Page 162 - Bridge and Highway Structure Rehabilitation and Repair

CHAPTER 4 AN ANALYTICAL APPROACH TO FRACTURE AND FAILURE 137

3. The LRFD method deals with uniform design, with the objective of equal probability of
failure everywhere on the bridge. It uses a probability-based reliability theory. The aim is
to achieve a probability index of 3.5 to 4.

= (Mean value of resistance 6 Load)
and is also known as a measure of standard deviation.

The load resistance factor method has a more advanced ultimate load approach than the
LFD method and in design aspects such as using a wide range of load combinations, selection
of load factors, and resistance factors. Its use is now mandatory by AASHTO.
4.2.4 Structural Systems

The structural behavior of primary members in a bridge is a function of span length and the
selected material. A primary system can be idealized as:
1. Beam action—applicable to small and medium spans of composite slab-beam systems.
2. Truss action—applicable to medium and long spans of through trusses braced transversely
by fl oor beams.
3. Arch action—applicable to medium and long spans of curved compression members.
4. Suspension cables—applicable to very long spans of cable supported bridges.

4.2.5 Substructure Type
Substructure systems fall into the following general categories:
1. Solid wall full-height abutments and piers (long cantilever behavior).
2. Stub or partial-height abutments (short cantilever behavior).
3. Frame type abutments and piers (short column bent frames).
4. Pile bent type piers (long column bent frames).

4.3 REVIEW OF ELASTIC ANALYSIS

4.3.1 Fundamental Equations

Elastic analysis for dead load, live load, and other applicable loads forms the starting point
of the factored design method. Using different factors for each type of load, elastic moments,
shear forces, and reactions are either exaggerated or modified to simulate ultimate load effects.

Analysis in all cases must comply with the laws of equilibrium and stability.
Well-known laws of equilibrium may be stated as:
Sum of vertical forces, 5V 3 0 (4.1a)
Sum of horizontal forces, 5H 3 0 (4.1b)
Sum of moments, 5M 3 0 (4.1c)
Beam bending: The most commonly used beam bending equation for bending stress, result-

ing from a bending curvature (or deflection) and stiffness (or shape, size, and material property)
is well known:
f/y 3 E/R 3 M/I (4.2)

2
2
2 3/2
where 1/R 3 (d w/dx )/(1 4 (dw/dx) ) (4.3a)

f 3 stress, y 3 distance of fiber from neutral axis, E 3 modulus of elasticity, R 3 radius of
curvature, M 3 bending moment, I 3 moment of inertia.