# How to calculate flexural yield strength?

• tellmethetruth
In summary, the attachment illustrates a simple riveted joint. The rivet is used to demonstrate the stress being applied to the extruded-cut round part of the epoxy piece. The rivet is merely a point of application for the stress, and is not the actual stressors. The actual stressors are the load and geometry of the structure.
tellmethetruth
TL;DR Summary
I need to calculate how much force a part can take before breaking.
I'm trying to learn some new engineering, so if something I ask doesn't make sense -- remember I'm new to this.

I need to calculate how much force a part can take before breaking.

Material: resin (Flexural Yield Strength: 6752 psi) - (Tensile Strength: 3390 psi) - (Density [lbs/gal]: 9.64) - (Durometer Hardness: 78) -- if this isn't enough info, substitute your own material as an example.

Force: variable (make any up), applied by rivets onto contact surface (refer to attachment link for specifications) ibb.co/b2d7T87 (for higher quality pic)If someone could at least give me the steps needed to calculate this.

#### Attachments

• Cross section.PNG
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Strength of Materials Short Course

Generally speaking there are three major strength criteria for most construction materials.
They are:
Tensional Strength – Pulling apart
Compression Strength – Pushing together
Shear Strength – Slicing across.
Each of these criteria have a ‘yield’ value and an ‘ultimate’ value, determined by the shape of the Stress – Strain curve for the material. In some materials these two points are close together while in other materials they are far apart.

Most all calculations used in determining a structure’s ability to carry a load center around these three characteristics; or some combination of them. (The word ‘structure’ herein means anything from a simple riveted joint to a huge building.)

There are other material and dimensional characteristics that effect load bearing performance of a given design. Some of these are: design geometry optimization, part tolerance, machining accuracy, surface finish of materials, surface hardness, heat treatment and environmental considerations of temperature, humidity, cleanliness, corrosion, etc.

BTW – A structure is not considered a failure only when it breaks apart. A structure is generally considered a failure at the point of permanent deformation of one of the load bearing elements. This may occur much earlier than total destruction or the two may occur simultaneously.

Bending, flexure and torsional characteristics of a structure are controlled by the above three major material strength values and the geometry of the part as related to the point of load application.

If you are pulling on the ends of a simple round cross section steel shaft the calculation is very simple but, if you have an irregular shaped beam sticking out of a wall, with a load out at the end, the calculation becomes a bit more complicated.

jrmichler and JBA
AZFIREBALL said:
Strength of Materials Short Course

Generally speaking there are three major strength criteria for most construction materials.
They are:
Tensional Strength – Pulling apart
Compression Strength – Pushing together
Shear Strength – Slicing across.
Each of these criteria have a ‘yield’ value and an ‘ultimate’ value, determined by the shape of the Stress – Strain curve for the material. In some materials these two points are close together while in other materials they are far apart.

Most all calculations used in determining a structure’s ability to carry a load center around these three characteristics; or some combination of them. (The word ‘structure’ herein means anything from a simple riveted joint to a huge building.)

There are other material and dimensional characteristics that effect load bearing performance of a given design. Some of these are: design geometry optimization, part tolerance, machining accuracy, surface finish of materials, surface hardness, heat treatment and environmental considerations of temperature, humidity, cleanliness, corrosion, etc.

BTW – A structure is not considered a failure only when it breaks apart. A structure is generally considered a failure at the point of permanent deformation of one of the load bearing elements. This may occur much earlier than total destruction or the two may occur simultaneously.

Bending, flexure and torsional characteristics of a structure are controlled by the above three major material strength values and the geometry of the part as related to the point of load application.

If you are pulling on the ends of a simple round cross section steel shaft the calculation is very simple but, if you have an irregular shaped beam sticking out of a wall, with a load out at the end, the calculation becomes a bit more complicated.
Thanks for the information.

What calculation would I need to determine the breaking point? Please refer to the attachment posted.

Are you asking this in regard to the simple riveted joint illustrated in the attachment, or some other structure?

AZFIREBALL said:
Are you asking this in regard to the simple riveted joint illustrated in the attachment, or some other structure?
Yes regarding the rivet in the attachment. This wouldn't be a traditional steel rivet joint, but a 2 piece screw rivet.
I'd like to know how much force it takes until the bottom head of the rivet, breaks/deforms the epoxy resin part (highlighted in red).
The rivet is merely to demonstrate the force being applied on the extruded-cut round part of the epoxy piece.

OK. Now we need to identify all the possible failure modes of this structure given the illustrated geometry and loads applied. This will help you find the 'weakest link' in your design.
In what ways do you think the structure might fail? Please be very precise. Try to visualize the actual failure interface (paths and directions). Also identify any distortions that might be caused by twisting, bending or flexing of the structures during the application of the loads. Identify the loading characteristics. Is the load applied slowly or rapidly? Is it intermittent, cycling, or steady state? What is its periodicity?
All of the above will allow you to calculate the strength of the structure in each of the possible failure modes identified and thereby provide data for the selection of materials for the structure or to evaluate the suitability of the given materials, or to point out the need for a redesign.

AZFIREBALL said:
OK. Now we need to identify all the possible failure modes of this structure given the illustrated geometry and loads applied. This will help you find the 'weakest link' in your design.
In what ways do you think the structure might fail? Please be very precise. Try to visualize the actual failure interface (paths and directions). Also identify any distortions that might be caused by twisting, bending or flexing of the structures during the application of the loads. Identify the loading characteristics. Is the load applied slowly or rapidly? Is it intermittent, cycling, or steady state? What is its periodicity?
All of the above will allow you to calculate the strength of the structure in each of the possible failure modes identified and thereby provide data for the selection of materials for the structure or to evaluate the suitability of the given materials, or to point out the need for a redesign.
The bottom face of the rivet head that's in contact with the part during the force taking place, will first deform and eventually break, as the center between the two holes begins to deform from stress.
All sharp angle corners will create a weak breaking point. There won't be any torsion force, just a static non-linear load.
The steady load is applied "slowly", relative to a shock force. Periodicity = 1.
What I'm really looking for is equations that can provide empirical data, that will allow optimization of material, thickness, etc.

Yes, I know you are just looking for equations that can provide empirical data. I am not just giving you a fish...I am teaching you HOW to fish. Don't you see this?
Shall I continue, or not?

AZFIREBALL said:
Yes, I know you are just looking for equations that can provide empirical data. I am not just giving you a fish...I am teaching you HOW to fish. Don't you see this?
Shall I continue, or not?
I know how to fish, I just need the right bait (equations).

If you know how to fish, then you should be able to figure it out for yourself. I am done.

AZFIREBALL said:
If you know how to fish, then you should be able to figure it out for yourself. I am done.
In other words "I don't have an answer, so I'm going to have a fit and leave"

tellmethetruth said:
Summary: I need to calculate how much force a part can take before breaking.

If someone could at least give me the steps needed to calculate this.
Step 1: Buy this book: Fundamentals of Machine Component Design, by Juvinall and Marshek.
Step 2: Read the entire book.
Step 3: Apply what you learned to your problem.

If you have trouble understanding that book, then get a book on the mechanics of materials. If the mechanics of materials book gives you trouble, then get a book on statics. If that book gives you trouble, then a book on physics. If that book gives you trouble, then a book on calculus. It is difficult to answer your question because it requires material from the third year of a mechanical engineering curriculum.

I am not being facetious or snarky here. You received some excellent advice from @AZFIREBALL, especially in post #2. Providing an equation is not enough without understanding how to apply that equation.

jrmichler said:
Step 1: Buy this book: Fundamentals of Machine Component Design, by Juvinall and Marshek.
Step 2: Read the entire book.
Step 3: Apply what you learned to your problem.

If you have trouble understanding that book, then get a book on the mechanics of materials. If the mechanics of materials book gives you trouble, then get a book on statics. If that book gives you trouble, then a book on physics. If that book gives you trouble, then a book on calculus. It is difficult to answer your question because it requires material from the third year of a mechanical engineering curriculum.

I am not being facetious or snarky here. You received some excellent advice from @AZFIREBALL, especially in post #2. Providing an equation is not enough without understanding how to apply that equation.
I think you're being snarky without realizing it.
Telling me to buy a book is the equivalent of saying, "google it". The point of a forum is to get an answer for your question, not go on a goose chase. I understand there's more than applying an equation, it's a matter of understanding, and clearly I've proven I understand.
I mean, you guys would be miserable professors, and I sincerely hope you're not. Like they say, if you can't explain it to a 5 year old; you don't know it well enough yourself. I'm starting to think people here aren't engineers, or at most are pompous first year students.

I gave azfireball all of the information he asked for, to which he got upset because I asked for equations??
I know how to apply physics...I'm just asking for the applicable equations.
What a miserable first experience on this forum. A joke at best.

## 1. What is flexural yield strength?

Flexural yield strength is the maximum stress that a material can withstand before it permanently deforms or breaks under bending. It is an important mechanical property that measures a material's ability to resist bending forces.

## 2. How is flexural yield strength calculated?

Flexural yield strength is typically calculated by applying a three-point or four-point bending test to a sample of the material. The yield strength is then determined by measuring the stress at which the material begins to deform and comparing it to the cross-sectional area of the sample.

## 3. What factors can affect the flexural yield strength of a material?

The flexural yield strength of a material can be affected by a variety of factors, including the material's composition, microstructure, and processing methods. Other factors such as temperature, humidity, and loading rate can also have an impact on the yield strength.

## 4. How is flexural yield strength different from tensile yield strength?

Flexural yield strength measures a material's resistance to bending forces, while tensile yield strength measures its resistance to pulling forces. In general, materials tend to have a higher tensile yield strength than flexural yield strength, as they are more likely to experience pulling forces in real-world applications.

## 5. Why is flexural yield strength important in materials testing?

Flexural yield strength is an important mechanical property that helps determine a material's suitability for specific applications. It is particularly important in materials used for structural purposes, such as building materials, as it can indicate the material's ability to withstand bending forces without failure.

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