The Chinese Rainbow Bridge:

An Analysis of its Structural Capabilities By: Robert Asselin and Andrew Maier III

Department of Civil and Environmental Engineering

David and Lorraine Freed Undergraduate Research Symposium March 15, 2011

We would like to thank Dr. Clay Naito, Tom F. Peters, our Chinese collaborators at Tongji University, and the China Bridge Cohort for their support.

Also, we would like to express our gratitude to the Henry Luce Foundation for the grant enabling the China Bridge Project to succeed.

Objectives:

• Establish streamlined testing method and simplified structural

model

• Improve understanding of structural response mode

• Arch vs. beam or hybrid system

• Explore potential for modern reinterpretation of a traditional building

method with use of modern materials

Background:

• Traditional Rainbow Bridge concepts traced back to 12th Century

China

• Recent NOVA Rainbow Bridge completed in 1999 in Jilin,China

• Bridge characteristics of interest:

• Unique interweaving of beam members

• Basic bridge unit consists of two separate arches, overlapping

a 3-piece arch with a 4-piece arch

Procedure:

• Design variables

• Height to span ratio

• Asymmetrical loading response

• Utilization of metal tubes in place of traditional wood members

• Compare structural capacity to load demands (C/D > 1.0)

• Allowable stress calculated and checked against actual demand

based on four conditions: flexural, shear, axial compression, and

a combined flexural-axial

• NDS Allowable flexural stress in wood (typ.)

• Fbb = Fb x Cd x Cm x Ct x Cf x Cfu x Ci x Cr x CL

• AISC Allowable flexural stress in steel

• φMn = Fy x Z

General Assumptions:

• Tributary area used to simplify bridge deck loading

• Uniform loading transferred through sub deck to point loads at the five

transverse structural members

• AASHTO Pedestrian Bridge Load requirements

• DL = 100 psf (self weight of bridge)

• LL = 85 psf (non-permanent loads, i.e. pedestrians)

• Transverse members modeled as pin connections to mimic flexural

freedom of traditionally lashed joints

Results and Discussions:

• Flexural capacity was the most limiting variable in each of the trials

• Axial compressive capacity became a controlling design element as the

height to span ratio decreased

• 3-piece arch unit controlled in each trial except the lowest height to

span ratio

• 4-piece arch controlled in asymmetrical loading case due to load

redistribution

• As-built configuration achieves lowest, most even foundation reactions

• Steel member bridge provided more consistent C/D ratios on all

members, allowing for a 75% reduction in member size, and offering

increased efficiency and uniform structural behavior

Width

P

Tributary Width:

References:

• American Forest and Paper Association. National Design Specification for Wood Construction. Washington,

D.C.: American Forest and Paper Association, 2006.

• American Institute of Steel Construction. Steel Construction Manual 13th Edition. American Institute of Steel

Construction, 2005.

Loading Assumption:

Hybrid Arch-Beam Unit: Prototype Model:

4-Piece Arch

3-Piece Arch

1

2

3

4

3 2

1

Asymmetrical Deflection:

Deflection: Flexure:

Axial:

Conclusions and Recommendations:

• Rainbow Bridge structure exceeds all AASHTO loading requirements

• Rainbow Bridge acts as a hybrid or combination arch/beam structural

system

• Resists both flexural and axial compressive forces, most evident in

the asymmetrical case

• Application of steel for modern implementation of structural form

• Readily available cross sections are economical and easy to acquire

• Superior, more predictable structural capability and response across

all members

• Current exploration into the possibilities of prefabricated methods of

connection for easier, more rapid assembly

Legend: Red= Max (+), Blue = Min (-)

1 2 3 1 2 3 4 Rx (kips) Ry (kips)

Tall Bridge 5.32 4.22 5.32 25.98 15.01 14.95 25.98 7.78 8.80

Medium Bridge 4.74 5.17 4.74 20.99 18.41 18.41 20.99 12.79 8.63

Short Bridge 6.12 4.90 6.12 8.24 4.92 4.92 8.24 38.10 8.52

Asymmetrical 1.81 5.21 1.15 16.03 1.15 1.10 30.32 12.78 8.63

Steel Bridge 1.31 1.28 1.31 285.70 8.92 8.92 285.70 11.22 7.56

Tall Bridge 16.86 22.90 16.86 19.43 26.89 26.89 19.49

Medium Bridge 12.57 14.45 12.57 14.69 16.48 16.48 14.69

Short Bridge 4.96 5.04 4.96 5.42 5.48 5.48 5.42

Asymmetrical 12.80 14.84 12.69 10.93 18.97 14.62 22.34

Steel Bridge 4.25 3.88 4.25 5.60 4.94 4.94 5.60

Reactions

*Red values denote the critical or limiting values

3 - Piece Arch 4 - Piece Arch

Fle

xu

ral C

/D

Ra

tio

s

Ax

ial C

/D

Ra

tio

s

*Note that C/D values represent the average C/D ratios computed during each of the trials

+ -