Page 202 - Bridge and Highway Structure Rehabilitation and Repair

CHAPTER 4 AN ANALYTICAL APPROACH TO FRACTURE AND FAILURE 177

4.16.3 Compatibility Model (Strips and Elements)
1. In a research project carried out at Northwestern University as a follow-up of recommenda-
tions of the ACI Shear Committee, use of high strength concrete in the design of reinforced
and prestressed girders was investigated. The author investigated the validity and application
of MCFT to high strength concrete beams for both buildings and bridges. Many of AASHTO
formulae for shear design have developed from widely used ACI codes including ACI 318.
The method and results are briefly described here.

A finite element approach was used. The beam is idealized into strips or multi-layered

elements.
Typical elements lie in the vertical plane of beams, with the depth of element equal to the
depth of each strip (Figure 4.20a).
2. Two types of elements are considered:
• Elements containing longitudinal rebars and transverse stirrups only (Figure 4.20b)
• Elements containing transverse stirrups only (Figure 4.20c).
The assumptions used are:
1. Steel and concrete have plasticity.
2. No bond exists between concrete and web reinforcement.
3. The angle of cracking varies and is dependent on the ratio of percentage of longitudinal
steel to transverse steel.

(a) (b)

Figure 4.20 (a) Idealization of beam, (b) element-2,
(c) (c) element-3.