07.10.24 Stress Transformation

How are principal stresses related to the orientation of the planes?

• Principal stresses occur only in two-dimensional stress states.
• Principal stresses are always equal in all directions.
• Principal stresses are the normal stresses acting on the planes, where shear stress is zero.

• Principal planes are defined by maximum shear stress.

If the shear stress τ_xyτ_yx is zero, the principal stresses are equal to which stresses?

• σx and σy.

• τxy and τyx

• σx and σy.

• The principal stresses are equal to the maximum shear stress.

Which of the following conditions would result in zero principal stresses?

• A state of hydrostatic stress

• A state of uniform loads or no external loads applied.

• A state of uniaxial tension.
• A state of triaxial compression.

The major and minor principal stresses at a point are 3MPa and -3MPa respectively. The maximum shear stress at the point is

• 6MPa

• 0 MPa

• -1 MPa
• 3 MPa

Consider the following statements:

1. On a Principal plane, only normal stress acts

2. On a Principal plane, both normal and shear stresses acts

3. On a Principal plane, only shear stress acts

4. Isotropic state of stress is independent of frame of reference.

Which of the above statements is/are correct?

• 1,2,4

• 1 , 4

• 2,4

• 1,3,4

If a body is acted upon by a set of mutually perpendicular shear stresses, the diagonal planes are likely to have-

• Only normal stress.
• tension only

• compression only

• tension and compression

A thin-walled tube experiences internal pressure causing σ_x=200 MPa,

σ_y=50 MPa, and τ_xy=30 MPa. Calculate average normal stress?

• 122MPa

• 125MPa.

• 120MPa.

• 130MPa.