 58.5 ad ro 65 he t f 71.5 ho gt n 78 Le
91 97.5 E
F
Deflection of the roadway [mm]
Deflections of under-crane roadway beams
835
104
Fig. 1. Diagram of permanent deflections of girders of 25 m span and 12 m length.
Fig. 2. Levelling of the road by the use of graduated pad plates put between the rail and the upper flange of the under-crane girder.
2. Experimental and numerical analysis The objective of experimental investigations was the determination of the effect of technological prestressing on the stability of plate girders. Two models of sheet girders have been made to realize this task. One of them was prestressed with two side overlay plates (Fig. 3c) when the other for comparison purposes was nonprestressed (Fig. 3a, b). The sections of analyzed girders were classified as belonging to fourth class [5], so they can lose stability, when maximum compression or average shear stresses are less then yield limit [1,2]. The process of prestressing the girder with two sides overlaying the plates resulted in its upward bending over by 4 mm. On the bases of the value of maximum deflection, the values of prestression forces and moments were
calculated according to the computational model developed for box girders [3]. Calculation based on the standard [5] proved that the critical force value for nonprestressed girder was 28.7 kN when in the case of prestressed girder it was 34 kN. Therefore the process of technological prestressing resulted in the increase of critical force value and in the same way increased the stability of technologically prestressed sheet girders. This result has been confirmed in experimental tests. In tests plate girders shown in Fig. 3 were used. The test stand is shown in Fig. 4. Program of experiments included:
Measurement of maximum deflection of not prestressed girder and prestressed girder loaded with concentrated loads.
ARTICLE IN PRESS 836
A. Blum, D. Chodorowska / Thin-Walled Structures 45 (2007) 834–839
Fig. 3. Plate girder, (a) general view of not prestressed girder, (b) section A-A of not prestressed girder, (c) section A-A of the girder prestressed with side overlay plates.
Fig. 4. General view of the test stand.
Measurement of stresses of not prestressed girder and prestressed girder loaded with concentrated loads. Measurement of transverse displacement of web plates.
Stress measurements have been performed using strain gauges located as shown in Fig. 5a. Transverse displacements of web plates were measured with the use of dial indicators mounted in the special supports in the section shown in Fig. 5b.
Subsequently, the numerical analysis was carried out. The finite element method calculations were performed using of professional programme package ANSYS 10.0 [6]. Calculations were carried out with the use of shell finite elements SHELL 93. The analysis of results carried out by FEM proved high agreement with results obtained in experiments. In Figs. 6 and 7 the example of the numerical model of the sheet girder whereas in Table 1 the values of vertical displacements for particular three cases are shown.
ARTICLE IN PRESS A. Blum, D. Chodorowska / Thin-Walled Structures 45 (2007) 834–839
837
Fig. 5. Location of strain gauges (a) and dial indicators (b).
Subsequently Tables 2 and 3 show the results of stress measurements made in the section C-C of nonprestressed girder loaded with the force 30 kN and the girder prestressed with two sides overplayed plates and loaded with the force 30 kN. Fig. 7 illustrates the result of numerical analysis in this section. The analysis has shown high compatibility of stresses results obtained from theoretical, numerical and experimental calculations. It has been proved for experimental measurements as well for numerical and analytical calculations that the values of stresses in prestressed girder are less then values of stresses in nonprestressed girder. Subsequently in Table 4 are presented the values of transverse displacements of web plates in nonprestressed and prestressed girder both loaded with force 30 kN. Experimental investigations of transverse displacements of web plates confirmed the increase of stability of the prestressed girder. Loading of nonprestressed and prestressed girders with critical forces has shown that in
nonprestressed girder the mode of displacements takes the form of two sine half-waves of high amplitudes, when in the prestressed girder displacements have the form of a single half-wave of significantly less amplitude. 3. Conclusions Results of investigations show a significant increase of stability of the prestressed girder in comparison with nonprestressed. Prestressing caused bending of the girder with upward convexity, resulting in tension stresses introduced into the area compressed by external loading and compression stresses introduced into the tension area. This process essentially affected both stability and stiffness of the prestressed girder. Additional forces and prestressing moments introduced into the structure ensure increase of the critical force. The only reservation that can appear when applying this method on a technical scale concerns the possibility of it causing the post-buckling state of the structure by forces and prestressing moments. Therefore it
ARTICLE IN PRESS 838
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Fig. 6. Numerical model of vertical displacements of not prestressed girder loaded with the force 30 kN (a) and prestressed with two side overlay plates (b), prestressed with two side overlay plates and loaded with the force 30 kN (c).
Fig. 7. The result of numerical calculations of stresses in not prestressed girder (a) and prestressed girder (b) in section C-C shown in Fig. 5a.
ARTICLE IN PRESS A. Blum, D. Chodorowska / Thin-Walled Structures 45 (2007) 834–839
839
Table 1 The values of vertical displacements of sheet girders Deflection of not prestressed girder loaded with force 28 kN (mm) Results of experiment Results of numerical calculations
2.18 1.918
Table 2 The values of stresses of not prestressed girder loaded with the force 30 kN Number of measurement point Fig. 5a
1 2 3 4 5 6 7 8
Calculated stress values (by standard rules [5]) (MPa) 72.16 72.16 38.59 13.49 17.88 49.26 72.16 72.16
Experimental stress values (MPa)
71.30 72.70 45.30 17.30 19.45 76.10 71.70 72.30
Numerical calculation values (MPa)
59.82 59.82 41.12 14.42 11.98 32.18 58.24 58.24
Table 3 The values of stresses of the girder prestressed with two side overlay plates and loaded with the force 30 kN Number of measurement point Fig. 5a
1 2 3 4 5 6 7 8
Calculated stress values (by standard rules [5]) (MPa) 61.06 61.06 32.65 11.41 15.13 41.68 51.06 51.06
Experimental stress values (MPa)
50.30 51.75 32.90 20.20 17.80 55.05 49.51 40.80
Numerical calculation values (MPa)
59.78 59.78 32.47 13.86 10.27 30.64 45.27 45.27
Table 4 Transverse displacement of web plates (section C-C, Fig. 5b) Measurement points Fig. 5b
Transverse displacements of web plates (mm)
Not prestressed girder loaded Prestressed girder loaded with force 28 kN (mm) with force 34 kN (mm) 1 2 3 4 5
1.14 1.70 1.23 0.35 0.23
0.38 0.69 0.72 0.48 0.09
seems reasonable to determine the applicability limits of technological prestressing procedure. In the authors’ opinion the method presented gives the proper solution
Deflection of the girder prestressed by two side overlay plates (mm)
Deflection of prestressed girder loaded with force 34 kN (mm)
3.5 3.517
1.88 1.915
for levelling the plate structures that have been permanently deformed in vertical plane.
References [1] Wolmir AS. Stability of deformable systems. Moscow: Publishing House ‘‘Nauka’’; 1967. [2] Kro´lak M, Ko"akowski Z. Stability of thin walled girder loaded by axial force and bending moment. Volume XXX, Warszawa, 1983. [3] Blum A. Research and development project No 7T07C.01595C/2716. Regeneration of permanently deformed steel box girders of traveling cranes by the method of technological prestressing. Krakow 1998. [4] Blum A. Diagnostic and strength regeneration of the steel box girders of traveling cranes. Radom 2002. [5] Standard no PN-90/B-3200 Steel construction. Static calculations and design. Warszawa 1990. [6] ANSYS University Intermediate. License. Mesco. Tarnowskie Gory.
Thin-Walled Structures 45 (2007) 834–839 www.elsevier.com/locate/tws
Experimental analysis of prestressed thin-walled structures stability A. Bluma,, D. Chodorowskab a
AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krako´w, Poland The State Higher School of Vocational Education in Krosno, ul. Wyspian´skiego 20, 38-400 Krosno, Poland
b
Available online 17 October 2007
Abstract In this paper the results of experimental investigations and numerical calculations of thin-walled plate girders are presented. The objective of this investigation was to determine the effect of prestressing technology based on weld shrinkage of fillet welds joining additional overlay plates welded in the area of the structure tension on their stability. r 2007 Published by Elsevier Ltd. Keywords: Technological prestressing; Structure stability
1. Introduction The process of permanent deflection accumulation in structures has been taking place with different rates as the result of multiyear operation of mechanical facilities and road and railway bridges, where main bodies are thinwalled plates and box girders. The progress of permanent deflection increment is as a rule the prelude to the next stage of the structure failure, i.e. cracks in girders. These problems are actually of serious significance as the process of permanent deflection accumulation of thin-walled under-crane girders is more and more frequently observed in industrial plants. Fig. 1 presents the isometric diagram of permanent deflection of under-crane roadway beam in a heavy industry plant. The reasons for permanent deflections are complex: they are loaded over the rated capacity or the process of lamellar cracks propagation develops with operational time. The lamellar cracks formed as the result of joining nonmetallic inclusions decrease the structure capacity. At present the permanent deflection phenomenon is a significant problem for users of load-bearing structures with plate girders. As a matter of fact the increase of Corresponding author. Tel.: +48 126173088.
E-mail address: [email protected] (A. Blum). 0263-8231/$ - see front matter r 2007 Published by Elsevier Ltd. doi:10.1016/j.tws.2007.08.040
permanent deflection results in the structure strength exhaustion and at the same time it influences the improper operation of overhead cranes due to the increase of motion resistance on deformed road. Present market trend is aimed at minimization of investment costs which means limitations in purchase of new devices and machines. It is the reason for more and more common use of temporary levelling of the truck by application of graduated pads put between the rail and the upper flange as it is presented in Fig. 2. This method improves traction conditions, however it does not affect the removal of the strength effects resulting from permanent deformation. What is more, strength effects are additionally worsened by applying the weight of pad plates to the permanently deformed girders. The method, which has been successfully examined in box girders, is technological prestressing [3]. The method of technological prestressing engages the phenomenon of shrinkage of fillet welds connecting additional overlay plates put in the tension area due to their own weight and operational load of the sheet girders. Welding stresses cause tension of the compressed area of the structure and compression of the tension area resulting in bending of the girder with convexity directed upwards [4]. Anyway the essential and up to now not examined matter is the estimation of the effect of prestressing on the stability of sheet girders in comparison with the stability of not prestressed girders.
ARTICLE IN PRESS A. Blum, D. Chodorowska / Thin-Walled Structures 45 (2007) 834–839
60 50 40 30 20 10 0
26 32.5
84.5
13 19.5
6.5
0
39 45.5 ] 52 [m ay w 58.5 ad ro 65 he t f 71.5 ho gt n 78 Le
91 97.5 E
F
Deflection of the roadway [mm]
Deflections of under-crane roadway beams
835
104
Fig. 1. Diagram of permanent deflections of girders of 25 m span and 12 m length.
Fig. 2. Levelling of the road by the use of graduated pad plates put between the rail and the upper flange of the under-crane girder.
2. Experimental and numerical analysis The objective of experimental investigations was the determination of the effect of technological prestressing on the stability of plate girders. Two models of sheet girders have been made to realize this task. One of them was prestressed with two side overlay plates (Fig. 3c) when the other for comparison purposes was nonprestressed (Fig. 3a, b). The sections of analyzed girders were classified as belonging to fourth class [5], so they can lose stability, when maximum compression or average shear stresses are less then yield limit [1,2]. The process of prestressing the girder with two sides overlaying the plates resulted in its upward bending over by 4 mm. On the bases of the value of maximum deflection, the values of prestression forces and moments were
calculated according to the computational model developed for box girders [3]. Calculation based on the standard [5] proved that the critical force value for nonprestressed girder was 28.7 kN when in the case of prestressed girder it was 34 kN. Therefore the process of technological prestressing resulted in the increase of critical force value and in the same way increased the stability of technologically prestressed sheet girders. This result has been confirmed in experimental tests. In tests plate girders shown in Fig. 3 were used. The test stand is shown in Fig. 4. Program of experiments included:
Measurement of maximum deflection of not prestressed girder and prestressed girder loaded with concentrated loads.
ARTICLE IN PRESS 836
A. Blum, D. Chodorowska / Thin-Walled Structures 45 (2007) 834–839
Fig. 3. Plate girder, (a) general view of not prestressed girder, (b) section A-A of not prestressed girder, (c) section A-A of the girder prestressed with side overlay plates.
Fig. 4. General view of the test stand.
Measurement of stresses of not prestressed girder and prestressed girder loaded with concentrated loads. Measurement of transverse displacement of web plates.
Stress measurements have been performed using strain gauges located as shown in Fig. 5a. Transverse displacements of web plates were measured with the use of dial indicators mounted in the special supports in the section shown in Fig. 5b.
Subsequently, the numerical analysis was carried out. The finite element method calculations were performed using of professional programme package ANSYS 10.0 [6]. Calculations were carried out with the use of shell finite elements SHELL 93. The analysis of results carried out by FEM proved high agreement with results obtained in experiments. In Figs. 6 and 7 the example of the numerical model of the sheet girder whereas in Table 1 the values of vertical displacements for particular three cases are shown.
ARTICLE IN PRESS A. Blum, D. Chodorowska / Thin-Walled Structures 45 (2007) 834–839
837
Fig. 5. Location of strain gauges (a) and dial indicators (b).
Subsequently Tables 2 and 3 show the results of stress measurements made in the section C-C of nonprestressed girder loaded with the force 30 kN and the girder prestressed with two sides overplayed plates and loaded with the force 30 kN. Fig. 7 illustrates the result of numerical analysis in this section. The analysis has shown high compatibility of stresses results obtained from theoretical, numerical and experimental calculations. It has been proved for experimental measurements as well for numerical and analytical calculations that the values of stresses in prestressed girder are less then values of stresses in nonprestressed girder. Subsequently in Table 4 are presented the values of transverse displacements of web plates in nonprestressed and prestressed girder both loaded with force 30 kN. Experimental investigations of transverse displacements of web plates confirmed the increase of stability of the prestressed girder. Loading of nonprestressed and prestressed girders with critical forces has shown that in
nonprestressed girder the mode of displacements takes the form of two sine half-waves of high amplitudes, when in the prestressed girder displacements have the form of a single half-wave of significantly less amplitude. 3. Conclusions Results of investigations show a significant increase of stability of the prestressed girder in comparison with nonprestressed. Prestressing caused bending of the girder with upward convexity, resulting in tension stresses introduced into the area compressed by external loading and compression stresses introduced into the tension area. This process essentially affected both stability and stiffness of the prestressed girder. Additional forces and prestressing moments introduced into the structure ensure increase of the critical force. The only reservation that can appear when applying this method on a technical scale concerns the possibility of it causing the post-buckling state of the structure by forces and prestressing moments. Therefore it
ARTICLE IN PRESS 838
A. Blum, D. Chodorowska / Thin-Walled Structures 45 (2007) 834–839
Fig. 6. Numerical model of vertical displacements of not prestressed girder loaded with the force 30 kN (a) and prestressed with two side overlay plates (b), prestressed with two side overlay plates and loaded with the force 30 kN (c).
Fig. 7. The result of numerical calculations of stresses in not prestressed girder (a) and prestressed girder (b) in section C-C shown in Fig. 5a.
ARTICLE IN PRESS A. Blum, D. Chodorowska / Thin-Walled Structures 45 (2007) 834–839
839
Table 1 The values of vertical displacements of sheet girders Deflection of not prestressed girder loaded with force 28 kN (mm) Results of experiment Results of numerical calculations
2.18 1.918
Table 2 The values of stresses of not prestressed girder loaded with the force 30 kN Number of measurement point Fig. 5a
1 2 3 4 5 6 7 8
Calculated stress values (by standard rules [5]) (MPa) 72.16 72.16 38.59 13.49 17.88 49.26 72.16 72.16
Experimental stress values (MPa)
71.30 72.70 45.30 17.30 19.45 76.10 71.70 72.30
Numerical calculation values (MPa)
59.82 59.82 41.12 14.42 11.98 32.18 58.24 58.24
Table 3 The values of stresses of the girder prestressed with two side overlay plates and loaded with the force 30 kN Number of measurement point Fig. 5a
1 2 3 4 5 6 7 8
Calculated stress values (by standard rules [5]) (MPa) 61.06 61.06 32.65 11.41 15.13 41.68 51.06 51.06
Experimental stress values (MPa)
50.30 51.75 32.90 20.20 17.80 55.05 49.51 40.80
Numerical calculation values (MPa)
59.78 59.78 32.47 13.86 10.27 30.64 45.27 45.27
Table 4 Transverse displacement of web plates (section C-C, Fig. 5b) Measurement points Fig. 5b
Transverse displacements of web plates (mm)
Not prestressed girder loaded Prestressed girder loaded with force 28 kN (mm) with force 34 kN (mm) 1 2 3 4 5
1.14 1.70 1.23 0.35 0.23
0.38 0.69 0.72 0.48 0.09
seems reasonable to determine the applicability limits of technological prestressing procedure. In the authors’ opinion the method presented gives the proper solution
Deflection of the girder prestressed by two side overlay plates (mm)
Deflection of prestressed girder loaded with force 34 kN (mm)
3.5 3.517
1.88 1.915
for levelling the plate structures that have been permanently deformed in vertical plane.
References [1] Wolmir AS. Stability of deformable systems. Moscow: Publishing House ‘‘Nauka’’; 1967. [2] Kro´lak M, Ko"akowski Z. Stability of thin walled girder loaded by axial force and bending moment. Volume XXX, Warszawa, 1983. [3] Blum A. Research and development project No 7T07C.01595C/2716. Regeneration of permanently deformed steel box girders of traveling cranes by the method of technological prestressing. Krakow 1998. [4] Blum A. Diagnostic and strength regeneration of the steel box girders of traveling cranes. Radom 2002. [5] Standard no PN-90/B-3200 Steel construction. Static calculations and design. Warszawa 1990. [6] ANSYS University Intermediate. License. Mesco. Tarnowskie Gory.