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I'm currently writing a lab report following an experiment to compare the Theory of Macaulays method to the lab results. My query is, None of the lectures or teaching I received has considered the beam and it's ability to sagg under it's own weight. The experimental results were quite different in comparison. Until I included the weight of the beam as a UDL which provided a more accurate result. Is there any reason way the weight of the beam is not considered in the method? and Should I include this in my initial analysis or leave it until the discussion later on in the report to clarify why there's such a variance ?

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2 Answers 2

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The weight of the beam is frequently ignored in homework and at the lecture or the class, for simplicity. Unless it is given in the question.

And for the second part of your question, I would say first do the test without self-weight and then with that, with a comment explaining the difference, this way it will be more clear. As you already know the weight of the beam moment is,

$$M_x=\frac{w}{2}\langle x-a\rangle^2 $$

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Macaulay and UDL

If by Macaulay's method you mean the use of singularity function (the use of Macaulay's bracket <>), then the method can account for distributed load.

For example the moment for a Uniform distributed load (UDL) starting at point x=a and carrying until the end of the beam is :

$$M(x) = \frac{w}{2}\langle x-a\rangle^2$$

Discrepancy in the results

You state that:

The experimental results were quite different in comparison

However, you are not providing any numerical data for the loading conditions, the structure (material and geometry) and on the deflection results. Without those it is not possible to make an assessment.

However, since this is part of a lab exercise, I am inclined to doubt that the lecturers would not include the self weight, if it was important.

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