H. Namiki*, H. Matsuhisa and Y. Hirakawa
Kyobashi Construction Corp.
2-2-21, Shiginonishi,Jotoku,536-0014, Osaka, Japan
KEIHAN railway main line is connecting famous historical city Kyoto to Osaka, the biggest city in West Japan. Sekime Route 1 Over Bridge is on this line and crosses over National Highway Route 1 near Osaka. This bridge was rebuilt in 1968, and since then engineers had to repair shoe beds periodically. It was obvious that the skew angle 43.8 degree caused these damages, such value is forbidden now, and the box girders had enough rigidity to float themselves at their acute angle side from the abutment.
Wansleben1) solved this problem about 50 years ago. In the case of skewed bridge, even loading on the central axis of the bridge results in torsional deformation around bridge axis. As a results of this torsion, train loads are concentrated to the obtuse side bearings, and causes of various damages. Recently on annual inspection, fatigue cracks were newly found in welding bead just upper the obtuse angle side bearing.
To rehabilitate this bridge, a new method via elastic bearing was proposed. This method is to make subsidence on obtuse side bearings by using elastic bearings, while rigid bearings on acute side. When a train go on board a beam, elastic deformation on acute side canceled by subsidence of obtuse side elastic bearing. It is expected that the beam keeps flat, and no torsional moment occurs.
Analysis of this elastic bearing model was developed from Wasleben’s solutions. And bearing loads by a single load at a distance c from left end of the beam could be expressed adding 2nd term to Wasleben’s solution as below.
and βis a supplementary angle of skew angleθ. Torsional moment is uniform through the beam and expressed as,
1st term was lead by Wasleben in the case of rigid bearings. To make definite integral of this equation, in a case of uniform load could be gained.
and to putoptimum spring constan of the elastic bearing could be decided as,
Applying elastic bearings having this optimum spring constant, torsional moment could be reduced nearly equal zero even in a case of train loads as shown in Fig.10 at Sekime Rout 1 Over Bridge.
Further investigation to estimate the amount of the sudden sinking when train board on the girder rapidly had been done, and through computer simulation no significant change had observed as shown in Fig.6(a) as expected. It was concluded that applying this method, no particular dynamic analysis is needed.
Fig.11 Replaced elastic bearing (Osaka side)
Special rubber bearings were made, replaced to the existing rigid bearings, and fatigue cracks were completely repaired. After these rehabilitation works had been finished, measured deflections showed good coincidence with theoretical values, and the effectiveness of this new method was confirmed.
1) F.Wansleben:Beitrag zur Berechnung Schiefer,drillsteifer Brucken, Stahlbau, 24, 10(1955)