# Help needed for transformation of stresses in beer and johnston book

• chiraganand
In summary, the conversation is about a person having doubts about the transformation of stresses in the Mechanics of Materials book by Beer and Johnston. They are trying to resolve the force components in the x' and y' directions but are getting a different solution than what is shown in the book. They are using the Pythagorean theorem to determine the resolved forces. The person asks for help and another person suggests writing it out in math. The first person then explains their calculations and realizes their mistake in taking the reference wrong.
chiraganand
Transformation of stresses in beer and johnston mechanics of materials. While reading the section on trsnformation of stresses they have solved by using the force components in x' and y' directions. I have attached a screenshot of the relevant page and the figure. I have few doubt as to how the force components in the x direction are resolved as shown in the book.

When i tried resolving the forces in x' and y' direction i am not getting the solution as in the book but a totally differnt solution. using the pythagoras theorem to determine the resolved forces.

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• beer and johnston transformation of stresses.jpg
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Can you show us what you got when you tried? It's a pretty straightforward problem of resolving vectors into their components.

whenever is try to resolve the horizontal force in the x' direction i am getting the force component as sigma x into area.. whereas in the book he's getting it as sigma x into (cos theeta) ^2 ... don't know where i am gong wrong..

Well, I can't make sense of what you're trying to say. Could you write it out in math?

vela said:
Well, I can't make sense of what you're trying to say. Could you write it out in math?

When i resolve the component of the horizontal force σ ΔA cos θ in the x' direction i am getting = σ ΔA
whereas in the book it is σ (ΔA cos θ)cosθ

Why are you dividing by the cosine?

coz when i a m resolving it i am getting cos θ = σΔAcosθ/(component in x' direction)

You do realize that σΔAcosθ is the hypotenuse, right? It's not one of the legs go the triangle as you appear to be assuming.

yep now i got it.. taking the reference wrong..

## 1. What is the concept of stress transformation in the Beer and Johnston book?

The concept of stress transformation in the Beer and Johnston book refers to the process of determining the equivalent stresses acting on an element in different directions. This is important in engineering design as it helps to ensure that a structure can withstand different types of loading.

## 2. Why is stress transformation important in engineering?

Stress transformation is important in engineering because it allows engineers to analyze the strength and stability of a structure under different loading conditions. This helps to ensure the safety and reliability of the structure.

## 3. How is stress transformation calculated?

Stress transformation is calculated using the equations and principles outlined in the Beer and Johnston book. This involves using trigonometric functions, such as sine and cosine, to calculate the stresses acting in different directions.

## 4. What is the difference between principal stresses and maximum shear stresses?

Principal stresses are the maximum and minimum stresses acting on an element in different directions, while maximum shear stresses are the stresses that act parallel to the maximum normal stress. In other words, principal stresses indicate the state of stress at a point, while maximum shear stresses indicate the magnitude of the shear stress at that point.

## 5. How can stress transformation be applied in real-world engineering problems?

Stress transformation can be applied in real-world engineering problems by using it to analyze the stresses acting on different components of a structure, such as beams or columns. This information can then be used to determine the strength and stability of the structure and make any necessary design modifications.

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