Exercise Mohr's Circle

 Mechanical Behavior of Materials

HW-1

1.  A body is loaded under a stress state σ_x = 400, σ_y = 100, τ_xy = 120, τ_yz = τ_zx = σ_z = 0.

a. Sketch the Mohr’s circle diagram.

b. Calculate the principal stresses.

• What is the largest shear stress in the body?

    2.      A state of stress is given by

σ₁₁ = −500 MPa,

σ₂₂ = 300 MPa,

σ₁₂ = 150 MPa.

Determine the principal stresses and the maximum shear stress, as well as their   orientation, using the Mohr circle construction.

3.  Consider an aluminum single crystal under a stress state σ_x = 250 MPa, σ_y =−50 MPa, τ_yz = τ_zx = τ_xy = σ_z = 0, where x = [100], y = [010], and z = [001].

a. What is the resolved shear stress, τ_nd, on the (111) plane in the [1-10] direction, that is, with n = [111], d = [1-10]?

b. What is the resolved shear stress on the (11-1) plane in the [101] direction?

Caustic Soda Calculations of Molarity

Molecular Formula : NaOH
Molecular Weight : 35.5+16+1.008=52.508=53 (gm/mole) approximately
Nature : Alkaline
Sold In Solid state

For Liquid solution we use its specific amount dissolved in water as per required

For Example,If we want to prepare 1 molar (Molarity) solution of NaOH
First understand what is Molarity
Molarity is moles/dm3
Formula:
Concentration(Amount per decimeter cube)=Molarity*Molecular weight
=1(moles/dm3)*52.508 (gm/moles)
= 52.508 gm/dm3

It means 52.508 gm of solid NaOH in 1000 ml (1 Liter) of distilled water

Now, if you are asked to prepare 100ml,0.5 molar solution from above prepared 1 molar solution then,
Remember,
M1 * V1 = M2 * V2
where,
M1= molarity of required solution = 0.5 molar
V1= volume of required solution =100ml
M2= molarity of given solution =1 molar
V2= volume of given solution =?
(we find the volume of 1 molar solution which we used to prepare 0.5 molar solution)
Now use above Formula,
1 * V1 = 0.5 *100
V1 = 50 ml (of 1 molar solution)
You have to prepare 100ml of 0.5 molar solution thus take 50 ml 1 molar solution and mix it with 50 ml distilled water. This is your 100ml .5 molar Solution.
Note: Don't mix 50ml 1 molar solution with 100ml water its then not 0 .5 molar solution. You could also check it by reverse formula.

Questions:
What is difference between basic and alkaline?
What is Molarity,Molality and Normality?
Calculate the molarity of parent solution if its volume is 30ml used to prepare 300 ml of 0.3 molar solution?