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 [...]

Reinforced Concrete Section Analysis - 3

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The theory presented in the previous 2 posts in this series has been incorporated into an Excel UDF, allowing concrete and reinforcement stresses and strains to be evaluated quickly and easily for reinforced and prestressed members of complex cross-section, subject to combined bending and axial load.
The Excel file also includes UDFs [...]

Reinforced Concrete Section Analysis - 2

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Pseudo-code for elastic analysis of a layered reinforced concrete section under eccentric axial load and pre-stress load:
 Read data
‘For each reinforcement layer: Find area, first moment of area about top ,and depth of centroid.
Find total reinforcement section properties over all layers
For each reinforcement layer: adjust section properties for compression from the top surface to the [...]

The history of the theory of beam bending - Part 2

Before moving on from Galileo, Mariotte and Parent, let’s examine a peculiarity arising from the testing of their formulas.
Jacques Heyman in “The Science of Structural Engineering” states:
“… then the new calculation of bending strength [by Parent] gave a coefficient or 1/6 instead of the 1/2 of Galileo or 1/3 of Mariotte. For the first time, [...]

Reinforced Concrete Section Analysis - 1

Increased yield strengths of reinforcing steels have increased the importance of the Serviceability Limit State in reinforced concrete design, with SLS reinforcement stresses, crack widths, or deflections often controlling the design.
Elastic analysis of a rectangular section under pure bending can be solved easily with a quadratic equation, but for more complex shapes or combined bending and [...]

The history of the theory of beam bending - Part 1

The theory of the flexural strength and stiffness of beams is now attributed to Bernoulli and Euler, but developed over almost 400 years, with several twists, turns and dead ends on the way.
Galileo Galilei is often credited with the first published theory of the strength of beams in bending, but with the discovery of “The Codex [...]