Redundancy analysis - Computational Analysis and Design of Bridge Structures - page 472

The results of these analyses are summarized in Table 15.7 under the title
of “no cut” in the column to identify an element cut. By investigation the
most critical stresses for a “no cut” case are -37.96 ksi (261.7 MPa) at
element 62 under load 2-a: 1.25Dc + 1.5DW + 1.3*1.33P-82 (at L/3).
Because it is considered as extreme event III, the allowable stress is the
yield stress of the section, which is 50 ksi (345 MPa) in this case. Also,
the worst vertical displacements are 104 mm (4.1″) under load case 1-a.
Displacement of 104 mm (4.1″) of the 43.5-m (142′-8 1/2″) Foxstop Road
Bridge corresponding to L/418 is adequate for the extreme event III limit
state.
15.3.2.2 Extreme event IV
As stated in Section 15.3.2, the test of redundancy required a 3D frame
analysis of the entire system under conditions of severing a single bottom
chord of any twin-channel bottom chord member while sustaining the
full AASHTO (or Penn DOT) dead and live loads applied to attain the
maximum stresses. Or the severed members may be identified as diagonal
tension members as listed in Table 15.6. The results of these analyses also
are given in Table 15.7 for the various member-cut conditions. A sum-
mary of these results follows:
1. Five (5) cut cases are identified, and their maximum stresses and
elastic and inelastic strains are summarized in Table 15.7. With
four load cases, there are 20 runs in total. Among these 20 runs,
one case for bottom chord cut case (load case 1-b-cut 1) and four
cases for diagonal cut cases (load cases 1-b-cut 28, 2-b-cut 28,
3-b-cut 28, 4-b-cut 28) have members plastified. After plastifica-
tion, stresses stay at the level of yield stress, and strains may still
grow to their respective maximum strains under the current load-
ing condition.
2. Ductility ratio listed under column (7) is defined as the maximum
strain divided by the yield strain (0.001724). Resulting from all analy-
ses, the maximum ductility ratio identified is 4.45, which is associated
with “load case 2-b with element 28 cut.”
3. The same “load case 2-b with element 28 cut” gives vertical ( y -direction)
displacements of 95 mm (3.75″). Displacement of 95 mm (3.75″) of
the 43.5-m (142′-8 1/2″) Foxstop Road Bridge corresponds to L/457,
which is also considered adequate for the extreme event IV limit
state.