Chapter 6, Yield and Fracture Video Solutions, Mechanics of Materials

02:15

Problem 2

Repeat the previous problem, but with the pressure vessel now being closed-ended.

Keshav Singh

Numerade Educator

01:14

Problem 3

A steel plate is clad with a thin layer of aluminum on both sides at room temperature, and the temperature then raised. At what temperature increase $\Delta T$ will the aluminum yield?

Mayukh Banik

Numerade Educator

03:38

If the temperature in the previous problem is raised $40 \backslash$ circ $\}$ C beyond the value at which yielding occurs, and is thereafter lowered back to room temperature, what is the residual stress left in the aluminum?

Jordan Moore

Numerade Educator

03:34

Problem 5

Copper alloy is subjected to the stress state $\sigma_{x}=100, \sigma_{y}=-200, \tau_{x y}=100$ (all in MPa). Determine whether yield will occur according to the (a) Tresca and (b) von Mises criterion.

Khoobchandra Agrawal

Numerade Educator

04:24

Problem 6

Repeat the previous problem, but with the stress state $\sigma_{x}=190, \sigma_{y}=90, \tau_{x y}=120$ (all in MPa).

Hunza Gilgit

Numerade Educator

04:22

Problem 7

A thin-walled tube is placed in simultaneous tension and torsion, causing a stress state as shown here. Construct a plot of $\tau / \sigma_{Y}$ vs. $\sigma / \sigma_{Y}$ at which yield will occur according to the (a) Tresca and (b) von Mises criterion. ( $\sigma$ is the tensile yield stress.)

Khoobchandra Agrawal

Numerade Educator

01:26

Problem 8

A solid circular steel shaft is loaded by belt pulleys at both ends as shown. Determine the diameter of the shaft required to avoid yield according to the von Mises criterion, with a factor of safety of 2 .

Surendra Kumar

Numerade Educator

04:04

Problem 9

For polycarbonate, the kinetic parameters in $6.1 .4$ are found to be are $\dot{\epsilon}_{0}=448 s^{-1}, E_{Y}^{*}=309 \mathrm{~kJ} / \mathrm{mol}$, and $V *=3.9 \times 10^{-3} \mathrm{~m}^{3} / \mathrm{mol}$. Find the yield stress $\sigma_{Y}$ at a strain rate of $\dot{\epsilon}=10^{2} s^{-1}$ and temperature $40^{\circ} \mathrm{C} .$

Anthony Han

Numerade Educator

01:26

Problem 10

Yield stresses (in MPa) have been measured at various strain rates and temperatures as follows:

Manik Pulyani

Numerade Educator

01:42

Problem 11

The yield stress of a polymer is measured to be $20 \mathrm{MPa}$ at a temperature of $300 \mathrm{~K}$ and a strain rate of $10^{-3} \mathrm{~s}^{-1}$. When the strain rate is doubled from this value, the yield stress is observed to increase by $10 \%$. What is the apparent activation volume for yield in this case?

Anatole Borisov

Numerade Educator

01:50

Problem 12

Show the von Mises stress can be written in index notation as $\sigma_{M}=\sqrt{3 \Sigma_{i j} \Sigma_{i j} / 2}$

Manik Pulyani

Numerade Educator

02:47

Problem 13

A sample of linear polyethylene was tested in uniaxial loading at $T=23^{\circ} \mathrm{C}$ and $\dot{\epsilon}=10^{-3} \mathrm{~s}^{-1}$. The yield stress $\sigma_{Y}$ was found to be $30.0$ MPa in tension and $31.5$ MPa in compression. Determine the pressure-dependency constant $A$ in Eqn. 3 .

Khoobchandra Agrawal

Numerade Educator

00:48

Problem 14

A circular shaft of radius $\mathrm{R}$ is subjected to a torque $T$.
(a) What value of $T$ will be just large enough to induce yielding at the outer surface?
(b) As the value of $T$ is increased beyond the level found in (a), determine the radius re within which the material is still in the elastic range.
(c) What value of $T$ will make the shaft fully plastic; i.e. $r_{e}=0 ?$

Hast Aggarwal

Numerade Educator

06:37

Problem 15

A two-element truss frame is constructed of steel with the geometry shown. What load $P$ can the frame support without yielding in either element?

Satpal Satpal

Numerade Educator

02:48

Problem 16

A three-element truss frame is constructed of steel with the geometry shown. What load $P$ can the frame support before all three elements have yielded?

Chai Santi

Numerade Educator

07:27

Problem 17

If the frame of the previous problem is loaded until all three members have yielded and the load then reduced to zero, find the residual stress in the central element.

Katie Mcalpine

Numerade Educator

04:08

Problem 18

A rigid beam is hinged at one end as shown and supported by two vertical rods as shown.
(a) What load $P$ can the structure support before both vertical rods have yielded?
(b) What is the residual stress in the vertical rods after the load has been reduced to zero?