Questions and Answers of Mechanics Of Materials

Determine the torsional strain energy in the 2014-T6 aluminum shaft. The tube shaft has an outer and inner diameter of $60 \mathrm{~mm}$ and $40 \mathrm{~mm}$, respectively. 12 kNm 10 kNm 6 kNm
Determine the torsional strain energy in the A-36 steel shaft. The shaft has a radius of $40 \mathrm{~mm}$. 8 kNm 6 kNm 12 kNm 0.6 m 0.4 m 0.5 m
Determine the torsional strain energy stored in the tapered rod when it is subjected to the torque $\mathbf{T}$. The rod is made of material having a modulus of rigidity of $G$. L 2ro To T
Determine the bending strain energy in the A-36 steel beam. $I=99.2\left(10^{6}\right) \mathrm{mm}^{4}$. 6 m 9 kN/m
If $P=10$ kip, determine the total strain energy in the truss. Each member has a diameter of $2 \mathrm{in}$. and is made of A992 steel. 4 ft A 3 ft B VP 3 ft- C
Determine the maximum force $P$ and the corresponding maximum total strain energy that can be stored in the truss without causing any of the members to have permanent deformation. Each member of
Consider the thin-walled tube of Fig. 5-26. Use the formula for shear stress, $\tau_{\text {avg }}=T / 2 t A_{m}$, Eq. 5-18, and the general equation of shear strain energy, Eq. 14-11, to show that
Determine the ratio of shearing strain energy to bending strain energy for the rectangular cantilever beam when it is subjected to the loading shown. The beam is made of material having a modulus of
Determine the bending strain energy in the beam. $E I$ is constant. T 22
Determine the bending strain energy in the A-36 steel beam due to the distributed load. $I=122\left(10^{6}\right) \mathrm{mm}^{4}$. A -3 m- 15 kN/m B
Determine the bending strain energy in the beam due to the loading shown. $E I$ is constant. Mo -- B 22 -- C
Determine the bending strain energy in the 2-in.-diameter A-36 steel rod. 80 lb 2 ft 2 ft 80 lb
Determine the bending strain energy in the beam and the axial strain energy in each of the two rods. The beam is made of 2014-T6 aluminum and has a square cross section $50 \mathrm{~mm}$ by \(50
The beam shown is tapered along its width. If a force $\mathbf{P}$ is applied to its end, determine the strain energy in the beam and compare this result with that of a beam that has a constant
The pipe lies in the horizontal plane. If it is subjected to a vertical force $\mathbf{P}$ at its end, determine the strain energy due to bending and torsion. Express the results in terms of the
Determine the bending strain energy in the cantilever beam. Solve the problem two ways. (a) Apply Eq. 14-17. (b) The load $w d x$ acting on a segment $d x$ of the beam is displaced a distance
Determine the bending strain energy in the simply supported beam. Solve the problem two ways. (a) Apply Eq. 14-17. (b) The load $w d x$ acting on the segment $d x$ of the beam is displaced a
Determine the horizontal displacement of joint $C . A E$ is constant. L P L A -L. B
Determine the horizontal displacement of joint $D . A E$ is constant. P D A C L 0.6 L 0.8 L B
Determine the horizontal displacement of joint $A$. Each bar is made of A992 steel and has a cross-sectional area of $1.5 \mathrm{in}^{2}$. 10 kip A 3 ft D 3 ft -- B C - 4 ft.
Determine the vertical displacement of joint $C$. The members of the truss are 2014-T6 aluminum, $40 \mathrm{~mm}$ diameter rods. 1.5 m A 2 m- D B 2 m 30 kN
Determine the slope at the end $B$ of the A-36 steel beam. $I=80\left(10^{6}\right) \mathrm{mm}^{4}$. A 8 m 6 kNm
Determine the slope of the beam at the pin support $A$. $E I$ is constant. Mo L B
Determine the vertical displacement of point $B$ on the A992 steel beam. Take $I=80\left(10^{6}\right) \mathrm{mm}^{4}$. A 3m- 20 kN B -5 m- C
The cantilever beam is subjected to a couple moment $M_{0}$ applied at its end. Determine the slope of the beam at $B$. EI is constant. -L- B Mo
Determine the displacement of point $B$ on the A992 steel beam. $I=250 \mathrm{in}^{4}$. A 15 ft 8 kip B -10 ft- C
The A-36 steel bars are pin connected at $B$. If each has a square cross section, determine the vertical displacement of $B$. 800 lb A B D 8 ft 4 ft 10 ft 2 in. H I2 I 2 in.
The A992 steel bars are pin connected at $C$. If they each have a diameter of 2 in., determine the displacement of point $E$. 2 kip E B C -6 ft 6ft 10 ft 8 ft D
Determine the vertical displacement of point $C$ of the simply supported 6061-T6 aluminum beam. Consider both shearing and bending strain energy. A 100 kip C La -1.5 ft- -1.5 ft- B
Determine the deflection of the beam at its center caused by shear. The shear modulus is $G$. I 27 - 22
The curved rod has a diameter $d$. Determine the vertical displacement of end $B$ of the rod. The rod is made of material having a modulus of elasticity of $E$. Consider only bending strain
The rod has a circular cross section with a moment of inertia $I$. If a vertical force $\mathbf{P}$ is applied at $A$, determine the vertical displacement at this point. Only consider the
The rod has a circular cross section with a polar moment of inertia $J$ and moment of inertia $I$. If a vertical force $\mathbf{P}$ is applied at $A$, determine the vertical displcement at
Determine the vertical displacement of end $B$ of the frame.Consider only bending strain energy. The frame is made using two A-36 steel W460 $\times 68$ wide-flange sections. 4 m A -3 m- B 20 kN
A bar is $4 \mathrm{~m}$ long and has a diameter of $30 \mathrm{~mm}$. Determine the total amount of elastic energy that it can absorb from an impact loading if (a) it is made of steel for which
Determine the diameter of a red brass C83400 bar that is $8 \mathrm{ft}$ long if it is to be used to absorb $800 \mathrm{ft} \cdot \mathrm{lb}$ of energy in tension from an impact loading. No
Determine the speed $v$ of the $50-\mathrm{Mg}$ mass when it is just over the top of the steel post, if after impact, the maximum stress developed in the post is $550 \mathrm{MPa}$. The post
The collar has a weight of $50 \mathrm{lb}$ and falls from rest down the titanium bar. If the bar has a diameter of 0.5 in., determine the maximum stress developed in the bar if the weight is (a)
A steel cable having a diameter of 0.4 in. wraps over a drum and is used to lower an elevator having a weight of $800 \mathrm{lb}$. The elevator is $150 \mathrm{ft}$ below the drum and is
The diver weighs $150 \mathrm{lb}$ and, while holding himself rigid, strikes the end of the wooden diving board. Determine the maximum height $h$ from which he can jump from rest onto the board
The $50-\mathrm{kg}$ block is dropped from rest at a height of $h=600 \mathrm{~mm}$ onto the bronze C86100 tube. Determine the minimum length $L$ the tube can have without causing the tube to
The $50-\mathrm{kg}$ block is dropped from rest at a height of $h=600 \mathrm{~mm}$ onto the bronze C86100 tube. If $L=900 \mathrm{~mm}$ determine the maximum normal stress developed in the
The sack of cement has a weight of $90 \mathrm{lb}$. If it is dropped from rest at a height of $h=4 \mathrm{ft}$ onto the center of the W10 $\times 39$ structural steel A-36 beam, determine the
The sack of cement has a weight of $90 \mathrm{lb}$. Determine the maximum height $h$ from which it can be dropped from rest onto the center of the $\mathrm{W} 10 \times 39$ structural steel
A cylinder having the dimensions shown is made from magnesium Am 1004-T61. If it is struck by a rigid block having a weight of $800 \mathrm{lb}$ and traveling at $2 \mathrm{ft} / \mathrm{s}$,
The composite aluminum 2014-T6 bar is made from two segments having diameters of $7.5 \mathrm{~mm}$ and $15 \mathrm{~mm}$. Determine the maximum axial stress developed in the bar if the
The composite aluminum 2014-T6 bar is made from two segments having diameters of $7.5 \mathrm{~mm}$ and $15 \mathrm{~mm}$. Determine the maximum height $h$ from which the 10-kg collar should be
The 50-lb weight is falling $3 \mathrm{ft} / \mathrm{s}$ at the instant it is $2 \mathrm{ft}$ above the spring and post assembly. Determine the maximum stress in the post if the spring has a
A 20-lb weight is dropped from rest at a height of $h=3 \mathrm{ft}$ onto end $A$ of the $\mathrm{A} 992$ steel cantilever beam. If the beam is a W16 $\times 50$, determine the maximum
If the maximum allowable bending stress for the W16 $\times 50$ structural A992 steel beam is $\sigma_{\text {allow }}=30 \mathrm{ksi}$, determine the maximum height $h$ from which a 30-lb
A 20-lb weight is dropped from rest at a height of $h=3 \mathrm{ft}$ onto end $A$ of the $\mathrm{A} 992$ steel cantilever beam. If the beam is a W16 $\times 50$, determine the slope of its
The simply supported W10 $\times 15$ structural A-36 steel beam is in the horizontal plane and acts as a shock absorber for the 500-lb block which is traveling toward it at \(5 \mathrm{ft} /
The 5 - $\mathrm{kg}$ block is traveling with the speed of $v=4 \mathrm{~m} / \mathrm{s}$ just before it strikes the 6061-T6 aluminum stepped cylinder. Determine the maximum normal stress
The 2014-T6 aluminum bar $A B$ can slide freely along the guides mounted on the rigid crash barrier. If the railcar of mass $10 \mathrm{Mg}$ is traveling with a speed of \(v=1.5 \mathrm{~m} /
The 2014-T6 aluminum bar $A B$ can slide freely along the guides mounted on the rigid crash barrier. Determine the maximum speed $v$ of the $10-\mathrm{Mg}$ railcar without causing the bar to
The $50-\mathrm{kg}$ block $C$ is dropped from rest at $h=1.5 \mathrm{~m}$ onto the simply supported beam. If the beam is an A-36 steel W250 × 45 wide-flange section, determine the maximum
Rods $A B$ and $A C$ have a diameter of $20 \mathrm{~mm}$ and are made of 6061-T6 aluminum alloy. They are connected to the rigid collar $A$ which slides freely along the vertical guide rod.
Rods $A B$ and $A C$ have a diameter of $20 \mathrm{~mm}$ and are made of 6061-T6 aluminum alloy. They are connected to the rigid collar which slides freely along the vertical guide rod.
A 40-lb weight is dropped from rest at a height of $h=2 \mathrm{ft}$ onto the center of the W10 $\times 15$ structural A992 steel beam. Determine the maximum bending stress in the beam. A -5 ft-
If the maximum allowable bending stress for the $\mathrm{W} 10 \times 15$ structural A992 steel beam is $\sigma_{\text {allow }}=20 \mathrm{ksi}$, determine the maximum height $h$ at which a
A 40-lb weight is dropped from rest at a height of $h=2 \mathrm{ft}$ onto the center of the W10 $\times 15$ structural A992 steel beam. Determine the vertical displacement of its end $B$ due to
The car bumper is made of polycarbonate polybutylene terephthalate. If $E=2.0 \mathrm{GPa}$, determine the maximum deflection and maximum stress in the bumper if it strikes the rigid post when the
Determine the vertical displacement of joint $A$. Each A992 steel member has a cross-sectional area of $400 \mathrm{~mm}^{2}$. A B -1.5 m E 40 kN 60 kN -3 m- 2 m
Determine the horizontal displacement of joint $B$. Each A-36 steel member has a cross-sectional area of $2 \mathrm{in}^{2}$. A 60 B 5 ft 800 lb 30
Determine the vertical displacement of joint $B$. Each A992 steel member has a cross-sectional area of $4.5 \mathrm{in}^{2}$. A F E 8 ft B -8 ft 5 kip 6 ft
Determine the horizontal displacement of joint $B$. Each A992 steel member has a cross-sectional area of $400 \mathrm{~mm}^{2}$. 5 kN -2 m- 4 kN C B D A 1.5 m
Determine the vertical displacement of joint $C$. The truss is made from A-36 steel bars having a cross-sectional area of $150 \mathrm{~mm}^{2}$. Af H F 2 m B -1.5 m 1.5m C 1.5 m-1.5 m 6 kN 6 kN
Determine the vertical displacement of joint $G$. The truss is made from A-36 steel bars having a cross-sectional area of $150 \mathrm{~mm}^{2}$ H Aro B D 15m 5m1.5m1.5m-1.5 m -1.5m- 6 kN 6 kN 12
The W14 $\times 26$ structural A-36 steel member is used as a 20 -ft-long column that is assumed to be fixed at its top and fixed at its bottom. If the 15-kip load is applied at an eccentric
The W14 $\times 26$ structural A-36 steel member is used as a column that is assumed to be fixed at its top and pinned at its bottom. If the 15-kip load is applied at an eccentric distance of 10
Determine the maximum eccentric load $P$ the 2014-T6aluminum-alloy strut can support without causing it either to buckle or yield. The ends of the strut are pin connected. a $150 mm 150 mm 100 mm
The W250 28 A-36 steel column is fixed at its base. Its top is constrained to rotate about the $y-y$ axis and free to move along the $y-y$ axis. If $e=350 \mathrm{~mm}$, determine the allowable
The W250 $\times 28$ A-36 steel column is fixed at its base. Its top is constrained to rotate about the $y-y$ axis and free to move along the $y-y$ axis. Determine the force $\mathbf{P}$ and
The W14 $\times 53$ structural A992 steel column is fixed at its base and free at its top. If $P=$ kip, determine the sidesway displacement at its top and the maximum stress in the column. 10 in.
The W14 $\times 53$ column is fixed at its base and free at its top. Determine the maximum eccentric load $P$ that it can support without causing it to buckle or yield. Take $E_{\mathrm{st}}=$
A column of intermediate length buckles when the compressive stress is $40 \mathrm{ksi}$. If the slenderness ratio is 60 , determine the tangent modulus.
Determine the critical buckling load for the column. The column material can be assumed rigid. T P k ww
Determine the critical buckling load for the column. The column material can be assumed rigid. P 22. 2 k www A
The aircraft link is made from an A992 steel rod. Determine the smallest diameter of the rod, to the nearest $\frac{1}{16}$ in., that will support the load of 2 kip without buckling. The ends are
Determine the critical buckling load for the column. The column material can be assumed rigid. Each spring has a stiffness $k$. www A
An A-36 steel column has a length of $4 \mathrm{~m}$ and is pinned at both ends. If the cross-sectional area has the dimensions shown, determine the critical load. -25 mm 25 mm- 10 mm 25 mm 10 mm
Solve Prob. 13-5 if the column is fixed at its bottom and pinned at its top.Data from Prob. 13-5An A-36 steel column has a length of $4 \mathrm{~m}$ and is pinned at both ends. If the
The $\mathrm{W} 10 \times 45$ is made of $\mathrm{A}-36$ steel and is used as a column that has a length of $15 \mathrm{ft}$. If its ends are assumed pin supported, and it is subjected to an
The $\mathrm{W} 10 \times 45$ is made of A- 36 steel and is used as a column that has a length of $15 \mathrm{ft}$. If the ends of the column are fixed supported, can the column support the
The W14 $\times 38$ column is made of A-36 steel and is fixed supported at its base. If it is subjected to an axial load of $P=15$ kip, determine the factor of safety with respect to buckling. P
The W14 $\times 38$ column is made of A-36 steel. Determine the critical load if its bottom end is fixed supported and its top is free to move in plane about the strong axis and is pinned about the
The 2014-T6 aluminum angle has a cross-sectional area of $A=2.67$ in $^{2}$ and a radius of gyration about the $x$ axis of $r_{x}=1.25$ in. and about the $y$ axis of $r_{y}=1.06$ in. The
The W18 $\times 40$ is used as a structural A992 steel column that can be assumed pinned at top and fixed at the base. Determine the largest axial force $P$ that can be applied without causing it
An L-2 steel link in a forging machine is pin connected to the forks at its ends as shown. Determine the maximum load $P$ it can carry without buckling. Use a factor of safety with respect to
The W12 $\times 87$ structural A-36 steel column has a length of $12 \mathrm{ft}$. If its bottom end is fixed supported while its top is free, and it is subjected to an axial load of $P=380$
The W12 $\times 87$ structural A-36 steel column has a length of $12 \mathrm{ft}$. If its bottom end is fixed supported while its top is free, determine the largest axial load it can support. Use
An A36 steel hollow circular tube has an outer diameter of $200 \mathrm{~mm}$ and inner diameter of $180 \mathrm{~mm}$. If it is pinned at both ends, determine the largest axial load that can be
The 10 -ft wooden rectangular column has the dimensions shown. Determine the critical load if the ends are assumed to be pin connected. \(E_{\mathrm{w}}=1.6\left(10^{3}\right) \mathrm{ksi},
The 10 -ft wooden column has the dimensions shown. Determine the critical load if the bottom is fixed and the top is pinned. Take \(E_{\mathrm{w}}=1.6\left(10^{3}\right) \mathrm{ksi}, \sigma_{Y}=5
Determine the maximum force $P$ that can be applied to the handle so that the A992 steel control $\operatorname{rod} A B$ does not buckle. The rod has a diameter of $1.25 \mathrm{in}$. It is
The strongback $B C$ is made of an A992 steel hollow circular section with an outer diameter of $d_{o}=60 \mathrm{~mm}$ and inner diameter of $d_{i}=40 \mathrm{~mm}$. Determine the maximum
The strongback is made of an A992 steel hollow circular section with the outer diameter of $d_{o}=60 \mathrm{~mm}$. If it is designed to withstand the lifting force of $P=60 \mathrm{kN}$,
The members of the truss are assumed to be pin connected. If member $G F$ is an $\mathrm{A}-36$ steel rod having a diameter of 2 in., determine the greatest magnitude of load $\mathbf{P}$ that
The members of the truss are assumed to be pin connected. If member $A G$ is an $\mathrm{A}-36$ steel rod having a diameter of 2 in., determine the greatest magnitude of load $\mathbf{P}$ that
Determine the maximum distributed load that can be applied to the bar so that the $\mathrm{A}-36$ steel strut $A B$ does not buckle. The strut has a diameter of 2 in. It is pin connected at its

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