Any-shaped Shear Walls

The program generates the Pn-Mn nominal-capacity interaction diagram for any-shaped concrete section with any arrangement of non-prestressed reinforcing steel.

The program is entirely based on the equilibrium of forces and compatibility of deformations. The following assumptions have been made:
a) Strains are directly proportional to the distance from the neutral axis.
b) Plane sections before bending remain plane after bending.
c) For concrete, the Hognestad stress distribution is used.
d) For reinforcing steel, the elasto-plastic model is used, taking into account the strain hardening effect.

The section is divided in horizontal layers, or segments of the same thickness, whose number is defined by the user. The strain, and therefore the stress, is assumed to be constant throughout the thickness of each segment, and equal to that present at its mid-depth.

Of course, the greater the number of segments, the more precise the results obtained. The designer's judgement plays an important role in deciding how accurate are the results obtained. The maximum number of segments allowed is 100.

Input Data

The data required includes the materials' properties, the ultimate concrete strain, the total section length, and the number of segments in which that section length will be divided. In addition, the program requires the width and steel area of each defined segment. The required input data is presented schematically in the figure below.

Example

As an example, consider the channel section shown below reinforced as indicated, and subjected to a moment about its weak principal axis causing tension at the web and compression at the ends of the flanges. Find the capacity interaction diagram of the section.

Output

In this example the section was divided into 36 layers, 2 inches thick each, whose properties are shown in the fugure to the right above. When all the data has been entered, choose the Solve option from the Design menu to generate the interaction diagram.

This program's template with the example data is shown in the figure to the right below

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Procedure

The interaction diagram is generated by first defining the position of the neutral axis. The strain and stress in each segment are then computed, and the equilibrium of forces checked. This way, one point in the interaction diagram is found. The procedure is repeated changing the neutral axis to another position, and so on, until the diagram is completed.