There are times when engineers would have to design and evaluate bridge structures that fall outside of the AASHTO design guideline. Therefore, when do we define a structure as irregular? How is evaluating an irregular bridge different from evaluating a regular bridge? How to minimize errors during the construction of irregular bridges? We invited midas expert Percy Penafiel, Professional Engineer Specialist from Nevada Department of Transportation, to answer some of the frequently asked questions from our users regarding evaluating irregular bridge structures. 

When we talk about prestressed concrete, the things that we are mostly concerned about are the compressive strength gain with respect to time, and the prestressing tendon relaxation with respect to time. Figure 1 shows various time-dependent effects for concrete including creep and shrinkage.

The factors that affect the creep rate include water/cement ratio, age and strength of the concrete when it is subjected to stress, and ambient temperature and humidity. Creep rate also depends on many other factors related to the quality of the concrete and conditions of exposure such as the type, amount, and maximum size of aggregate; type of cement; amount of cement paste; size and shape of the concrete mass; amount of steel reinforcement; and curing conditions (Robert Salca, tech support, midas UK).

For shrinkage, its rate decreases much faster with time compared with creep as shown in figure 1. Finer aggregates and finer gels result in increased shrinkage, the moisture content of the concrete and the relative humidity of the ambient medium have a big influence on carbonation shrinkage, and harder aggregates with higher modulus of elasticity decrease shrinkage. 

Concrete Shear Equation

Findings and remarks

Optimum crack angle θ

From the previous example, we can catch that there are some possible crack angle ranges for the given εx and vu/f’c. Now our question is which values of θ and β are the optimums? The previous example shows that, without considering longitudinal reinforcements, mostly (not always) the lowest crack angle results in the least number of stirrups. However, with considering longitudinal reinforcements, the optimum crack angle increases. The methodology to find out the optimum crack angle is proposed by Rahal and Collins (Background to the general method of shear design in the 1994 CSA-A23.3 standard, Canadian Journal of Civil Engineering, February 2011).

Solving the previous example from full iteration

Now it’s time to solve the previous example from full iteration. For simplicity, interaction with flexure is not considered. In other words, it is assumed that the status is in a pure shear condition which rarely exists in the real world.