The midas model is for a multi-channel prestressed girders bridge 30 ft span and 24.75 ft width. The bridge is composed of 9-channel prestressed girders placed side by side. The bridge was modeled with frame elements for the girder's webs and plate elements for the girder's flange. Bridge dimensions and midas models are shown below.

The scary part of FEM is sometimes FEM gives wrong results without any error message. The analysis may be meaningless if an engineer cannot check or interpret the results. Let’s consider a simple example similar to the case from Dr. Gallagher (Finite Element Analysis: Fundamentals, 1975).

For the previous example, we can use high-order triangular elements. This element has six nodes per element and assumes the displacement is quadratic within an element. Also, each side edge can be curved, as shown.

Creep Analysis 5 MIDAS Example 

Continuing on to the third part of this multi-part blog, another option is a quadrilateral element. As always, let’s start with an example.

So you have learned about column buckling under a point load applied at the end of the column, do you know if columns can buckle under their self-weight? Let’s explore it and run some analyses using midas Civil.

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.

Composite Section Analysis

Finally we came to the composite section analysis. One of the best examples is from Dr. Gilbert and Dr. Ranzi (Example 5.10, Time-dependent behavious of concrete structures, CRC Press, 2010.)

The Question

4th-order differential equation

Eq(2) is a 4th-order differential equation, and we can imagine it is not simple to solve.