Mechanics of Materials

R. C. Hibbeler

Chapter 7

Transverse Shear - all with Video Answers

Educators

+ 2 more educators

Chapter Questions

Problem 1

If the wide-flange beam is subjected to a shear of $V=20 \mathrm{kN},$ determine the shear stress on the web at $A$ Indicate the shear-stress components on a volume element located at this point.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 2

If the wide-flange beam is subjected to a shear of $V=20 \mathrm{kN},$ determine the maximum shear stress in the beam.

Chai Santi

Numerade Educator

Problem 3

If the wide-flange beam is subjected to a shear of $V=20 \mathrm{kN},$ determine the shear force resisted by the web of the beam.

Chai Santi

Numerade Educator

Problem 4

If the beam is subjected to a shear of $V=30 \mathrm{kN}$ determine the web's shear stress at $A$ and $B$. Indicate the shear-stress components on a volume element located at these points. Set $w=200 \mathrm{mm}$. Show that the neutral axis is located at $\bar{y}=0.2433 \mathrm{m}$ from the bottom and $I=0.5382\left(10^{-3}\right) \mathrm{m}^{4}$

Hast Aggarwal

Numerade Educator

Problem 5

If the wide-flange beam is subjected to a shear of $V=30 \mathrm{kN},$ determine the maximum shear stress in the beam. Set $w=300 \mathrm{mm}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 6

The wood beam has an allowable shear stress of $\tau_{\text {allow }}=7$ MPa. Determine the maximum shear force $V$ that can be applied to the cross section.

Chai Santi

Numerade Educator

Problem 7

The shaft is supported by a thrust bearing at $A$ and a journal bearing at $B$. If $P=20 \mathrm{kN}$, determine the absolute maximum shear stress in the shaft.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 8

The shaft is supported by a thrust bearing at $A$ and a journal bearing at $B$. If the shaft is made from a material having an allowable shear stress of $\tau_{\text {allow }}=75 \quad \mathrm{MPa}$ determine the maximum value for $P.$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 9

Determine the largest shear force $V$ that the member can sustain if the allowable shear stress is $\tau_{\text {allow }}=8 \mathrm{ksi}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 10

If the applied shear force $V=18$ kip, determine the maximum shear stress in the member.

Chai Santi

Numerade Educator

Problem 11

The overhang beam is subjected to the uniform distributed load having an intensity of $w=50 \mathrm{kN} / \mathrm{m}$ Determine the maximum shear stress in the beam.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 12

The beam is made from a polymer and is subjected to a shear of $V=7$ kip. Determine the maximum shear stress in the beam and plot the shear-stress distribution over the cross section. Report the values of the shear stress every 0.5 in. of beam depth.

Ajay Singhal

Numerade Educator

Problem 13

Determine the maximum shear stress in the strut if it is subjected to a shear force of $V=20 \mathrm{kN}$

Chai Santi

Numerade Educator

Problem 14

Determine the maximum shear force $V$ that the strut can support if the allowable shear stress for the material is $\tau_{\text {allow }}=40 \mathrm{MPa}$

Chai Santi

Numerade Educator

Problem 15

Sketch the intensity of the shear-stress distribution acting over the beam's cross-sectional area, and determine the resultant shear force acting on the segment $A B .$ The shear force acting at the section is $V=35$ kip. Show that $I_{N A}=872.49$ in $^{4}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 16

Plot the shear-stress distribution over the cross section of a rod that has a radius $c .$ By what factor is the maximum shear stress greater than the average shear stress acting over the cross section?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 17

If the beam is subjected to a shear of $V=15 \mathrm{kN}$ determine the web's shear stress at $A$ and $B$. Indicate the shear-stress components on a volume element located at these points. Set $w=125 \mathrm{mm}$. Show that the neutral axis is located at $\bar{y}=0.1747 \mathrm{m}$ from the bottom and $I_{N A}=0.2182\left(10^{-3}\right) \mathrm{m}^{4}$

Chai Santi

Numerade Educator

Problem 18

If the wide-flange beam is subjected to a shear of $V=30 \mathrm{kN},$ determine the maximum shear stress in the beam. Set $w=200 \mathrm{mm}$

Chai Santi

Numerade Educator

Problem 19

If the wide-flange beam is subjected to a shear of $V=30 \mathrm{kN},$ determine the shear force resisted by the web of the beam. Set $w=200 \mathrm{mm}$

Narayan Hari

Numerade Educator

Problem 20

Determine the length of the cantilevered beam so that the maximum bending stress in the beam is equivalent to the maximum shear stress.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 21

If the beam is made from wood having an allowable shear stress $\tau_{\text {allow }}=400$ psi, determine the maximum magnitude of $\mathbf{P}$. Set $d=4$ in.

Chai Santi

Numerade Educator

Problem 22

Determine the largest intensity $w$ of the distributed load that the member can support if the allowable shear stress is $\tau_{\text {allow }}=800$ psi. The supports at $A$ and $B$ are smooth.

Prashant Bana

Numerade Educator

Problem 23

If $w=800$ lb/ft, determine the absolute maximum shear stress in the beam. The supports at $A$ and $B$ are smooth.

Ajay Singhal

Numerade Educator

Problem 24

Determine the shear stress at point $B$ on the web of the cantilevered strut at section $a-a$

Chai Santi

Numerade Educator

Problem 25

Determine the maximum shear stress acting at section $a-a$ of the cantilevered strut.

Chai Santi

Numerade Educator

Problem 26

Railroad ties must be designed to resist large shear loadings. If the tie is subjected to the 34 -kip rail loadings and an assumed uniformly distributed ground reaction, determine the intensity $w$ for equilibrium, and calculate the maximum shear stress in the tie at section $a-a,$ which is located just to the left of the rail.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 27

The beam is slit longitudinally along both sides. If it is subjected to a shear of $V=250 \mathrm{kN}$, compare the maximum shear stress in the beam before and after the cuts
were made.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 28

The beam is to be cut longitudinally along both sides as shown. If it is made from a material having an allowable shear stress of $\tau_{\text {allow }}=75$ MPa, determine the maximum allowable shear force $\mathbf{V}$ that can be applied before and after the cut is made.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 29

The composite beam is constructed from wood and reinforced with a steel strap. Use the method of Sec. 6.6 and calculate the maximum shear stress in the beam when it is subjected to a shear of $V=50 \mathrm{kN}$. Take $E_{\mathrm{st}}=200 \mathrm{GPa}$ $E_{\mathrm{w}}=15 \mathrm{GPa}$

Hast Aggarwal

Numerade Educator

Problem 30

The beam has a rectangular cross section and is subjected to a load $P$ that is just large enough to develop a fully plastic moment $M_{p}=P L$ at the fixed support. If the material is elastic perfectly plastic, then at a distance $x<L$ the moment $M=P x$ creates a region of plastic yielding with an associated elastic core having a height $2 y^{\prime} .$ This situation has been described by Eq. $6-30$ and the moment $\mathbf{M}$ is distributed over the cross section as shown in Fig. $6-48 e$ Prove that the maximum shear stress in the beam is given by $\tau_{\max }=\frac{3}{2}\left(P / A^{\prime}\right),$ where $A^{\prime}=2 y^{\prime} b,$ the cross-sectional area of the elastic core.

Hast Aggarwal

Numerade Educator

Problem 31

The beam in Fig. $6-48 f$ is subjected to a fully plastic moment $\mathbf{M}_{p} .$ Prove that the longitudinal and transverse shear stresses in the beam are zero. Hint: Consider an element of the beam shown in Fig. $7-4 d$

Hast Aggarwal

Numerade Educator

Problem 32

The beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every 4 in. If each nail can support a 400 -lb shear force, determine the maximum shear force $V$ that can be applied to the beam.

Hast Aggarwal

Numerade Educator

Problem 33

The beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every 4 in. If a shear force of $V=900$ lb is applied to the boards, determine the shear force resisted by each nail.

Hast Aggarwal

Numerade Educator

Problem 34

The beam is constructed from three boards. If it is subjected to a shear of $V=5$ kip, determine the maximum allowable spacing $s$ of the nails used to hold the top and bottom flanges to the web. Each nail can support a shear force of $500 \mathrm{lb}$

Hast Aggarwal

Numerade Educator

Problem 35

The beam is constructed from three boards. Determine the maximum shear $V$ that it can support if the allowable shear stress for the wood is $\tau_{\text {allow }}=400$ psi. What is the maximum allowable spacing $s$ of the nails if each nail can resist a shear force of $400 \mathrm{lb} ?$

Hast Aggarwal

Numerade Educator

Problem 37

The double T-beam is fabricated by welding the three plates together as shown. If the weld can resist a shear stress $\tau_{\text {allow }}=90 \mathrm{MPa}$, determine the maximum shear $V$ that can be applied to the beam.

Hast Aggarwal

Numerade Educator

Problem 38

The beam is constructed from three boards. Determine the maximum loads $P$ that it can support if the allowable shear stress for the wood is $\tau_{\text {allow }}=400$ psi. What is the maximum allowable spacing $s$ of the nails used to hold the top and bottom flanges to the web if each nail can resist a shear force of $400 \mathrm{lb} ?$

Hast Aggarwal

Numerade Educator

Problem 39

A beam is constructed from three boards bolted together as shown. Determine the shear force in each bolt if the bolts are spaced $s=250 \mathrm{mm}$ apart and the shear is $V=35 \mathrm{kN}$

Hast Aggarwal

Numerade Educator

Problem 40

The simply supported beam is built up from three boards by nailing them together as shown. The wood has an allowable shear stress of $\tau_{\text {allow }}=1.5 \mathrm{MPa}$, and an allowable bending stress of $\sigma_{\text {allow }}=9$ MPa. The nails are spaced at $s=75 \mathrm{mm},$ and each has a shear strength of $1.5 \mathrm{kN}$ Determine the maximum allowable force $\mathbf{P}$ that can be applied to the beam.

Chai Santi

Numerade Educator

Problem 41

The simply supported beam is built up from three boards by nailing them together as shown. If $P=12 \mathrm{kN}$ determine the maximum allowable spacing $s$ of the nails to support that load, if each nail can resist a shear force of $1.5 \mathrm{kN}$

Chai Santi

Numerade Educator

Problem 42

The T-beam is constructed as shown. If each nail can support a shear force of $950 \mathrm{lb}$, determine the maximum shear force $V$ that the beam can support and the corresponding maximum nail spacing $s$ to the nearest $\frac{1}{8}$ in. The allowable shear stress for the wood is $\tau_{\text {allow }}=450$ psi.

Hast Aggarwal

Numerade Educator

Problem 43

The box beam is constructed from four boards that are fastened together using nails spaced along the beam every 2 in. If each nail can resist a shear force of $50 \mathrm{lb}$, determine the largest force $P$ that can be applied to the beam without causing failure of the nails.

Hast Aggarwal

Numerade Educator

Problem 44

The box beam is constructed from four boards that are fastened together using nails spaced along the beam every 2 in. If a force $P=2$ kip is applied to the beam, determine the shear force resisted by each nail at $A$ and $B$.

Hast Aggarwal

Numerade Educator

Problem 45

The member consists of two plastic channel strips 0.5 in. thick, glued together at $A$ and $B$. If the distributed load has a maximum intensity of $w_{0}=3$ kip/ft, determine the maximum shear stress resisted by the glue.

Rashmi Sinha

Numerade Educator

Problem 46

The member consists of two plastic channel strips 0.5 in. thick, glued together at $A$ and $B .$ If the glue can support an allowable shear stress of $\tau_{\text {allow }}=600 \mathrm{psi}$ determine the maximum intensity $w_{0}$ of the triangular distributed loading that can be applied to the member based on the strength of the glue.

Hast Aggarwal

Numerade Educator

Problem 47

The beam is made from four boards nailed together as shown. If the nails can each support a shear force of 100 Ib., determine their required spacing $s^{\prime}$ and $s$ if the beam is subjected to a shear of $V=700 \mathrm{lb}$

Chai Santi

Numerade Educator

Problem 48

The beam is made from three polystyrene strips that are glued together as shown. If the glue has a shear strength of $80 \mathrm{kPa}$, determine the maximum load $P$ that can be applied without causing the glue to lose its bond.

Hast Aggarwal

Numerade Educator

Problem 49

The timber T-beam is subjected to a load consisting of $n$ concentrated forces, $P_{n}$. If the allowable shear $V_{\text {nail }}$ for each of the nails is known, write a computer program that will specify the nail spacing between each load. Show an application of the program using the values $L=15 \mathrm{ft}$
\[
\begin{array}{l}
a_{1}=4 \mathrm{ft}, P_{1}=600 \mathrm{lb}, a_{2}=8 \mathrm{ft}, P_{2}=1500 \mathrm{lb}, b_{1}=1.5 \mathrm{in} . \\
h_{1}=10 \mathrm{in.}, b_{2}=8 \mathrm{in.}, h_{2}=1 \text { in., and } V_{\text {nail }}=200 \mathrm{lb}
\end{array}
\]

Hast Aggarwal

Numerade Educator

Problem 50

A shear force of $V=300 \mathrm{kN}$ is applied to the box girder. Determine the shear flow at points $A$ and $B$

Chai Santi

Numerade Educator

Problem 51

A shear force of $V=450 \mathrm{kN}$ is applied to the box girder. Determine the shear flow at points $C$ and $D$

Chai Santi

Numerade Educator

Problem 52

A shear force of $V=18 \mathrm{kN}$ is applied to the box girder. Determine the shear flow at points $A$ and $B$

Hast Aggarwal

Numerade Educator

Problem 53

A shear force of $V=18 \mathrm{kN}$ is applied to the box girder. Determine the shear flow at point $C$

Hast Aggarwal

Numerade Educator

Problem 54

The aluminum strut is $10 \mathrm{mm}$ thick and has the cross section shown. If it is subjected to a shear of $V=150 \mathrm{N}$ determine the shear flow at points $A$ and $B$

Chai Santi

Numerade Educator

Problem 55

7-61. The assembly is subjected to a vertical shear of $V=7$ kip. Determine the shear flow at points $A$ and $B$ and the maximum shear flow in the cross section.

Hast Aggarwal

Numerade Educator

Problem 56

The beam is subjected to a shear force of $V=50$ kip. Determine the shear flow at points $A$ and $B$

Hast Aggarwal

Numerade Educator

Problem 57

The beam is subjected to a shear force of $V=50$ kip. Determine the maximum shear flow in the cross section.

Hast Aggarwal

Numerade Educator

Problem 58

The H-beam is subjected to a shear of $V=80 \mathrm{kN}$ Determine the shear flow at point $A$

Hast Aggarwal

Numerade Educator

Problem 59

The H-beam is subjected to a shear of $V=80 \mathrm{kN}$ Sketch the shear-stress distribution acting along one of its side segments. Indicate all peak values.

Hast Aggarwal

Numerade Educator

Problem 60

The built-up beam is formed by welding together the thin plates of thickness 5 mm. Determine the location of the shear center $O$

Chai Santi

Numerade Educator

Problem 61

The assembly is subjected to a vertical shear of $V=7$ kip. Determine the shear flow at points $A$ and $B$ and the maximum shear flow in the cross section.

Chai Santi

Numerade Educator

Problem 62

The box girder is subjected to a shear of $V=15 \mathrm{kN}$ Determine the shear flow at point $B$ and the maximum shear flow in the girder's web $A B$

Hast Aggarwal

Numerade Educator

Problem 63

Determine the location $e$ of the shear center, point $O$ for the thin-walled member having a slit along its section.

Hast Aggarwal

Numerade Educator

Problem 64

Determine the location $e$ of the shear center, point $O$ for the thin-walled member. The member segments have the same thickness $t$

Hast Aggarwal

Numerade Educator

Problem 65

The beam supports a vertical shear of $V=7$ kip. Determine the resultant force in segment $A B$ of the beam.

Hast Aggarwal

Numerade Educator

Problem 66

The stiffened beam is constructed from plates having a thickness of 0.25 in. If it is subjected to a shear of $V=8$ kip, determine the shear-flow distribution in segments $A B$ and $C D .$ What is the resultant shear supported by these segments? Also, sketch how the shear flow passes through the cross section. The vertical dimensions are measured to the centerline of each horizontal segment.

Hast Aggarwal

Numerade Educator

Problem 67

The pipe is subjected to a shear force of $V=8$ kip. Determine the shear flow in the pipe at points $A$ and $B$.

Hast Aggarwal

Numerade Educator

Problem 68

Determine the location $e$ of the shear center, point $O$ for the thin-walled member. The member segments have the same thickness $t$

Hast Aggarwal

Numerade Educator

Problem 69

A thin plate of thickness $t$ is bent to form the beam having the cross section shown. Determine the location of the shear center $O$

Chai Santi

Numerade Educator

Problem 70

Determine the location $e$ of the shear center, point $O$ for the tube having a slit along its length.

Hast Aggarwal

Numerade Educator