C8.1 Equations of Strain Transformation

In essence, strain transformation is pretty much the same as stress transformation; except that σ_x and σ_y are swapped with ε_x and ε_y. *However τ_xy is actually converted to γ_xy/2 instead (you can check any textbooks for the derivation to see why).

Again, the equations are presented for completeness sake and it’s still recommended for you to use the Mohr’s circle instead, which we will cover in Chapter 8.2.

General equations of strain transformation

C8.1 Equations of Strain Transformation

In essence, strain transformation is pretty much the same as stress transformation; except that σ_x and σ_y are swapped with ε_x and ε_y. *However τ_xy is actually converted to γ_xy/2 instead (you can check any textbooks for the derivation to see why).

Again, the equations are presented for completeness sake and it’s still recommended for you to use the Mohr’s circle instead, which we will cover in Chapter 8.2.

General equations of strain transformation

And here are the formulas for principal strains ε₁, ε₂ and the maximum in-plane shear strain γ_{max in-plane}:

formula for principal strain and maximum in-plane shear strain

*Always, always remember to multiply γ_x'y'/2 by 2 after conversion to get the final γ_x'y'. Students always miss this crucial last step as they get carried away after performing the long transformations.

Let’s look at an example now.

And here are the formulas for principal strains ε₁, ε₂ and the maximum in-plane shear strain γ_{max in-plane}:

formula for principal strain and maximum in-plane shear strain

*Always, always remember to multiply γ_x'y'/2 by 2 after conversion to get the final γ_x'y'. Students always miss this crucial last step as they get carried away after performing the long transformations.

Let’s look at an example now.