# Moment Curvature Plot: Explaining the Significance of the Slope

• Civilian2
In summary, the conversation discusses a beam with point loads and how to calculate the curvature and elastic modulus of the beam using deflection measurements. The slope of the moment versus curvature plot represents the elastic modulus of the steel times the second moment of area. It is also referred to as the flexural rigidity of the beam, which is used to calculate strain. This information can be separated if the dimensions of the beam are known. The conversation concludes with the realization that the topic took longer to figure out than it was worth.
Civilian2
Hi, I was really hoping someone could help me...

I have a beam, simply supported and I place 2 point loads on it (equidistant from either end). I measure a range of deflections (of the beam) using gauges as I increase the loads (always having the same load at each point). I measure these deflections at each point load and at the centre of the beam.

By using a BMD (or just by experience) we know that the moment will be constant inbetween the two point loads (i.e over the centre of the beam).

By knowing the difference in deflection between the point at the centre of the beam (max deflection) and the point under one of the loads, I can calculate the curvature of that constant moment section of the beam.

I can then plot the Moment verus the curvature (x-axis). I get a straight line.

Can someone explain to me in layman terms what I get? As in, what the slope of the graph represents?

I get a straight line for this plot. Looking at it, I think I'm looking at a similar thing to the elastic section of a stress strain curve, so I'm thinking that slope of the moment curvature plot is the elastic modulus of the beam. I'm unsure about this though.

Anyone able to explain? The significance of this slope?

Right, well I've figured it out.

So for those of you who care... its actually an extremely simple connection... the hours I spent completely unwarranted.

I in bending theory you find that

Curvature, or, 1/r = M/EI
where r is the radiius of curvature and M is the moment.

The slope of a moment vs curvature plot is M/(1/r)
Which is M * r

Since 1/r = M/EI then r = EI/M
therefore M*r = M * EI/M
which equals EI

which is the elastic modulus of the steel times the second moment of area.

Although I can't separate the two, EI give me the flexural rigidity of the beam which allows me to calculate strain.

So you see, this was one of those things that took me a lot more time than it was worth lol.

If you know the dimensions of the beam, you may well be able to separate the two

Last edited:
Whoa. Thanks for digging this one up. Just a little over two years old now...

## 1. What is a moment curvature plot?

A moment curvature plot is a graphical representation of the relationship between the moment applied to a structural element and the resulting curvature. It is commonly used in structural engineering to analyze the behavior of beams, columns, and other structural elements under various loads.

## 2. Why is the slope of a moment curvature plot important?

The slope of a moment curvature plot represents the stiffness of a structural element. It can provide important information about the structural integrity and load-bearing capacity of a building or structure. A steeper slope indicates a higher stiffness, while a flatter slope indicates a lower stiffness.

## 3. How is the slope of a moment curvature plot calculated?

The slope of a moment curvature plot is calculated by dividing the change in moment by the change in curvature. This is known as the flexural rigidity of the structural element and is typically denoted by the symbol EI.

## 4. What does a positive or negative slope on a moment curvature plot indicate?

A positive slope on a moment curvature plot indicates that the structural element is under tension, while a negative slope indicates that it is under compression. This information is important for understanding the behavior and potential failure modes of the element under different loads.

## 5. How is a moment curvature plot used in structural design?

Moment curvature plots are commonly used in structural design to determine the appropriate size and reinforcement of structural elements. By analyzing the slope and shape of the plot, engineers can make informed decisions about the strength and stability of a structure, ensuring it can withstand expected loads and forces.

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