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.

4th-order differential equation

Analysis of suspension bridges - Peery’s methods use integration

To calculate the area of influence lines, Simpson’s method has been applied. Simpson’s method results in a very accurate value if the number of divisions is even and each division has the same length.

The previous article (Curvature effects on a medium-span curved bridge) showed that we should be cautious to get reasonable torsional moments through simple beam analysis. One of the easiest ways to refine the results is to add more nodes at the inner support locations, however, we still have a question about “how many?”. Now we are reviewing the effect of curvature for bending moments. 
We are trying to find bending moments for three spans continuous curved girder, 150
ft + 223 ft + 150 ft = 523 ft, the radius is 1182’-6” as shown.

I girder vs. tub girder

Our next question may be “What are the differences between an I and a tub girder?”

Table of Contents

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A complex bridge is one of the most common engineering projects nowadays. This category of structures includes movable, cable-stayed, segmental concrete, and other bridges with unusual characteristics. These types of structures will require specialized expertise to design and build. One of our Expert Engineers, Yazeed Abuhassan, a Structural Design Engineer from Bergmann PC, shared his tips about designing a complex bridge.

One tip that could be useful to many is how he usually model the deck as an eccentric deck plate for moving load distribution purposes (creating an influence surface) without having to perform a beam/deck plate cut diagram to view the true moments in the composite girders.

1. Introduction

Finite Element Analysis or FEA is a numerical method used in engineering to solve complex problems by dividing a system or structure into smaller, simpler, and more manageable parts called finite elements. FEA involves the application of mathematical algorithms and computer software to simulate and analyze the behavior of a system under various conditions.