Mechanics of Materials in SI Units

Russell C. Hibbeler

Chapter 2

Strain - all with Video Answers

Educators

Chapter Questions

Problem 1

An air-filled rubber ball has a diameter of 150 mm . If the air pressure within it is increased until the ball's diameter becomes 175 mm , determine the average normal strain in the rubber.

Narayan Hari

Narayan Hari

Numerade Educator

Problem 2

A thin strip of rubber has an unstretched length of 375 mm . If it is stretched around a pipe having an outer diameter of 125 mm , determine the average normal strain in the strip.

Narayan Hari

Numerade Educator

Problem 3

If the load $\mathbf{P}$ on the beam causes the end $C$ to be displaced 10 mm downward, determine the normal strain in wires $C E$ and $B D$.

Surendra Kumar

Numerade Educator

Problem 4

The force applied at the handle of the rigid lever causes the lever to rotate clockwise about the pin $B$ through an angle of $2^{\circ}$. Determine the average normal strain in each wire. The wires are unstretched when the lever is in the horizontal position.

Surendra Kumar

Numerade Educator

Problem 5

he pin-connected rigid rods $A B$ and $B C$ are inclined at $\theta=30^{\circ}$ when they are unloaded. When the force $\mathbf{P}$ is applied $\theta$ becomes $30.2^{\circ}$. Determine the average normal strain in wire $A C$.

Surendra Kumar

Numerade Educator

Problem 6

The wire $A B$ is unstretched when $\theta=45^{\circ}$. If a load is applied to the bar $A C$, which causes $\theta$ to become $47^{\circ}$, determine the normal strain in the wire.

Rashmi Sinha

Numerade Educator

Problem 7

If a horizontal load applied to the bar $A C$ causes point $A$ to be displaced to the right by an amount $\Delta L$, determine the normal strain in the wire $A B$. Originally, $\theta=45^{\circ}$.

Surendra Kumar

Numerade Educator

Problem 8

The rectangular plate is subjected to the deformation shown by the dashed line. Determine the average shear strain $\gamma_{x y}$ in the plate.

Surendra Kumar

Numerade Educator

Problem 9

The square deforms into the position shown by the dashed lines. Determine the shear strain at each of its corners, $A, B, C$, and $D$, relative to the $x, y$ axes. Side $D^{\prime} B^{\prime}$ remains horizontal.

Surendra Kumar

Numerade Educator

Problem 10

Part of a control linkage for an airplane consists of a rigid member $C B$ and a flexible cable $A B$. If a force is applied to the end $B$ of the member and causes it to rotate by $\theta=0.5^{\circ}$, determine the normal strain in the cable. Originally the cable is unstretched.

Surendra Kumar

Numerade Educator

Problem 11

Part of a control linkage for an airplane consists of a rigid member $C B$ and a flexible cable $A B$. If a force is applied to the end $B$ of the member and causes a normal strain in the cable of $0.004 \mathrm{~mm} / \mathrm{mm}$, determine the displacement of point $B$. Originally the cable is unstretched.

Surendra Kumar

Numerade Educator

Problem 12

Determine the shear strain $\gamma_{x y}$ at corners $A$ and $B$ if the plastic distorts as shown by the dashed lines.

Surendra Kumar

Numerade Educator

Problem 13

Determine the shear strain $\gamma_{x y}$ at corners $D$ and $C$ if the plastic distorts as shown by the dashed lines.

Surendra Kumar

Numerade Educator

Problem 14

The material distorts into the dashed position shown. Determine the average normal strains $\boldsymbol{\epsilon}_{\boldsymbol{x}}, \boldsymbol{\epsilon}_{\mathrm{y}}$ and the shear strain $\gamma_{x y}$ at $A$, and the average normal strain along line $B E$.

Surendra Kumar

Numerade Educator

Problem 15

The material distorts into the dashed position shown. Determine the average normal strains along the diagonals $A D$ and $C F$.

Surendra Kumar

Numerade Educator

Problem 16

The nylon cord has an original length $L$ and is tied to a bolt at $A$ and a roller at $B$. If a force $\mathbf{P}$ is applied to the roller, determine the normal strain in the cord when the roller is at $C$, and at $D$. If the cord is originally unstrained when it is at $C$, determine the normal strain $\epsilon_D^{\prime}$ when the roller moves to $D$. Show that if the displacements $\Delta_C$ and $\Delta_D$ are small, then $\epsilon_D^{\prime}=\epsilon_D-\epsilon_C$.

Surendra Kumar

Numerade Educator

Problem 17

. A thin wire, lying along the $x$ axis, is strained such that each point on the wire is displaced $\Delta x=k x^2$ along the $x$ axis. If $k$ is constant, what is the normal strain at any point $P$ along the wire?

Surendra Kumar

Numerade Educator

Problem 18

. The block is deformed into the position shown by the dashed lines. Determine the average normal strain along line $A B$.

Surendra Kumar

Numerade Educator

Problem 19

Nylon strips are fused to glass plates. When moderately heated the nylon will become soft while the glass stays approximately rigid. Determine the average shear strain in the nylon due to the load $\mathbf{P}$ when the assembly deforms as indicated.

Manik Pulyani

Numerade Educator

Problem 20

. The guy wire $A B$ of a building frame is originally unstretched. Due to an earthquake, the two columns of the frame tilt $\theta=2^{\circ}$. Determine the approximate normal strain in the wire when the frame is in this position. Assume the columns are rigid and rotate about their lower supports.

Rashmi Sinha

Numerade Educator

Problem 21

The rectangular plate is deformed into the shape shown by the dashed lines. Determine the average normal strain along diagonal $A C$, and the average shear strain at corner $A$ relative to the $x, y$ axes.

Surendra Kumar

Numerade Educator

Problem 22

. The corners $B$ and $D$ of the square plate are given the displacements indicated. Determine the shear strains at $A$ and $B$.

Surendra Kumar

Numerade Educator

Problem 23

Determine the shear strain $\gamma_{x y}$ at corners $A$ and $B$ if the plate distorts as shown by the dashed lines.

Surendra Kumar

Numerade Educator

Problem 24

Determine the shear strain $\gamma_{x y}$ at corners $D$ and $C$ if the plate distorts as shown by the dashed lines.

Surendra Kumar

Numerade Educator

Problem 25

Determine the average normal strain that occurs along the diagonals $A C$ and $D B$.

Surendra Kumar

Numerade Educator

Problem 26

If the unstretched length of the bowstring is 8875 mm , determine the average normal strain in the string when it is stretched to the position shown.

Averell Hause

Carnegie Mellon University

Problem 27

The triangular plate is fixed at its base, and its apex $A$ is given a horizontal displacement of 5 mm . Determine the shear strain, $\gamma_{x y}$, at $A$.

Narayan Hari

Numerade Educator

Problem 28

The triangular plate is fixed at its base, and its apex $A$ is given a horizontal displacement of 5 mm . Determine the average normal strain $\epsilon_x$ along the $x$ axis.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 29

The triangular plate is fixed at its base, and its apex $A$ is given a horizontal displacement of 5 mm . Determine the average normal strain $\epsilon_{x^{\prime}}$ along the $x^{\prime}$ axis.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 30

The rubber band $A B$ has an unstretched length of 1 m . If it is fixed at $B$ and attached to the surface at point $A^{\prime}$, determine the average normal strain in the band. The surface is defined by the function $y=\left(x^2\right) \mathrm{m}$, where $x$ is in meters.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 31

The rectangular plate is deformed into the shape shown by the dashed lines. Determine the average normal strain along diagonal $B D$, and the average shear strain at corner $B$ relative to the $x, y$ axes

Surendra Kumar

Numerade Educator

Problem 32

The nonuniform loading causes a normal strain in the shaft that can be expressed as $\epsilon_x=k \sin \left(\frac{\pi}{L} x\right)$, where $k$ is a constant. Determine the displacement of the center $C$ and the average normal strain in the entire rod.

Surendra Kumar

Numerade Educator

Problem 33

The fiber $A B$ has a length $L$ and orientation $\theta$. If its ends $A$ and $B$ undergo very small displacements $u_A$ and $v_B$ respectively, determine the normal strain in the fiber when it is in position $A^{\prime} B^{\prime}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 34

If the normal strain is defined in reference to the final length $\Delta s^{\prime}$, that is,

$$
\epsilon^{\prime}=\lim _{\Delta r^{\prime} \rightarrow 0}\left(\frac{\Delta s^{\prime}-\Delta s}{\Delta s^{\prime}}\right)
$$

instead of in reference to the original length, Eq. 2-2, show that the difference in these strains is represented as a second-order term, namely, $\epsilon-\epsilon^{\prime}=\boldsymbol{\epsilon} \epsilon^{\prime}$.

Surendra Kumar

Numerade Educator