Fig. 13 Comparisons between the gusset plate thickness and the uniaxial forces in horizontal truss members plotted in Fig. 7a: (a) upper chords; (b) lower level chords.
4. WHY THE GUSSET PLATES UNDERSIZED
Plotted in Fig.13 are the comparisons between the actual gusset thicknesses from Fig. 12 and the uniaxial forces of upper and lower-chards that were given in Fig. 6(a). An obvious coincidence between the force distributions and gusset thicknesses can be seen except near the end nodes All half-inch gusset plates are at or close to the locations with the lowest truss force. This fact seems implying that the plates’ thicknesses were designed based on the forces in horizontal trusses.
However, by checking the results plotted in Fig. 6(a) carefully, one can find another fact: the force in diagonal member almost reaches its peak value at the location, for example, between and , where the upper and lower chords forces change signs. The reason is obvious: at this location the diagonal truss transfers the deck load-induced compression force flow in middle upper chords of central span into lower chords and supporting bearings; whereas transfers the tension force flow in middle lower chords into upper chords above the piers; whereby the gusset plates like and are the “pivots” for these load paths of force flows, as explained in Fig. 14.
Therefore, a statement has been given in the third paragraph, section 5 of the report [27a]: “Due to the limited computation capability in past, it seems that the original design and subsequent early investigations could only treat the 9340 bridge as a truss-assembled structure, which led to the focus onto the forces and damage conditions in truss members….” Obviously, the truss force in upper and lower level chords had been used as the governing parameters for the gusset plate design, whereas the corresponding stress concentration in the gusset plates did not obtain sufficient consideration at the time.
Based on an examination of all original design drawings and the material evidences disclosed by NTSB’s investigation, several other “undersized” structural components have also been identified in the analysis . These components are the upper and lower chords attached to those undersized gusset plates in Fig. 12. It has been found that the thicknesses of upper chords’ wall and gusset plates are actually proportional to the bending moment solution of the one-dimensional influence line analysis illustrated in Fig. 10c. This fact reveals that the NTSB-disclosed undersized gusset plates are the consequence of a bias toward a “one-dimensional model” in the original design, which did not give sufficient consideration to the effects of the forces from diagonal truss members input into gusset plates .
The solved force, normalized to the dimension of stress, is plotted in Fig. 20. A brief introduction of the “Modified Whitemore Model” is given in .