Mechanics of Materials

R. C. Hibbeler

Chapter 1

Stress - all with Video Answers

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Chapter Questions

Problem 1

The shaft is supported by a smooth thrust bearing at $B$ and a journal bearing at $C .$ Determine the resultant internal loadings acting on the cross section at $E$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 2

Determine the resultant internal normal and shear force in the member at (a) section a–a and (b) section b–b, each of which passes through the centroid A. The 500-lb load is applied along the centroidal axis of the member.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 3

Determine the resultant internal loadings acting on section $b-b$ through the centroid $C$ on the beam.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 4

The shaft is supported by a smooth thrust bearing at $A$ and a smooth journal bearing at $B$. Determine the resultant internal loadings acting on the cross section at $C$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 5

Determine the resultant internal loadings acting on the cross section at point $B$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 6

Determine the resultant internal loadings on the cross section at point $D$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 7

Determine the resultant internal loadings at cross sections at points $E$ and $F$ on the assembly.

Prashant Bana

Numerade Educator

Problem 8

The beam supports the distributed load shown. Determine the resultant internal loadings acting on the cross section at point $\begin{array}{lllll}C . & \text { Assume the reactions at the }\end{array}$ supports $A$ and $B$ are vertical.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 9

The beam supports the distributed load shown. Determine the resultant internal loadings acting on the cross section at point $D$. Assume the reactions at the supports $A$ and $B$ are vertical.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 10

The boom $D F$ of the jib crane and the column $D E$ have a uniform weight of $50 \mathrm{lb} / \mathrm{ft}$. If the supported load is 300 Ib, determine the resultant internal loadings in the crane on cross sections at points $A, B,$ and $C$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 11

Determine the resultant internal loadings acting on the cross sections at points $D$ and $E$ of the frame.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 12

Determine the resultant internal loadings acting on the cross sections at points $F$ and $G$ of the frame.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 13

The blade of the hacksaw is subjected to a pretension force of $F=100 \mathrm{N}$. Determine the resultant internal loadings acting on section $a-a$ that passes through point $D$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 14

The blade of the hacksaw is subjected to a pretension force of $F=100 \mathrm{N}$. Determine the resultant internal loadings acting on section $b-b$ that passes through point $D$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 15

The beam supports the triangular distributed load shown. Determine the resultant internal loadings on the cross section at point $C .$ Assume the reactions at the supports $A$ and $B$ are vertical.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 16

The beam supports the distributed load shown. Determine the resultant internal loadings on the cross section at points $D$ and $E .$ Assume the reactions at the supports $A$ and $B$ are vertical.

Hast Aggarwal

Numerade Educator

Problem 17

The shaft is supported at its ends by two bearings $A$ and $B$ and is subjected to the forces applied to the pulleys fixed to the shaft. Determine the resultant internal loadings acting on the cross section at point $D$. The 400 -N forces act in the $-z$ direction and the 200 -N and 80 -N forces act in the $+y$ direction. The journal bearings at $A$ and $B$ exert only $y$ and $z$ components of force on the shaft.

Hast Aggarwal

Numerade Educator

Problem 18

The shaft is supported at its ends by two bearings $A$ and $B$ and is subjected to the forces applied to the pulleys fixed to the shaft. Determine the resultant internal loadings acting on the cross section at point $C .$ The 400 -N forces act in the $-z$ direction and the 200 -N and 80 -N forces act in the $+y$ direction. The journal bearings at $A$ and $B$ exert only $y$ and $z$ components of force on the shaft.

Hast Aggarwal

Numerade Educator

Problem 19

The hand crank that is used in a press has the dimensions shown. Determine the resultant internal loadings acting on the cross section at point $A$ if a vertical force of 50 lb is applied to the handle as shown. Assume the crank is fixed to the shaft at $B$

Hast Aggarwal

Numerade Educator

Problem 20

Determine the resultant internal loadings acting on the cross section at point $C$ in the beam. The load $D$ has a mass of $300 \mathrm{kg}$ and is being hoisted by the motor $M$ with constant velocity.

Hast Aggarwal

Numerade Educator

Problem 21

Determine the resultant internal loadings acting on the cross section at point $E .$ The load $D$ has a mass of $300 \mathrm{kg}$ and is being hoisted by the motor $M$ with constant velocity.

Hast Aggarwal

Numerade Educator

Problem 22

The metal stud punch is subjected to a force of $120 \mathrm{N}$ on the handle. Determine the magnitude of the reactive force at the pin $A$ and in the short link $B C$. Also, determine the resultant internal loadings acting on the cross section at point $D$

Hast Aggarwal

Numerade Educator

Problem 23

Determine the resultant internal loadings acting on the cross section at point $E$ of the handle arm, and on the cross section of the short link $B C$

Hast Aggarwal

Numerade Educator

Problem 24

Determine the resultant internal loadings acting on the cross section at point $C .$ The cooling unit has a total weight of 52 kip and a center of gravity at $G$

Hast Aggarwal

Numerade Educator

Problem 25

Determine the resultant internal loadings acting on the cross section at points $B$ and $C$ of the curved member.

Hast Aggarwal

Numerade Educator

Problem 26

Determine the resultant internal loadings acting on the cross section of the frame at points $F$ and $G$. The contact at $E$ is smooth.

Hast Aggarwal

Numerade Educator

Problem 27

The pipe has a mass of $12 \mathrm{kg} / \mathrm{m}$. If it is fixed to the wall at $A$, determine the resultant internal loadings acting on the cross section at $B$

Anand Jangid

Numerade Educator

Problem 28

The brace and drill bit is used to drill a hole at $O .$ If the drill bit jams when the brace is subjected to the forces shown, determine the resultant internal loadings acting on the cross section of the drill bit at $A$

Hast Aggarwal

Numerade Educator

Problem 29

The curved rod $A D$ of radius $r$ has a weight per length of $w .$ If it lies in the horizontal plane, determine the resultant internal loadings acting on the cross section at point $B .$ Hint: The distance from the centroid $C$ of segment $A B$ to point $O$ is $C O=0.9745 r$

Hast Aggarwal

Numerade Educator

Problem 30

A differential element taken from a curved bar is shown in the figure. Show that $d N / d \theta=V, d V / d \theta=-N$ $d M / d \theta=-T,$ and $d T / d \theta=M$

Hast Aggarwal

Numerade Educator

Problem 31

The supporting wheel on a scaffold is held in place on the leg using a 4 -mm-diameter pin. If the wheel is subjected to a normal force of $3 \mathrm{kN}$, determine the average shear stress in the pin. Assume the pin only supports the vertical 3-kN load.

Hast Aggarwal

Numerade Educator

Problem 32

Determine the largest intensity $w$ of the uniform loading that can be applied to the frame without causing either the average normal stress or the average shear stress at section $b-b$ to exceed $\sigma=15$ MPa and $\tau=16 \mathrm{MPa}$ respectively. Member $C B$ has a square cross section of $30 \mathrm{mm}$ on each side.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 33

The bar has a cross-sectional area $A$ and is subjected to the axial load $P .$ Determine the average normal and average shear stresses acting over the shaded section, which is oriented at $\theta$ from the horizontal. Plot the variation of these stresses as a function of $\theta\left(0 \leq \theta \leq 90^{\circ}\right)$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 34

The small block has a thickness of 0.5 in. If the stress distribution at the support developed by the load varies as shown, determine the force $\mathbf{F}$ applied to the block, and the distance $d$ to where it is applied.

Hast Aggarwal

Numerade Educator

Problem 35

If the material fails when the average normal stress reaches 120 psi, determine the largest centrally applied vertical load $\mathbf{P}$ the block can support.

Hast Aggarwal

Numerade Educator

Problem 36

If the block is subjected to a centrally applied force of $P=6$ kip, determine the average normal stress in the material. Show the stress acting on a differential volume element of the material.

Hast Aggarwal

Numerade Educator

Problem 37

The plate has a width of $0.5 \mathrm{m}$. If the stress distribution at the support varies as shown, determine the force $\mathbf{P}$ applied to the plate and the distance $d$ to where it is applied.

Hast Aggarwal

Numerade Educator

Problem 38

The board is subjected to a tensile force of 200 lb. Determine the average normal and average shear stress in the wood fibers, which are oriented along plane $a-a$ at $20^{\circ}$ with the axis of the board.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 39

The boom has a uniform weight of 600 lb and is hoisted into position using the cable $B C$. If the cable has a diameter of 0.5 in., plot the average normal stress in the cable as a function of the boom position $\theta$ for $0^{\circ} \leq \theta \leq 90^{\circ}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 40

Determine the average normal stress in each of the 20-mm-diameter bars of the truss. Set $P=40 \mathrm{kN}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 41

If the average normal stress in each of the 20-mm-diameter bars is not allowed to exceed $150 \mathrm{MPa}$ determine the maximum force $\mathbf{P}$ that can be applied to joint $C$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 42

Determine the maximum average shear stress in pin $A$ of the truss. A horizontal force of $P=40 \mathrm{kN}$ is applied to joint $C .$ Each pin has a diameter of $25 \mathrm{mm}$ and is subjected to double shear.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 43

If $P=5 \mathrm{kN}$, determine the average shear stress in the pins at $A, B,$ and $C .$ All pins are in double shear, and each has a diameter of $18 \mathrm{mm}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 44

Determine the maximum magnitude $P$ of the loads the beam can support if the average shear stress in each pin is not to exceed 80 MPa. All pins are in double shear, and each has a diameter of $18 \mathrm{mm}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 45

The column is made of concrete having a density of $2.30 \mathrm{Mg} / \mathrm{m}^{3} .$ At its top $B$ it is subjected to an axial compressive force of $15 \mathrm{kN}$. Determine the average normal stress in the column as a function of the distance $z$ measured from its base.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 46

The beam is supported by two rods $A B$ and $C D$ that have cross-sectional areas of $12 \mathrm{mm}^{2}$ and $8 \mathrm{mm}^{2}$, respectively. If $d=1 \mathrm{m},$ determine the average normal stress in each rod.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 47

The beam is supported by two rods $A B$ and $C D$ that have cross-sectional areas of $12 \mathrm{mm}^{2}$ and $8 \mathrm{mm}^{2}$, respectively. Determine the position $d$ of the $6-\mathrm{kN}$ load so that the average normal stress in each rod is the same.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 48

If $P=15 \mathrm{kN}$, determine the average shear stress in the pins at $A, B,$ and $C .$ All pins are in double shear, and each has a diameter of $18 \mathrm{mm}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 49

The railcar docklight is supported by the $\frac{1}{8}$ -in.-diameter pin at $A$. If the lamp weighs 4 lb, and the extension arm $A B$ has a weight of $0.5 \mathrm{lb} / \mathrm{ft}$, determine the average shear stress in the pin needed to support the lamp. Hint: The shear force in the pin is caused by the couple moment required for equilibrium at $A$

Anand Jangid

Numerade Educator

Problem 50

The plastic block is subjected to an axial compressive force of 600 N. Assuming that the caps at the top and bottom distribute the load uniformly throughout the block, determine the average normal and average shear stress acting along section $a-a$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 51

The two steel members are joined together using a $30^{\circ}$ scarf weld. Determine the average normal and average shear stress resisted in the plane of the weld.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 52

The bar has a cross-sectional area of $400\left(10^{-6}\right) \mathrm{m}^{2}$. If it is subjected to a triangular axial distributed loading along its length which is 0 at $x=0$ and $9 \mathrm{kN} / \mathrm{m}$ at $x=1.5 \mathrm{m},$ and to two concentrated loads as shown, determine the average normal stress in the bar as a function of $x$ for $0 \leq x<0.6 \mathrm{m}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 53

The bar has a cross-sectional area of $400\left(10^{-6}\right) \mathrm{m}^{2}$. If it is subjected to a uniform axial distributed loading along its length of $9 \mathrm{kN} / \mathrm{m},$ and to two concentrated loads as shown, determine the average normal stress in the bar as a function of $x$ for $0.6 \mathrm{m}<x \leq 1.5 \mathrm{m}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 54

The two members used in the construction of an aircraft fuselage are joined together using a $30^{\circ}$ fish-mouth weld. Determine the average normal and average shear stress on the plane of each weld. Assume each inclined plane supports a horizontal force of 400 lb.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 55

The 2 -Mg concrete pipe has a center of mass at point $G .$ If it is suspended from cables $A B$ and $A C$ determine the average normal stress in the cables. The diameters of $A B$ and $A C$ are $12 \mathrm{mm}$ and $10 \mathrm{mm},$ respectively.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 56

The 2-Mg concrete pipe has a center of mass at point $G .$ If it is suspended from cables $A B$ and $A C$ determine the diameter of cable $A B$ so that the average normal stress in this cable is the same as in the 10 -mm-diameter cable $A C$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 57

The pier is made of material having a specific weight $\gamma$. If it has a square cross section, determine its width $w$ as a function of $z$ so that the average normal stress in the pier remains constant. The pier supports a constant load $\mathbf{P}$ at its top where its width is $w_{1}$

Anand Jangid

Numerade Educator

Problem 58

Rods $A B$ and $B C$ have diameters of $4 \mathrm{mm}$ and $6 \mathrm{mm}$, respectively. If the $3 \mathrm{kN}$ force is applied to the ring at $B$, determine the angle $\theta$ so that the average normal stress in each rod is equivalent. What is this stress?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 59

The uniform bar, having a cross-sectional area of $A$ and mass per unit length of $m$, is pinned at its center. If it is rotating in the horizontal plane at a constant angular rate of $\omega$, determine the average normal stress in the bar as a function of $x$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 60

The bar has a cross-sectional area of $400\left(10^{-6}\right) \mathrm{m}^{2}$ If it is subjected to a uniform axial distributed loading along its length and to two concentrated loads, determine the average normal stress in the bar as a function of $x$ for $0<x \leq 0.5 \mathrm{m}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 61

The bar has a cross-sectional area of $400\left(10^{-6}\right) \mathrm{m}^{2}$. If it is subjected to a uniform axial distributed loading along its length and to two concentrated loads, determine the average normal stress in the bar as a function of $x$ for $0.5 \mathrm{m}<x \leq 1.25 \mathrm{m}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 62

The prismatic bar has a cross-sectional area $A$. If it is subjected to a distributed axial loading that increases linearly from $w=0$ at $x=0$ to $w=w_{0}$ at $x=a,$ and then decreases linearly to $w=0$ at $x=2 a$, determine the average normal stress in the bar as a function of $x$ for $0 \leq x<a$

Neelesh Sharma

Numerade Educator

Problem 63

The prismatic bar has a cross-sectional area $A$. If it is subjected to a distributed axial loading that increases linearly from $w=0$ at $x=0$ to $w=w_{0}$ at $x=a,$ and then decreases linearly to $w=0$ at $x=2 a$, determine the average normal stress in the bar as a function of $x$ for $a<x \leq 2 a$

Neelesh Sharma

Numerade Educator

Problem 64

The bars of the truss each have a cross-sectional area of 1.25 in $^{2}$. Determine the average normal stress in members $A B, B D,$ and $C E$ due to the loading $P=6$ kip. State whether the stress is tensile or compressive.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 65

The bars of the truss each have a cross-sectional area of 1.25 in $^{2}$. If the maximum average normal stress in any bar is not to exceed 20 ksi, determine the maximum magnitude $P$ of the loads that can be applied to the truss.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 66

Determine the largest load $\mathbf{P}$ that can be applied to the frame without causing either the average normal stress or the average shear stress at section $a-a$ to exceed $\sigma=150 \mathrm{MPa}$ and $\tau=60 \mathrm{MPa},$ respectively. Member $C B$ has a square cross section of $25 \mathrm{mm}$ on each side.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 67

Determine the greatest constant angular velocity $\omega$ of the flywheel so that the average normal stress in its rim does not exceed $\sigma=15$ MPa. Assume the rim is a thin ring having a thickness of $3 \mathrm{mm}$, width of $20 \mathrm{mm}$, and a mass of $30 \mathrm{kg} / \mathrm{m} .$ Rotation occurs in the horizontal plane. Neglect the effect of the spokes in the analysis. Hint: Consider a free-body diagram of a semicircular segment of the ring. The center of mass for this segment is located at $\hat{r}=2 r / \pi$ from the center.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 68

The radius of the pedestal is defined by $r=\left(0.5 e^{-0.08 y^{2}}\right) \mathrm{m},$ where $y$ is in meters. If the material has a density of $2.5 \mathrm{Mg} / \mathrm{m}^{3},$ determine the average normal stress at the support.

Narayan Hari

Numerade Educator

Problem 69

If $A$ and $B$ are both made of wood and are $\frac{3}{8}$ in. thick, determine to the nearest $\frac{1}{4}$ in. the smallest dimension $h$ of the vertical segment so that it does not fail in shear. The allowable shear stress for the segment is $\tau_{\text {allow }}=300$ psi.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 70

The lever is attached to the shaft $A$ using a key that has a width $d$ and length of $25 \mathrm{mm}$. If the shaft is fixed and a vertical force of $200 \mathrm{N}$ is applied perpendicular to the handle, determine the dimension $d$ if the allowable shear stress for the key is $\tau_{\text {allow }}=35 \mathrm{MPa}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 71

The connection is made using a bolt and nut and two washers. If the allowable bearing stress of the washers on the boards is $\left(\sigma_{b}\right)_{\text {allow }}=2 \mathrm{ksi},$ and the allowable tensile stress within the bolt shank $S$ is $\left(\sigma_{t}\right)_{\text {allow }}=18 \mathrm{ksi}$, determine the maximum allowable tension in the bolt shank.The bolt shank has a diameter of 0.31 in., and the washers have an outer diameter of 0.75 in. and inner diameter (hole) of 0.50 in.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 72

The tension member is fastened together using two bolts, one on each side of the member as shown. Each bolt has a diameter of 0.3 in. Determine the maximum load $P$ that can be applied to the member if the allowable shear stress for the bolts is $\tau_{\text {allow }}=12 \mathrm{ksi}$ and the allowable average normal stress is $\sigma_{\text {allow }}=20 \mathrm{ksi}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 73

The steel swivel bushing in the elevator control of an airplane is held in place using a nut and washer as shown in Fig. $(a) .$ Failure of the washer $A$ can cause the push rod to separate as shown in Fig. $(b)$. If the maximum average shear stress is $\tau_{\max }=21$ ksi, determine the force $\mathbf{F}$ that must be applied to the bushing. The washer is $\frac{1}{16}$ in. thick.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 74

The spring mechanism is used as a shock absorber for a load applied to the drawbar $A B .$ Determine the force in each spring when the 50 -kN force is applied. Each spring is originally unstretched and the drawbar slides along the smooth guide posts $C G$ and $E F$. The ends of all springs are attached to their respective members. Also, what is the required diameter of the shank of bolts $C G$ and $E F$ if the allowable stress for the bolts is $\sigma_{\text {allow }}=150 \mathrm{MPa} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 75

Determine the size of square bearing plates $A^{\prime}$ and $B^{\prime}$ required to support the loading. Take $P=1.5$ kip. Dimension the plates to the nearest $\frac{1}{2}$ in. The reactions at the supports are vertical and the allowable bearing stress for the plates is $\left(\sigma_{b}\right)_{\text {allow }}=400$ psi.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 76

Determine the maximum load $\mathbf{P}$ that can be applied to the beam if the bearing plates $A^{\prime}$ and $B^{\prime}$ have square cross sections of 2 in. $\times 2$ in. and 4 in. $\times 4$ in. respectively, and the allowable bearing stress for the material is $\left(\sigma_{b}\right)_{\text {allow }}=400$ psi.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 77

Determine the required diameter of the pins at $A$ and $B$ to the nearest $\frac{1}{16}$ in. if the allowable shear stress for the material is $\tau_{\text {allow }}=6 \mathrm{ksi} .$ Pin $A$ is subjected to double shear, whereas pin $B$ is subjected to single shear.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 78

If the allowable tensile stress for wires $A B$ and $A C$ is $\sigma_{\text {allow }}=200 \mathrm{MPa}$, determine the required diameter of each wire if the applied load is $P=6 \mathrm{kN}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 79

If the allowable tensile stress for wires $A B$ and $A C$ is $\sigma_{\text {allow }}=180 \mathrm{MPa}$, and wire $A B$ has a diameter of $5 \mathrm{mm}$ and $A C$ has a diameter of $6 \mathrm{mm}$, determine the greatest force $P$ that can be applied to the chain.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 80

The cotter is used to hold the two rods together. Determine the smallest thickness $t$ of the cotter and the smallest diameter $d$ of the rods. All parts are made of steel for which the failure normal stress is $\sigma_{\text {tail }}=500 \mathrm{MPa}$ and the failure shear stress is $\tau_{\text {fail }}=375 \mathrm{MPa}$. Use a factor of safety of $(\mathrm{F} \cdot \mathrm{S} \cdot)_{t}=2.50$ in tension and $(\mathrm{FS} .)_{s}=1.75$ in shear

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 81

Determine the required diameter of the pins at $A$ and $B$ if the allowable shear stress for the material is $\tau_{\text {allow }}=100 \mathrm{MPa} .$ Both pins are subjected to double shear.

Anand Jangid

Numerade Educator

Problem 82

The steel pipe is supported on the circular base plate and concrete pedestal. If the thickness of the pipe is $t=5 \mathrm{mm}$ and the base plate has a radius of $150 \mathrm{mm}$ determine the factors of safety against failure of the steel and concrete. The applied force is $500 \mathrm{kN}$, and the normal failure stresses for steel and concrete are $\left(\sigma_{ \text {fail } )_{\text {st }}}=350 \mathrm{MPa}\right.$ and $\left(\sigma_{ \text {fail } )_{\text {con }}}=25$ MPa, respectively. \right.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 83

The boom is supported by the winch cable that has a diameter of 0.25 in. and an allowable normal stress of $\sigma_{\text {allow }}=24$ ksi. Determine the greatest weight of the crate that can be supported without causing the cable to fail if $\phi=30^{\circ} .$ Neglect the size of the winch.

Anand Jangid

Numerade Educator

Problem 84

The boom is supported by the winch cable that has an allowable normal stress of $\sigma_{\text {allow }}=24 \mathrm{ksi}$. If it supports the 5000 lb crate when $\phi=20^{\circ},$ determine the smallest diameter of the cable to the nearest $\frac{1}{16}$ in.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 85

The assembly consists of three disks $A, B,$ and $C$ that are used to support the load of 140 kN. Determine the smallest diameter $d_{1}$ of the top disk, the largest diameter $d_{2}$ of the opening, and the largest diameter $d_{3}$ of the hole in the bottom disk. The allowable bearing stress for the material is $\left(\sigma_{b}\right)_{\text {allow }}=350 \mathrm{MPa}$ and allowable shear stress is $\tau_{\text {allow }}=125 \mathrm{MPa}$

Anand Jangid

Numerade Educator

Problem 86

The two aluminum rods support the vertical force of $P=20 \mathrm{kN} .$ Determine their required diameters if the allowable tensile stress for the aluminum is $\sigma_{\text {allow }}=150 \mathrm{MPa}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 87

The two aluminum rods $A B$ and $A C$ have diameters of $10 \mathrm{mm}$ and $8 \mathrm{mm}$, respectively. Determine the largest vertical force $\mathbf{P}$ that can be supported. The allowable tensile stress for the aluminum is $\sigma_{\text {allow }}=150 \mathrm{MPa}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 88

Determine the required minimum thickness $t$ of member $A B$ and edge distance $b$ of the frame if $P=9$ kip and the factor of safety against failure is $2 .$ The wood has a normal failure stress of $\sigma_{\text {fail }}=6 \mathrm{ksi}$, and a shear failure stress of $\tau_{\text {fail }}=1.5 \mathrm{ksi}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 89

Determine the maximum allowable load $\mathbf{P}$ that can be safely supported by the frame if $t=1.25$ in. and $b=3.5$ in. The wood has a normal failure stress of $\sigma_{\text {fail }}=6 \mathrm{ksi},$ and a shear failure stress of $\tau_{\text {fail }}=1.5$ ksi. Use a factor of safety against failure of 2

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 90

The compound wooden beam is connected together by a bolt at $B$. Assuming that the connections at $A, B, C$ and $D$ exert only vertical forces on the beam, determine the required diameter of the bolt at $B$ and the required outer diameter of its washers if the allowable tensile stress for the bolt is $\left(\sigma_{t}\right)_{\text {allow }}=150 \mathrm{MPa}$ and the allowable bearing stress for the wood is $\left(\sigma_{b}\right)_{\text {allow }}=28$ MPa. Assume that the hole in the washers has the same diameter as the bolt.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 91

The hanger is supported using the rectangular pin. Determine the magnitude of the allowable suspended load $\mathbf{P}$ if the allowable bearing stress is $\left(\sigma_{b}\right)_{\text {allow }}=220 \mathrm{MPa}$, the allowable tensile stress is $\left(\sigma_{t}\right)_{\text {allow }}=150 \mathrm{MPa},$ and the allowable shear stress is $\tau_{\text {allow }}=130 \mathrm{MPa}$. Take $t=6 \mathrm{mm}$ $a=5 \mathrm{mm}$ and $b=25 \mathrm{mm}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 92

The hanger is supported using the rectangular pin. Determine the required thickness $t$ of the hanger, and dimensions $a$ and $b$ if the suspended load is $P=60$ kN. The allowable tensile stress is $\left(\sigma_{t}\right)_{\text {allow }}=150 \mathrm{MPa}$, the allowable bearing stress is $\left(\sigma_{b}\right)_{\text {allow }}=290 \mathrm{MPa},$ and the allowable shear stress is $\tau_{\text {allow }}=125 \mathrm{MPa}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 93

The rods $A B$ and $C D$ are made of steel. Determine their smallest diameter so that they can support the dead loads shown. The beam is assumed to be pin connected at $A$ and $C .$ Use the LRFD method, where the resistance factor for steel in tension is $\phi=0.9,$ and the dead load factor is $\gamma_{D}=1.4 .$ The failure stress is $\sigma_{\text {fuil }}=345 \mathrm{MPa}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 94

The aluminum bracket $A$ is used to support the centrally applied load of 8 kip. If it has a thickness of 0.5 in. determine the smallest height $h$ in order to prevent a shear failure. The failure shear stress is $\tau_{\text {fail }}=23$ ksi. Use a factor of safety for shear of $\mathrm{F}$. S. $=2.5$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 95

If the allowable tensile stress for the bar is $\left(\sigma_{t}\right)_{\text {allow }}=21 \mathrm{ksi},$ and the allowable shear stress for the pin is $\tau_{\text {allow }}=12 \mathrm{ksi},$ determine the diameter of the pin so that the load $P$ will be a maximum. What is this load? Assume the hole in the bar has the same diameter $d$ as the pin. Take $t=\frac{1}{4}$ in and $w=2$ in

Anand Jangid

Numerade Educator

Problem 96

The bar is connected to the support using a pin having a diameter of $d=1$ in. If the allowable tensile stress for the bar is $\left(\sigma_{t}\right)_{\text {allow }}=20 \mathrm{ksi},$ and the allowable bearing stress between the pin and the bar is $\left(\sigma_{b}\right)_{\text {allow }}=30 \mathrm{ksi}$ determine the dimensions $w$ and $t$ so that the gross area of the cross section is $w t=2$ in $^{2}$ and the load $P$ is a maximum. What is this maximum load? Assume the hole in the bar has the same diameter as the pin.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator