ESO202A/204: MECHANICS OF SOLIDS SEMESTER I: 2013-14

ESO202A-204/Dr Durgesh Rai/S-I-2013-14/Page 1 OF 1

Homework #5: Material-Property Relations & Yield/Failure Criterion Due September 26, 2013

Prob.#1

Determine the elongation of the square hollow bar when it is subjected to the axial force P=100 kN. If this axial force is increased to P=360 kN and released, find the permanent elongation of the bar. The bar is made of a metal alloy having a stress–strain diagram which can be approximated as shown. Note that the unloading curve is parallel to the initial loading curve. Prob.#2

The stress–strain diagram for a bone is shown, and can be described by the equation

6 10.45 10 0.36 10 2 3 where is in kPa. Determine (a) the yield strength assuming a 0.3% offset and (b) the modulus of toughness and the amount of elongation of a 200-mm long region just before it fractures if failure occurs at = 0.12 mm/mm. Note that modulus of toughness is the area under stress-strain curve upto fracture while modulus of resilience is the area up to yield point.

Prob.#3

A shear spring is made by bonding the rubber annulus to a rigid fixed ring and a plug.When an axial load P is placed on the plug, show that the slope at point y in the rubber is

tan tan[ (2 )]dy dr P hGr For small angles we

can write (2 )dy dr P hGr Integrate this

expression and evaluate the constant of integration using the condition that y=0 at r=ro. From the rcompute the deflection y =δ of the plug.

esult

Prob.#4

For the case of plane stress, show that Hooke’s law can be written as

2 2( ), ((1 ) (1 )x x y y y

E E)x

The principal strains at a point on the aluminum fuselage of a jet aircraft are and

and Determine the associated principal stresses at the point in the same plane. E=70 GPa and ν=0.33.

61 780 10

62 400 10

Prob.#5

The state of plane stress shown occurs in a machine component made of a steel with yield strength of 325 MPa. Using the maximum-distortion energy (von Mises) criterion, determine at what value of o yielding will occur.

Prob.#6

Solve the Prob. #5 using the maximum shear stress (Tresca) criterion.