The discussion centers on calculating shear strain using the equations εx = σx / E and εy = -vσx / E, where σx represents stress in the x-direction, E is the modulus of elasticity, and v is Poisson's ratio. Participants confirm that εx = σx / E is correct when stresses in the y and z directions are zero. The conversation highlights the importance of correctly rearranging equations and understanding the relationships between εx, εy, σx, and σy, particularly in the context of linear algebraic equations.
PREREQUISITESStudents in engineering and materials science, particularly those studying mechanics of materials and seeking to understand stress-strain relationships and their applications in real-world scenarios.
This is correct.chetzread said:
You did the algebra wrong.chetzread said:
Chestermiller said:
I'm going to let you figure that out. You have 2 linear algebraic equations in two unknowns, ##\sigma_x## and ##\sigma_y##. You should have learned how to solve such equations in first year algebra.chetzread said:
Are you sure ? Can you please look at it again ?Chestermiller said:
Yes, I'm sure that your answer is wrong, and I'm also sure that the book's answer is wrong? In the book answer, the terms in the numerators should have plus signs, not minus signs. Your answer should have a denominator which matches the book's denominator.chetzread said:
do you mean it should be σx = (Eεx + vσy ) / (1-(v^2)) ?Chestermiller said:
It's time for you to learn to use LaTex.$$\sigma_x=\frac{E(\epsilon_x+\nu \epsilon_y)}{(1-\nu^2)}$$chetzread said:
do you mean this ?Chestermiller said:
C'mon man. You need to learn algebra.chetzread said:
why my working is wrong ? I noticed that in your working , you used 2 equations which is $$E\epsilon_x$$ and $$E\epsilon_y$$Chestermiller said:
Like I said: Put your working in the Precalculus Mathematics Homework forum and let them help you figure out what you did wrong.chetzread said:
Of course you need to use two equations. There are two unknowns: ##\sigma_x## and ##\sigma_y##
sorry , just to verify my concept again... is εy = σy / E ?Chestermiller said:
check a third book.chetzread said:
It's really hard for me to get a third source . I already searched thru many websites , but i couldn't find this . I could only get simple explanation of poisson ratio, but not the the explanation about when the force is applied in a direction , find the strain in another direction .Chestermiller said:
so, εx= σx / E is correct ?Chestermiller said:
Yes, as long as the stresses in the y and z directions are zero.chetzread said:
