Redundancy analysis - Computational Analysis and Design of Bridge Structures - page 475

Table 15.8 Summary of maximum strains and ductility factors for the two extreme
load cases

Maximum strain

Element
cut

Ductility
factor Load case Tension Compression

1-a: 1.25Dc + 1.5DW + 1.3*1.33P-82
(at CL) (no cut)
1-b: 0.05Dc + 1.05DW + 1.15*1.33P-
82 (at CL) (cut)

1 0.002170 ‒ 0.002174 1.26

28 0.005324 ‒ 0.003396 3.088

2-a: 1.25Dc + 1.5DW + 1.3*1.33P-82
(at L/3) (no cut)
2-b: 0.05Dc + 1.05DW + 1.15*1.33P-
82 (at L/3) (cut)

28 0.007686 ‒ 0.006113 4.45

3-a: 1.25Dc + 1.5DW + 1.3Lane +
1.3*1.33PHL93 (at CL) (no cut)
3-b: 1.05Dc + 1.05DW + 1.15Lane +
1.15*1.33PHL93 (at CL) (cut)

28 0.003642 ‒ 0.001904 2.11

4-a: 1.25Dc + 1.5DW + 1.3Lane +
1.3*1.33PHL93 (at L/3) (no cut)
4-b: 1.05Dc + 1.05DW + 1.15Lane +
1.15*1.33PHL93 (at L/3) (cut)

28 0.004192 ‒ 0.002209 2.43

4. Only a limited number of elements yield by cutting any FCM. This
means the structure would shake down after a few members yielded.
A nonlinear analysis program is capable of redistributing the load
after any member plastifies. The sum of the elastic and plastic strains
yields a ductility ratio of 4.45, shown in Table 15.8.

15.4 3d Redundancy analysis undeR Blast
loading of a Pc BeaM BRidge, MaRyland

This example demonstrates the analysis under equivalent blast load on
a prestressed concrete beam bridge formed by 3D frame elements with
plastic hinges assigned at specific locations. The bridge was designed
using AASHTO's Standard Specifications for Highway Bridges for an
HS-20-44 live load. A representative prestressed concrete beam span is
simply supported, 18.3 m (60′) in length and 12.1 m (39′-8″) wide. There
are six AASHTO type III beams, spaced 2.2 m (7′-2″) center to center.
Figure 15.7 shows the bridge's typical half-section, with symmetry occur-
ring at the centerline.
The bridge deck is 178 mm (7″) thick, which includes a 13-mm (1/2″)
monolithic wearing surface. The AASHTO type III beam cross section