RIGA TECHNICAL UNIVERSITY V. Goremikins, K. Rocens, D. Serdjuks Riga Technical University Institute of Structural Engineering and Reconstruction CABLE TRUSS ANALYSES FOR SUSPENSION BRIDGE Vadims Goremikins, Karlis Rocens, Dmitrijs Serdjuks International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011 1
RIGA TECHNICAL UNIVERSITY V. Goremikins, K. Rocens, D. Serdjuks Introduction Main advantage of suspended cable structure: Typical cable: ● Tensioned elements can’t loose stability Disadvantage of suspended cable structure: ● Initial shape change under the action of non uniform load q q P The problem can be solved: ● Increasing of relation of dead weight and imposed loads ● Using of prestressing F j = 0,143 F a = 0,125 l ● Cable truss using f t b 1 = 1,5 a ; b 2 = a ; b 1 b 2 b 2 b 3 b 3 = 0,5 a ; 5 8 7 6 f b 4 3 2 F j 1 F j F j F j F j F j F j a a a a a a a a l International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011 2
RIGA TECHNICAL UNIVERSITY V. Goremikins, K. Rocens, D. Serdjuks The Aim of the Work The aim of this study to evaluate possibility of cable truss usage as the main load-bearing structure of suspension prestressed as the main load-bearing structure of suspension prestressed bridge and to choose the best, form the point of view of minimization of vertical displacements, type of the main load- bearing structure of suspension prestressed bridge in longitudinal and transversal direction International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011 3
RIGA TECHNICAL UNIVERSITY V. Goremikins, K. Rocens, D. Serdjuks Structure of Suspension Bridge A 1 4 2a 5 3 A 1 2 A 1 4 2b 5 3 4 4 A 1 – Pylon of the bridge, Actions on Bridges 2 – Main load caring cable, 7 8 6 3 – Stabilization cable, Self-weights Static loads 4 – Suspensions, Vertical loads 5 5 – Composite trussed beam, Dynamic loads Traffic loads 6 – Composite I type beams, 7 – Composite plank, Horizontal loads Climatic actions 8 – Cover of the bridge. Accidental actions 3 Execution actions International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011 4
RIGA TECHNICAL UNIVERSITY V. Goremikins, K. Rocens, D. Serdjuks Design Model of Suspension Bridge Applied load to the bridge q k = 82.2 kN/m g k = 57.1 kN/m Materials and cross-sections of cable truss: Traffic Loading Model:1 -Steel; 9 kN/m 9 kN/m -Modulus of elasticity: E 0 ° =167000 MPa; -Rope grade: R r =1960 MPa; 3 kN/m 3 kN/m 2.5 kN/m 2.5 kN/m -Cross-section: International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011 5
RIGA TECHNICAL UNIVERSITY V. Goremikins, K. Rocens, D. Serdjuks Rational Parameters of Cable Truss for Suspension Bridge • Rational relation of top x 1 chord camber and bottom chord camber: f t / f b =0.71 f t f b • Rational relation of bottom chord material x consumption and material consumption of whole consumption of whole truss: g b /g=0.6 Rational value of coordinate x 1 of web element on distance x from the pylon: Polynomial equation: = − + + x x x x 2 – 6.783 · 10 4 · 0.1817 · 2.108 1 where x – distance from the pylon to the bottom chord’s node, x1 – distance from the pylon to the top chord’s node International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011 6
RIGA TECHNICAL UNIVERSITY V. Goremikins, K. Rocens, D. Serdjuks Comparison of Different Types of Trusses with the Same Material Consumption (a) Uniformly Non uniformly Construction type distributed load distributed load w + =0.3039 m (a) – Single cable w - =0.4965 m w - =-0.6684 m (b) – Cable truss with w + =0.2522 m w - =0.6912m (b) w - =-0.6798 m inclined elements of the web w + =0.2076 m w + =0.2076 m (c) – Cable truss with the (c) – Cable truss with the w - =0.5560m w - =-0.6141 m cross web (c) International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011 7
RIGA TECHNICAL UNIVERSITY V. Goremikins, K. Rocens, D. Serdjuks Simplification of the Web of Cable Truss Uniformly Removing Non uniformly distributed load distributed load element element Displacements Displacements Displacements Displacements Displacements Displacements number upwards downwards downwards 0-0 w + =0.2076 m w - =-0.6141 m w - =0.5560m 2-11 w + =0.2053 m w - =-0.6214m w=-0.5500 m 3-11 w + =0.2031 m w - =-0.6194 m w=-0.5497 m 4-11 w + =0.2010 m w - =-0.6174 m w=-0.5496 m 5-11 w + =0.1995 m w - =-0.6157 m w=-0.5498 m 6-11 w + =0.2008 m w - =-0.6144 m w=-0.5502 m 7-11 w + =0.2039 m w - =-0.6138 m w=-0.5506 m 8-11 w + =0.2073 m w - =-0.6141 m w=-0.5510 m 5-10 w + =0.1999 m w - =-0.6139 m w=-0.5520 m 5-12 w + =0.2003 m w - =-0.6182 m w=-0.5476 m 3-12 w + =0.2033 m w - =-0.6214 m w=-0.5469 m 3-13 w + =0.2051 m w - =-0.6260 m w=-0.5430 m International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011 8
RIGA TECHNICAL UNIVERSITY V. Goremikins, K. Rocens, D. Serdjuks Behavior of Cable Truss Types under the Action of Different Loading Cases Traffic Simplified wed cable Dead load Full web cable truss Single cable load truss Loading scheme g, kN/m q, kN/m w - ,m w + , m w - ,m w + , m w - ,m w + , m q 77.1 110.9 -0.3161 -0.3531 -0.3378 0.0464 g q 77.1 110.9 -0.5168 0.0365 -0.5242 0.0460 -0.5645 0.0785 g q 77.1 110.9 -0.4842 0.1721 -0.5123 0.1652 -0.5553 0.2324 g q 57.1 190.5 -0.4599 0.1425 -0.4852 0.1355 -0.5368 0.1960 g q - 0.6279 77.1 110.9 0.2092 -0.6262 0.2009 -0.6693 0.3044 g International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011 9
RIGA TECHNICAL UNIVERSITY V. Goremikins, K. Rocens, D. Serdjuks Displacements of the Suspension Bridge under the Action of Non uniform load in transversal direction Design model of the Problem: bridge in transversal Applied Traffic Loading Model:1 The difference of displacements of direction 9 kN/m left and right side of the bridge: 0.3565 m, or 1/51 of bridge span in 3 kN/m 2.5 kN/m d=3cm transversal direction, or slope 1.12 ° . F=283kN 41.075 kN/m The aim: 1 2 The aim of this part of the article 20x10 32.44 kN/m 8.64 kN/m is to reduce the difference of displacements of left and right P=300kN P=300kN side of the bridge. International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011 10
RIGA TECHNICAL UNIVERSITY V. Goremikins, K. Rocens, D. Serdjuks Types of transversal construction of the suspension bridge h) c) b) a) d=3cm F=283kN F=283kN F=283kN F=283kN Construc Difference of tion displacements of 3 1 2 1 2 2 1 1 2 Type load application 20x10 side and opposite side P=600kN P=300kN P=300kN P=600kN P=300kN P=300kN i) a) 17.30mm d) e) f) b) 50.00 mm c) 20.94 mm F=283kN F=283kN F=283kN F=283kN d) 21.69 mm e) e) 17.05 mm 17.05 mm 1 2 3 2 f) 49.53 mm 1 1 2 1 2 g) 13.87 mm P=200kN P=200kN P=200kN P=200kN P=200kN P=200kN P=300kN P=300kN P=200kN P=200kN P=200kN h) 49.90 mm j) i) 20.97 mm j) 19.18 mm g) F=283kN F=283kN 3 2 1 1 2 P=200kN P=200kN P=200kN P=150kN P=150kN P=150kN P=150kN International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011 11
RIGA TECHNICAL UNIVERSITY V. Goremikins, K. Rocens, D. Serdjuks Rational Parameters of Elements F=283kN b 1 2 P=150kN P=150kN P=150kN P=150kN Distance Displacement Displacement Difference of load between in opposite in load displacements of bottom side of load application side application side and middle application opposite side supports 6 m 53.17 mm 67.94 mm 15.10 mm 10 m 53.45 mm 67.32 mm 13.87 mm 14 m 53.73 mm 66.76 mm 13.36 mm 18.2 m 53.84 mm 66.62 mm 13.11 mm 22.2 m 53.58 mm 67.17 mm 13.59 mm International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011 12
RIGA TECHNICAL UNIVERSITY V. Goremikins, K. Rocens, D. Serdjuks Conclusions • Different types of cable trusses where compared under the action of the uniformly and non uniformly distributed loads. It was shown, that the cable truss with the cross web is the best from the point of view of minimization of maximum vertical displacements in the case when non uniform load is applied. • It was stated, that usage of cable truss with the cross web instead of single cable allows to reduce maximum vertical displacements up to 32% in the case of non uniformly distributed load. • Rational structure of the cable truss’ web was developed for considered loading cases. It Rational structure of the cable truss’ web was developed for considered loading cases. It was shown, that the cross web can be replaced by the inclined suspensions in part of the span. • Applying of structure with four bottom chords and inclined and crossing suspensions instead of structure with two bottom chords and vertical suspensions for transversal construction of suspension bridge allow to reduce difference of displacements in transverse direction by 24% or by 0.085 m. International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011 13
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