[PPT] - CABLE TRUSS ANALYSES FOR SUSPENSION BRIDGE Vadims Goremikins, Karlis PowerPoint Presentation

SLIDE 1

RIGA TECHNICAL UNIVERSITY

V. Goremikins, K. Rocens, D. Serdjuks

Riga Technical University Institute of Structural Engineering and Reconstruction

CABLE TRUSS ANALYSES FOR SUSPENSION BRIDGE

International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011

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Vadims Goremikins, Karlis Rocens, Dmitrijs Serdjuks

SLIDE 2

RIGA TECHNICAL UNIVERSITY

V. Goremikins, K. Rocens, D. Serdjuks

Introduction

q q P

Initial shape change under the action of non uniform load

Disadvantage of suspended cable structure: Main advantage of suspended cable structure:

Tensioned elements can’t loose stability

Typical cable:

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International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011

F j F j F j F j F j F j F j f b a l a a a a a a a f t 1 2 3 4 5 6 7 8 F j = 0,143F a = 0,125l b1 = 1,5a; b2 = a; b3 = 0,5a; b1 b2 b2 b3

The problem can be solved:

Increasing of relation of dead weight and imposed loads
Using of prestressing
Cable truss using

SLIDE 3

RIGA TECHNICAL UNIVERSITY

V. Goremikins, K. Rocens, D. Serdjuks

The aim of this study to evaluate possibility of cable truss usage as the main load-bearing structure of suspension prestressed The Aim of the Work

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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

SLIDE 4

RIGA TECHNICAL UNIVERSITY

V. Goremikins, K. Rocens, D. Serdjuks

1 3 4 5 A A 1 3 4 5 A 2b 2a

1 4 2

Structure of Suspension Bridge

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A

8 5 6 7 4 3

1 – Pylon of the bridge, 2 – Main load caring cable, 3 – Stabilization cable, 4 – Suspensions, 5 – Composite trussed beam, 6 – Composite I type beams, 7 – Composite plank, 8 – Cover of the bridge.

International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011 Actions on Bridges

Self-weights Traffic loads Climatic actions Accidental actions Execution actions

Vertical loads Horizontal loads Static loads Dynamic loads

SLIDE 5

RIGA TECHNICAL UNIVERSITY

V. Goremikins, K. Rocens, D. Serdjuks

Design Model of Suspension Bridge Applied load to the bridge

qk=82.2 kN/m

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3 kN/m 9 kN/m 2.5 kN/m 3 kN/m 9 kN/m 2.5 kN/m

gk=57.1 kN/m

Traffic Loading Model:1 International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011

Materials and cross-sections of cable truss:

Steel;
Modulus of elasticity: E0°=167000 MPa;
Rope grade: Rr=1960 MPa;
Cross-section:

SLIDE 6

RIGA TECHNICAL UNIVERSITY

V. Goremikins, K. Rocens, D. Serdjuks

f t f b x x1

Rational relation of top

chord camber and bottom chord camber: ft/fb=0.71

Rational relation of

bottom chord material consumption and material consumption of whole Rational Parameters of Cable Truss for Suspension Bridge

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Rational value of coordinate x1 of web element on distance x from the pylon: Polynomial equation:

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– 6.783 · 10 4 · 0.1817 · 2.108 x x x x = − + +

where x – distance from the pylon to the bottom chord’s node, x1 – distance from the pylon to the top chord’s node

consumption of whole truss: gb/g=0.6 International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011

SLIDE 7

RIGA TECHNICAL UNIVERSITY

V. Goremikins, K. Rocens, D. Serdjuks

(a) (b)

Construction type Uniformly distributed load Non uniformly distributed load (a) – Single cable w-=0.4965 m w+=0.3039 m w-=-0.6684 m (b) – Cable truss with inclined elements of the web w-=0.6912m w+=0.2522 m w-=-0.6798 m (c) – Cable truss with the w+=0.2076 m

Comparison of Different Types of Trusses with the Same Material Consumption

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(c)

(c) – Cable truss with the cross web w-=0.5560m w+=0.2076 m w-=-0.6141 m

International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011

SLIDE 8

RIGA TECHNICAL UNIVERSITY

V. Goremikins, K. Rocens, D. Serdjuks

Simplification of the Web of Cable Truss

Removing element Non uniformly distributed load Uniformly distributed load Displacements Displacements Displacements

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element number Displacements upwards Displacements downwards Displacements downwards 0-0 w+=0.2076 m w-=-0.6141 m w-=0.5560m 2-11 3-11 4-11 5-11 6-11 7-11 8-11 5-10 5-12 3-12 3-13 w+=0.2053 m w+=0.2031 m w+=0.2010 m w+=0.1995 m w+=0.2008 m w+=0.2039 m w+=0.2073 m w+=0.1999 m w+=0.2003 m w+=0.2033 m w+=0.2051 m w-=-0.6214m w-=-0.6194 m w-=-0.6174 m w-=-0.6157 m w-=-0.6144 m w-=-0.6138 m w-=-0.6141 m w-=-0.6139 m w-=-0.6182 m w-=-0.6214 m w-=-0.6260 m w=-0.5500 m w=-0.5497 m w=-0.5496 m w=-0.5498 m w=-0.5502 m w=-0.5506 m w=-0.5510 m w=-0.5520 m w=-0.5476 m w=-0.5469 m w=-0.5430 m

International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011

SLIDE 9

RIGA TECHNICAL UNIVERSITY

V. Goremikins, K. Rocens, D. Serdjuks

Behavior of Cable Truss Types under the Action of Different Loading Cases

Loading scheme Dead load Traffic load Full web cable truss Simplified wed cable truss Single cable g, kN/m q, kN/m w-,m w+, m w-,m w+, m w-,m w+, m 77.1 110.9

0.3161
0.3531
0.3378

0.0464 77.1 110.9

0.5168

0.0365

0.5242

0.0460

0.5645

0.0785

g q g q

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77.1 110.9

0.4842

0.1721

0.5123

0.1652

0.5553

0.2324 57.1 190.5

0.4599

0.1425

0.4852

0.1355

0.5368

0.1960 77.1 110.9

0.6279

0.2092

0.6262

0.2009

0.6693

0.3044 g q

g q g q

International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011

SLIDE 10

RIGA TECHNICAL UNIVERSITY

V. Goremikins, K. Rocens, D. Serdjuks

F=283kN d=3cm

3 kN/m 9 kN/m 2.5 kN/m

Displacements of the Suspension Bridge under the Action of Non uniform load in transversal direction

The difference of displacements of left and right side of the bridge: 0.3565 m, or 1/51 of bridge span in transversal direction, or slope 1.12°. Applied Traffic Loading Model:1 Design model of the bridge in transversal direction Problem:

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International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011

P=300kN 1 2 20x10 P=300kN

41.075 kN/m 32.44 kN/m 8.64 kN/m

The aim of this part of the article is to reduce the difference of displacements of left and right side of the bridge. The aim:

SLIDE 11

RIGA TECHNICAL UNIVERSITY

V. Goremikins, K. Rocens, D. Serdjuks

3 F=283kN F=283kN

f)

F=283kN F=283kN 1 2 d=3cm 20x10

a) b) h) c)

F=283kN 1 2 F=283kN 1 2

d) i) e)

F=283kN 1 2 F=283kN P=300kN P=300kN P=600kN P=300kN P=300kN P=600kN

Construc tion Type Difference of displacements of load application side and opposite side a) 17.30mm b) 50.00 mm c) 20.94 mm d) 21.69 mm e) 17.05 mm

Types of transversal construction of the suspension bridge

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International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011

3 3 F=283kN 1 2 1 2 F=283kN 1 2 1 2

g)

P=200kN 1 2

j)

1 2 P=300kN P=300kN P=200kN P=200kN P=200kN P=200kN P=200kN

P=200kN

P=200kN P=200kN

P=200kN

P=200kN P=150kN P=150kN P=150kN P=150kN

e) 17.05 mm f) 49.53 mm g) 13.87 mm h) 49.90 mm i) 20.97 mm j) 19.18 mm

SLIDE 12

RIGA TECHNICAL UNIVERSITY

V. Goremikins, K. Rocens, D. Serdjuks

F=283kN 1 2

b

Rational Parameters of Elements

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International scientific conference “Civil engineering ’11” Jelgava, Latvia, May 12-13, 2011

P=150kN P=150kN P=150kN P=150kN Distance between bottom middle supports Displacement in opposite side of load application Displacement in load application side Difference of load displacements of application side and

pposite side

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

SLIDE 13

RIGA TECHNICAL UNIVERSITY

V. Goremikins, K. Rocens, D. Serdjuks
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

Conclusions

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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

SLIDE 14

RIGA TECHNICAL UNIVERSITY

V. Goremikins, K. Rocens, D. Serdjuks

Riga Technical University Institute of Structural Engineering and Reconstruction

CABLE TRUSS ANALYSES FOR SUSPENSION BRIDGE

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