search
Log In
1 vote

A rod of length $20$ mm is stretched to make a rod of length $40$ mm. Subsequently, it is compressed to make a rod of final length $10$ mm. Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is

  1. $-0.5$
  2. $-0.69$
  3. $-0.75$
  4. $-1.0$
in Mechanics of Materials 24.6k points
retagged by

1 Answer

1 vote
 
Best answer

True strain :

$\begin{align*} \epsilon_t = \sum \left ( \frac{\Delta L}{L} \right ) = \int_{L_i}^{L_f} \frac{dl}{l} = \ln \frac{L_f}{L_i} \end{align*}$

Now, here $L_f = 10 mm$  and  $L_i = 20 mm$

So, $\begin{align*} \epsilon_t = \ln \frac{10}{20} = -0.6931 \end{align*}$

Answer B

470 points
selected by
Answer:

Related questions

0 votes
0 answers
For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is $M(x)=5x^{2}+10x$, where $x$ is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at $x=10$ mm is __________.
asked Feb 27, 2017 in Mechanics of Materials Arjun 24.6k points
0 votes
0 answers
The rod $PQ$ of length $L=\sqrt{2}$ m, and uniformly distributed mass of $M=10$ kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces $OP$ and $OQ$. Assume acceleration due to gravity, $g=10 m/s^{2}$. The mass ... the figure is $(ML^{2}/12)$. At this instant, the magnitude of angular acceleration (in radian/$s^{2}$) of the rod is __________.
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
0 votes
0 answers
The principal stresses at a point in a critical section of a machine component are $\sigma _{1}=60$ MPa, $\sigma _{2}=5$ MPa and $\sigma _{3}=-40$ MPa. For the material of the component, the tensile yield strength is $\sigma _{y}=200$ MPa. According to the maximum shear stress theory, the factor of safety is $1.67$ $2.00$ $3.60$ $4.00$
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
0 votes
0 answers
For a single server with Poisson and exponential service time, the arrival rate is $12$ per hour. Which one of the following service rates will provide a steady state finite queue length? $6$ per hour $10$ per hour $12$ per hour $24$ per hour
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
0 votes
0 answers
The cantilever beam of Length $L$ and Flexural modulus $EI$ is subjected to a point load $P$ at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is $\dfrac{P^{2}L^{3}}{6EI} \\$ $\dfrac{P^{2}L^{3}}{3EI} \\$ $\dfrac{PL^{3}}{3EI} \\$ $\dfrac{PL^{3}}{6EI}$
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
...