Page 165 - Bridge and Highway Structure Rehabilitation and Repair

140 SECTION 2 STRENGTHENING AND REPAIR WORK

wheel load and distributed across the depth of slab.

4.5 METHODS OF ANALYSIS OF THE SUPERSTRUCTURE
4.5.1 Analytical and Computer Modeling Methods
For monolithic slab and beam bridges, AASHTO Section 4.6.1 shows a simplified line model

of a superstructure, neglecting modeling in transverse distribution if the span length exceeds 2.5

times the deck width. Primary flexural members may be idealized as:
1. Line girder—Stiffness matrix, moment distribution, strain energy, and area-moment meth-
ods.
2. Finite Strip—AASHTO Section 4.6.1 describes limitations of the strip method for skew
slabs. It is suitable for slab and beam bridges spanning in direction parallel to traffi c. Width
requirements for equivalent strips for concrete, steel, and timber decks are specifi ed in
AASHTO Table 4.6.2.1.3.1-1.
Empirical equations for deck bending moments and deflections are given in detail in

AASHTO Section 4.6.2.1.8.
3. Grillage.

4. Continuum (finite element modeling).
5. Frames.

An alternative to using a computer program is to develop equations for maximum bending
moment, shear forces, and reactions based on which upper bound values can be generated using
Excel spreadsheets or Mathcad software. The author has developed such an approach (Sections
4.8 and 4.9).

Table 4.1 shows mathematical modeling, grid idealization of girder and flange, and box beam

and flange and strip idealization. When using finite elements, the side aspect ratio of a rectangular
finite element is : 5. For beam models the number of nodes shall not be less than fi ve.

The mathematical model of foundations shall represent soil properties, elastic properties,

piles, and soil-pile interaction. Since it is difficult to obtain an accurate model, upper bound and
lower bound solutions can be considered.

The elastic theory using small deflections: The slab and beam system is subjected to small

live load deflections. Hooke’s Law is based on small linear deflections when measured relative
to the thickness of the member.
The comfort level while traveling on a bridge with heavy trucks is also a consideration in
maintaining small deflections and small accelerations. Damping of vibrations will depend upon

the type of deck surface.
In the case of a simple beam, bending is accompanied by shear force. Pure shear force usu-
ally does not exist by itself and is complementary to bending moment. Also in beam bending,
the moment is equivalent to two equal and opposite axial forces, with one acting as compression
on one side of a neutral axis and the other acting as tension on the other side.

4.5.2 Analysis of Trusses
Trusses may be analyzed as a special case of plane frame or space frame analysis. Out-of-
plane buckling of slender compression members needs to be evaluated. Both steel and concrete
trusses are common. Three types of bridge trusses are used:
• Trusses supporting deck slab: Analysis shall consider composite action.

• Through trusses with transverse floor beams spanning across the bottom flanges of trusses
and braced at the top. Floor beams are composite with deck slab.