Reinforced Concrete Section Analysis – 4

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The spreadsheet presented in the previous post in this series uses the basic equation given below to find the location of the neutral axis:

For a cross section with any applied axial load at eccentricity e, measured from the compression face, and depth of the neutral axis X below the compression face:

INA = QNA(X + e)

Where QNA and INA are the first and second moments of area about the neutral axis.

To illustrate this relationship the value of INA has been plotted for a range of neutral axis positions for a typical precast bridge beam, shown below, and compared with the value QNA(X + e) for 5 different values of e.

The intersection of the INA and QNA(X + e) lines gives the depth of the neutral axis for the corresponding value of load eccentricity, e.  This is illustrated in the second graph, where the value of (INA – QNA(X + e)) is plotted against the depth of the neutral axis, X, for a load eccentricity of 1 metre above the compression face.  The intersection of this line with the X axis gives the depth of the neutral axis for the specified load eccentricity.

Ina and Qna(x+e) v Depth NA

Ina - Qna(X+e) v Depth NA

This entry was posted in Beam Bending, Excel, Newton, UDFs, Uncategorized and tagged , , , , . Bookmark the permalink.

One Response to Reinforced Concrete Section Analysis – 4

  1. Pingback: Reinforced Concrete Section Analysis - 5; Ultimate Limit State « Newton Excel Bach, not (just) an Excel Blog

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