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## Homework Statement

Stress tensor at a point Q in a body has components:

p

_{ij}:

| 1 -1 0 |

|-1 2 1 |

| 0 1 3 |

(i) Calculate components of the stress force

**f**across a small area of surface at Q normal to

**n**= (2,1,-1).

(ii) The component of

**f**in the direction of

**n**is called the normal stress while the component of

**f**tangential to the surface is called the shear stress. Find the normal stress and the shear stress at Q.

## Homework Equations

**f**= f

_{i}= p

_{ij}n

_{j}

## The Attempt at a Solution

(i) I take the stress force at Q across the surface normal to

**n**to be the product of the stress tensor p

_{ij}and the normal vector

**n**and arrive at:

**f**= (1x2 + -1x1 + 0x-1)

**i**+ (-1x2 + 2x1 + 1x-1)

**j**+ (0x2 + 1x1 +3x-1)

**k**

= ( 1, -1, -2 )

(ii) I think this is a simple algebraic exercise - ie what components of ( 1, -1, -2) project onto

**n**to give the normal stress, and which components project onto the plane normal to

**n**to give the shear stress.

Am I reading this correctly, and what is the most efficient way of computing these components? I can't help but think the answer might be staring at me from within the tensor p

_{ij}.