## # Solid Mechanics Assignment

Notice: N is group number.

Send me your group’s name I will inform you your group number (N).

Send soft copy of your assignment through email (students@fhejazi.com) and  hard copy to my mail box in civil department up to your final exam.

Reference: Book, “Continuum Mechanics Fundamental”. S. Valliappan

Question 1

Find all stress strain relations and relevant details for reinforce concrete, steel and soil which are available in the literature. You can refer to any book, journal paper, conference paper or technical report. Add references for any stress strain relation.

Question 2

Show that the equivalent stress for the state of principal stress system (σ1, σ2, σ3) is always between the bounds obtained for the case of uniaxial loading and pure shear loading.

Question 3

The state of stress at a point is given by:

σx = (1000N) kPa
σy = (-2000N) kPa
σz = (500N) kPa

If the yield stress for the material under uniaxial test is (3000N) kPa, state whether there will be yielding as per Tresca criterion and von Mises criterion.

Question 4

The principal stresses at a point are given as follows:

σ2 = (5000N) kPa
σ3 = (8000N) kPa

If the yield stress for the material is (1000N) kPa, what is the minimum value of σ1 for yielding to occur as per:

(a) Tresca criterion and
(b) von Mises criterion.

Question 5

The state of stress at a point in a c – Φ material is given as:

σx = (900N) kPa
σy = (500N) kPa
σz = (800N) kPa
τxy = (200N) kPa

If the value of c = (1000N) kPa and Φ=0 , will there be yielding at that point?

Question 6

At a point in a material, the state of stress is given by:

σx = (1000N) kPa
σy = (2000N) kPa
τxy = (-500N) kPa

If the yield stress for the material is (2500N) kPa, modulus of elasticity is (30000N) kPa and Poisson’s ratio is 0.3, determine the strain components.
If the point is in the plastic range assume work hardening parameter (plastic modulus) to be 1/10 of modulus of elasticity
Use von Mises yield criterion and Prandtl-Reuss equations.