Mechanics of Materials

R. C. Hibbeler

Chapter 2

Strain - all with Video Answers

Educators

Chapter Questions

Problem 1

An air-filled rubber ball has a diameter of 6 in. If the air pressure within it is increased until the ball's diameter becomes 7 in., 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 15 in. If it is stretched around a pipe having an outer diameter of 5 in., determine the average normal strain in the strip.

Narayan Hari

Numerade Educator

Problem 3

The rigid beam is supported by a pin at $A$ and wires $B D$ and $C E .$ If the load $\mathbf{P}$ on the beam causes the end $C$ to be displaced $10 \mathrm{mm}$ downward, determine the normal strain developed in wires $C E$ and $B D.$

Narayan Hari

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 developed in each wire. The wires are unstretched when the lever is in the horizontal position.

Narayan Hari

Numerade Educator

Problem 5

The two wires are connected together at $A$. If the force $\mathbf{P}$ causes point $A$ to be displaced horizontally $2 \mathrm{mm}$ determine the normal strain developed in each wire.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 6

The rubber band of unstretched length $2 r_{0}$ is forced down the frustum of the cone. Determine the average normal strain in the band as a function of $z.$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 7

The 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 developed in wire $A C.$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 8

Part of a control linkage for an airplane consists of a rigid member $C B D$ and a flexible cable $A B .$ If a force is applied to the end $D$ of the member and causes it to rotate by $\theta=0.3^{\circ},$ determine the normal strain in the cable. Originally the cable is unstretched.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 9

Part of a control linkage for an airplane consists of a rigid member $C B D$ and a flexible cable $A B .$ If a force is applied to the end $D$ of the member and causes a normal strain in the cable of $0.0035 \mathrm{mm} / \mathrm{mm},$ determine the displacement of point $D$. Originally the cable is unstretched.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 10

The corners of the square plate are given the displacements indicated. Determine the shear strain along the edges of the plate at $A$ and $B$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 11

The corners of the square plate are given the displacements indicated. Determine the average normal strains along side $A B$ and diagonals $A C$ and $D B.$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 12

The piece of rubber is originally rectangular. Determine the average shear strain $\gamma_{x y}$ at $A$ if the corners $B$ and $D$ are subjected to the displacements that cause the rubber to distort as shown by the dashed lines.

Narayan Hari

Numerade Educator

Problem 13

The piece of rubber is originally rectangular and subjected to the deformation shown by the dashed lines. Determine the average normal strain along the diagonal $D B$ and side $A D.$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 14

The force P applied at joint $D$ of the square frame causes the frame to sway and form the dashed rhombus. Determine the average normal strain developed in wire $A C .$ Assume the three rods are rigid.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 15

The force $\mathbf{P}$ applied at joint $D$ of the square frame causes the frame to sway and form the dashed rhombus. Determine the average normal strain developed in wire $A E$ Assume the three rods are rigid.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 16

The triangular plate $A B C$ is deformed into the shape shown by the dashed lines. If at $A, \varepsilon_{A B}=0.0075$ $\varepsilon_{A C}=0.01$ and $\gamma_{x y}=0.005$ rad, determine the average normal strain along edge $B C.$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 17

The plate is deformed uniformly into the shape shown by the dashed lines. If at $A, \gamma_{x y}=0.0075$ rad., while $\epsilon_{A B}=\epsilon_{A F}=0,$ determine the average shear strain at point $G$ with respect to the $x^{\prime}$ and $y^{\prime}$ axes.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 18

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

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 19

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

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 20

The piece of plastic is originally rectangular. Determine the average normal strain that occurs along the diagonals $A C$ and $D B.$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 21

The rectangular plate is deformed into the shape of a parallelogram shown by the dashed lines. Determine the average shear strain $\gamma_{x y}$ at corners $A$ and $B.$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 22

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

Narayan Hari

Numerade Educator

Problem 23

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

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 24

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

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 25

The square rubber block is subjected to a shear strain of $\gamma_{x y}=40\left(10^{-6}\right) x+20\left(10^{-6}\right) y,$ where $x$ and $y$ are in mm. This deformation is in the shape shown by the dashed lines, where all the lines parallel to the $y$ axis remain vertical after the deformation. Determine the normal strain along edge $B C$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 26

The square plate is deformed into the shape shown by the dashed lines. If $D C$ has a normal strain $\epsilon_{x}=0.004, D A$ has a normal strain $\epsilon_{y}=0.005$ and at $D, \gamma_{x y}=0.02$ rad, determine the average normal strain along diagonal $C A.$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 27

The square plate is deformed into the shape shown by the dashed lines. If $D C$ has a normal strain $\epsilon_{x}=0.004, D A$ has a normal strain $\epsilon_{y}=0.005$ and at $D, \gamma_{x y}=0.02$ rad, determine the shear strain at point $E$ with respect to the $x^{\prime}$ and $y^{\prime}$ axes.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 28

The wire is subjected to a normal strain that is defined by $\epsilon=(x / L) e^{-(x / L)^{2}} .$ If the wire has an initial length $L,$ determine the increase in its length.

Narayan Hari

Numerade Educator

Problem 29

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 $A.$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 30

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 $B.$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 31

The nonuniform loading causes a normal strain in the shaft that can be expressed as $\epsilon_{x}=k x^{2},$ where $k$ is a constant. Determine the displacement of the end $B$. Also, what is the average normal strain in the rod?

Narayan Hari

Numerade Educator

Problem 32

The rubber block is fixed along edge $A B,$ and edge $C D$ is moved so that the vertical displacement of any point in the block is given by $v(x)=\left(v_{0} / b^{3}\right) x^{3}$. Determine the shear strain $\gamma_{x y}$ at points $(b / 2, a / 2)$ and $(b, a)$.

Khoobchandra Agrawal

Khoobchandra Agrawal

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, that is,
\[\epsilon_{n}^{\prime}=\lim _{p \rightarrow p^{\prime}}\left(\frac{\Delta s^{\prime}-\Delta s}{\Delta s^{\prime}}\right)\]
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, $\epsilon_{n}-\epsilon_{n}^{\prime}=\epsilon_{n} \epsilon_{n}^{\prime}.$

Narayan Hari

Numerade Educator