Mechanics of Materials, 7th Edition
7th Edition
ISBN: 9780073398235
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek
Publisher: McGraw-Hill Education
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Chapter 5.4, Problem 125P
(a)
To determine
Tabulate the shear, bending moment, and maximum normal stress using the singularity function.
(b)
To determine
The maximum normal stress with 2% accuracy.
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Students have asked these similar questions
Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a = 3.8 m, b = 7.6 m, c =
5.1 m, P = 11 kN, w = 41 kN/m, and Q = 29 kN. Label all significant points on each diagram and identify the maximum shear force and
bending moment along with their respective locations. Additionally:
(a) Determine V and M in the beam at a point located 0.50 m to the right of B.
(b) Determine V and M in the beam at a point located 1.15 m to the left of C.
Note that answers may be positive or negative. Here, "maximum" refers to the largest magnitude value, but you should enter your
shear force and bending moment with the correct sign, using the sign convention presented in Section 7.2 of the textbook. If the
magnitudes of the largest positive and largest negative values are the same, enter a positive number.
В
a
b
Answer:
Vmax
kN
Mmax
kN•m
(a) Vx1=
kN
Mx1 =
kN•m
(b) Vx2 =
kN
Mx2 =
kN•m
The distance between point A and the shear force VAB=0 *
a. 1.9074m
b. 1.9074mm
c. 1.8074m
d. 1.8074mm
Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a= 2.5 m, b= 7.0 m,
MB = 85 kN-m and Mc = 130 kN-m. Construct the shear-force and bending-moment diagrams on paper and use the results to
answer the questions in the subsequent parts of this GO exercise.
y
MB
Mc
В
C
D
Determine the shear force acting at each of the following locations:
(a) x = 0+ m (i.e., just to the right of point A)
(b) x = 2.5- m (i.e.,. just to the left of B)
(c) x = 2.5+ m (i.e., just to the right of B)
(d) x = 12.0- m (i.e. just to the left of D)
When entering your answers, use the shear force sign convention.
Answers:
(a) V = i
kN.
(b) V - i
kN.
(c) V = i
kN.
(d) V = i
kN.
Chapter 5 Solutions
Mechanics of Materials, 7th Edition
Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.7 and 5.8 Draw the shear and bending-moment...Ch. 5.1 - 5.7 and 5.8 Draw the shear and bending-moment...Ch. 5.1 - 5.9 and 5.10 Draw the shear and bending-moment...Ch. 5.1 - 5.9 and 5.10 Draw the shear and bending-moment...
Ch. 5.1 - 5.11 and 5.12 Draw the shear and bending-moment...Ch. 5.1 - 5.11 and 5.12 Draw the shear and bending-moment...Ch. 5.1 - 5.13 and 5.14 Assuming that the reaction of the...Ch. 5.1 - 5.13 and 5.14 Assuming that the reaction of the...Ch. 5.1 - 5.15 and 5.16 For the beam and loading shown,...Ch. 5.1 - 5.15 and 5.16 For the beam and loading shown,...Ch. 5.1 - For the beam and loading shown, determine the...Ch. 5.1 - For the beam and loading shown, determine the...Ch. 5.1 - 5.19 and 5.20 For the beam and loading shown,...Ch. 5.1 - 5.19 and 5.20 For the beam and loading shown,...Ch. 5.1 - Draw the shear and bending-moment diagrams for the...Ch. 5.1 - 5.22 and 5.23 Draw the shear and bending-moment...Ch. 5.1 - 5.22 and 5.23 Draw the shear and bending-moment...Ch. 5.1 - 5.24 and 5.25 Draw the shear and bending-moment...Ch. 5.1 - 5.24 and 5.25 Draw the shear and bending-moment...Ch. 5.1 - Knowing that W = 12 kN, draw the shear and...Ch. 5.1 - Determine (a) the magnitude of the counterweight W...Ch. 5.1 - Determine (a) the distance a for which the...Ch. 5.1 - Knowing that P = Q = 480 N, determine (a) the...Ch. 5.1 - Solve Prob. 5.29, assuming that P = 480 N and Q =...Ch. 5.1 - Determine (a) the distance a for which the...Ch. 5.1 - A solid steel rod of diameter d is supported as...Ch. 5.1 - A solid steel bar has a square cross section of...Ch. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.1a....Ch. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.2a....Ch. 5.2 - Prob. 36PCh. 5.2 - Prob. 37PCh. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.5a....Ch. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.6a....Ch. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.7. 5.7...Ch. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.8. 5.7...Ch. 5.2 - Prob. 42PCh. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.10....Ch. 5.2 - 5.44 and 5.45 Draw the shear and bending-moment...Ch. 5.2 - 5.44 and 5.45 Draw the shear and bending-moment...Ch. 5.2 - Prob. 46PCh. 5.2 - Prob. 47PCh. 5.2 - Prob. 48PCh. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.20....Ch. 5.2 - 5.50 and 5.51 Determine (a) the equations of the...Ch. 5.2 - 5.50 and 5.51 Determine (a) the equations of the...Ch. 5.2 - 5.52 and 5.53 Determine (a) the equations of the...Ch. 5.2 - 5.52 and 5.53 Determine (a) the equations of the...Ch. 5.2 - 5.54 and 5.55 Draw the shear and bending-moment...Ch. 5.2 - 5.54 and 5.55 Draw the shear and bending-moment...Ch. 5.2 - 5.56 and 5.57 Draw the shear and bending-moment...Ch. 5.2 - 5.56 and 5.57 Draw the shear and bending-moment...Ch. 5.2 - 5.58 and 5.59 Draw the shear and bending-moment...Ch. 5.2 - 5.58 and 5.59 Draw the shear and bending-moment...Ch. 5.2 - Knowing that beam AB is in equilibrium under the...Ch. 5.2 - Knowing that beam AB is in equilibrium under the...Ch. 5.2 - The beam AB supports two concentrated loads P and...Ch. 5.2 - The beam AB supports a uniformly distributed load...Ch. 5.2 - Beam AB supports a uniformly distributed load of 2...Ch. 5.3 - 5.65 and 5.66 For the beam and loading shown,...Ch. 5.3 - 5.65 and 5.66 For the beam and loading shown,...Ch. 5.3 - 5.67 and 5.68 For the beam and loading shown,...Ch. 5.3 - 5.67 and 5.68 For the beam and loading shown,...Ch. 5.3 - 5.69 and 5.70 For the beam and loading shown,...Ch. 5.3 - 5.69 and 5.70 For the beam and loading shown,...Ch. 5.3 - 5.71 and 5.72 Knowing that the allowable normal...Ch. 5.3 - 5.71 and 5.72 Knowing that the allowable normal...Ch. 5.3 - 5.73 and 5.74 Knowing that the allowable normal...Ch. 5.3 - 5.73 and 5.74 Knowing that the allowable normal...Ch. 5.3 - 5.75 and 5.76 Knowing that the allowable normal...Ch. 5.3 - 5.75 and 5.76 Knowing that the allowable normal...Ch. 5.3 - 5.77 and 5.78 Knowing that the allowable normal...Ch. 5.3 - 5.77 and 5.78 Knowing that the allowable normal...Ch. 5.3 - A steel pipe of 100-mm diameter is to support the...Ch. 5.3 - Two metric rolled-steel channels are to be welded...Ch. 5.3 - Two rolled-steel channels are to be welded back to...Ch. 5.3 - Two L4 3 rolled-steel angles are bolted together...Ch. 5.3 - Assuming the upward reaction of the ground to be...Ch. 5.3 - Assuming the upward reaction of the ground to be...Ch. 5.3 - Determine the largest permissible distributed load...Ch. 5.3 - Solve Prob. 5.85, assuming that the cross section...Ch. 5.3 - Determine the largest permissible value of P for...Ch. 5.3 - Solve Prob. 5.87, assuming that the T-shaped beam...Ch. 5.3 - Beams AB, BC, and CD have the cross section shown...Ch. 5.3 - Beams AB, BC, and CD have the cross section shown...Ch. 5.3 - Each of the three rolled-steel beams shown...Ch. 5.3 - A 54-kip load is to be supported at the center of...Ch. 5.3 - A uniformly distributed load of 66 kN/m is to be...Ch. 5.3 - A roof structure consists of plywood and roofing...Ch. 5.3 - Solve Prob. 5.94, assuming that the 6-kN...Ch. 5.3 - Prob. 96PCh. 5.3 - Assuming that the front and rear axle loads remain...Ch. 5.4 - 5.98 through 5.100 (a) Using singularity...Ch. 5.4 - 5.98 through 5.100 (a) Using singularity...Ch. 5.4 - 5.98 through 5.100 (a) Using singularity...Ch. 5.4 - 5.101 through 5.103 (a) Using singularity...Ch. 5.4 - Prob. 102PCh. 5.4 - Prob. 103PCh. 5.4 - Prob. 104PCh. 5.4 - Prob. 105PCh. 5.4 - Prob. 106PCh. 5.4 - Prob. 107PCh. 5.4 - Prob. 108PCh. 5.4 - Prob. 109PCh. 5.4 - Prob. 110PCh. 5.4 - Prob. 111PCh. 5.4 - Prob. 112PCh. 5.4 - 5.112 and 5.113 (a) Using singularity functions,...Ch. 5.4 - Prob. 114PCh. 5.4 - 5.114 and 5.115 A beam is being designed to be...Ch. 5.4 - 5.116 and 5.117 A timber beam is being designed to...Ch. 5.4 - Prob. 117PCh. 5.4 - Prob. 118PCh. 5.4 - Prob. 119PCh. 5.4 - 5.118 through 5.121 Using a computer and step...Ch. 5.4 - Prob. 121PCh. 5.4 - 5.122 and 5.123 For the beam and loading shown and...Ch. 5.4 - 5.122 and 5.123 For the beam and loading shown and...Ch. 5.4 - 5.124 and 5.125 For the beam and loading shown and...Ch. 5.4 - Prob. 125PCh. 5.5 - 5.126 and 5.127 The beam AB, consisting of a...Ch. 5.5 - Prob. 127PCh. 5.5 - 5.128 and 5.129 The beam AB, consisting of a...Ch. 5.5 - 5.128 and 5.129 The beam AB, consisting of a...Ch. 5.5 - Prob. 130PCh. 5.5 - Prob. 131PCh. 5.5 - Prob. 132PCh. 5.5 - 5.132 and 5.133 A preliminary design on the use of...Ch. 5.5 - Prob. 134PCh. 5.5 - Prob. 135PCh. 5.5 - Prob. 136PCh. 5.5 - Prob. 137PCh. 5.5 - Prob. 138PCh. 5.5 - Prob. 139PCh. 5.5 - Assuming that the length and width of the cover...Ch. 5.5 - Two cover plates, each 12 in. thick, are welded to...Ch. 5.5 - Two cover plates, each 12 in. thick, are welded to...Ch. 5.5 - Prob. 143PCh. 5.5 - Prob. 144PCh. 5.5 - Two cover plates, each 7.5 mm thick, are welded to...Ch. 5.5 - Prob. 146PCh. 5.5 - Prob. 147PCh. 5.5 - For the tapered beam shown, determine (a) the...Ch. 5.5 - Prob. 149PCh. 5.5 - Prob. 150PCh. 5.5 - Prob. 151PCh. 5 - Draw the shear and bending-moment diagrams for the...Ch. 5 - Draw the shear and bending-moment diagrams for the...Ch. 5 - Determine (a) the distance a for which the...Ch. 5 - For the beam and loading shown, determine the...Ch. 5 - Draw the shear and bending-moment diagrams for the...Ch. 5 - Beam AB, of length L and square cross section of...Ch. 5 - Prob. 158RPCh. 5 - Knowing that the allowable normal stress for the...Ch. 5 - Prob. 160RPCh. 5 - (a) Using singularity functions, find the...Ch. 5 - Prob. 162RPCh. 5 - Prob. 163RP
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- Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a = 2.2 m, b = 4.4 m, c = 3 m, P = 16 kN, w = 34 kN/m, and Q = 26 kN. Label all significant points on each diagram and identify the maximum shear force and bending moment along with their respective locations. Additionally:(a) Determine V and M in the beam at a point located 0.65 m to the right of B.(b) Determine V and M in the beam at a point located 1.40 m to the left of C.Note that answers may be positive or negative. Here, "maximum" refers to the largest magnitude value, but you should enter your shear force and bending moment with the correct sign, using the sign convention presented in Section 7.2 of the textbook. If the magnitudes of the largest positive and largest negative values are the same, enter a positive number.arrow_forwardUsing the coordinate axes shown, write equations for the shear V and bending moment M for anv section A beam is loaded and supported as shown in Fig. Using the coordinate axes shown, write equations for the shear V and bending moment M for any section of the beam In the interval 0arrow_forwardNote: Include all necessary free-body diagrams. Q.1) (a) Find the support reactions of the beam shown below. (b) Find the shear-force and the bending-moment in the beam at point B. (c) Write the expressions for shear-force (V) and bending-moment (M) for the beam as a function of distant 'x' from the left-end support of the beam. A | 1 100 lb/ft 4 ft 4 ft B 300 lb C O 1 2 ft 2 ft Darrow_forwardUse the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a= 3.5 ft, b= 8.0 ft, t, c= 5.0 ft, d= 3.0 ft, w = 8.5 kips/ft and P = 54 kips. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. P В D E b d For this loading, calculate the reaction forces A, and E, acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since A = 0, it has been omitted from the free-body diagram.) P B C E b d E, Answers: Ay = i kips, Ey = i kips.arrow_forwardUse the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a= 3.5 ft, b= 8.0 ft, t, c= 5.0 ft, d= 3.0 ft, w = 8.5 kips/ft and P = 54 kips. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. P В D E a d Determine the shear force acting at each of the following locations: (a) x = 0+ ft (i.e., just to the right of support A) (b) x = 3.5 ft (c) x = 11.5 ft (d) x = 16.5- ft (i.e., just to the left of D) (e) x = 16.5+ ft (i.e., just to the right of D) (f) x = 19.5- ft (i.e., just to the left of support E) When entering your answers, use the shear force sign convention. Answers: (a) V = i kips. (b) V - i kips. (c) V= i kips. (d) V = i kips. (e) V = i kips. (f) V = i kips.arrow_forwardUse the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a= 3.5 ft, b= 8.0 ft, t, c= 5.0 ft, d= 3.0 ft, w = 8.5 kips/ft and P = 54 kips. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. P В D E b d Calculate the maximum bending moment (i.e., either positive or negative) that occurs between points B and C. When entering your answers, use the bending moment sign convention. Answers: M = i kip-ft.arrow_forwardUse the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a= 3.5 ft, b= 8.0 ft, t, c= 5.0 ft, d= 3.0 ft, w = 8.5 kips/ft and P = 54 kips. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. P В D E d Use the graphical method to determine the bending moment acting at B (i.e., x = 3.5 ft). When entering your answers, use the bending moment sign convention. Answer: MB = i kip-ft.arrow_forwardUse the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a= 3.5 ft, b= 8.0 ft, t, c= 5.0 ft, d= 3.0 ft, w = 8.5 kips/ft and P = 54 kips. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. P В D E d Use the graphical method to calculate the bending moments at: (a) point C. (b) point D. When entering your answers, use the bending moment sign convention. Answers: (a) M = i kip-ft. (b) M = i kip-ft.arrow_forwardDetermine the bending moment M in the beam at the point located L = 3.45 m to the left of point C. The ground reactions and shear- force diagram are shown. 40.0 kN 7.0 kN/m A B 3 m 12 m 65.60 kN 58.40 kN 65.60 65.60 25,60 @x=6.66 m -58.40 O 170.9 kN-m O 118.8 kN-m O 129.1 kN-m O 222.0 kN-m O 159.8 kN-m Units: kNarrow_forwardUse the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a= 3.5 ft, b= 8.0 ft, t, c= 5.0 ft, d= 3.0 ft, w = 8.5 kips/ft and P = 54 kips. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. P В D E d The shear-force diagram crosses the V = 0 axis between points B and C. Determine the location x (measured from A) where V = 0 kips. Answer: x = i ft.arrow_forwardDetermine the bending moment M in the beam at the point located L = 4.60 m to the left of point C. The ground reactions and shear- force diagram are shown. A 65.60 kN Units: KN 40.0 KN 3m B 65.60 65.60 25.60 O 183.3 kN-m O 263.5 kN-m O 194.6 kN-m O 224.5 kN-m O 252.1 kN-m 7.0 kN/m 12 m @x=6.66 m 58.40 kN -58.40arrow_forwardDetermine the shear force V in the beam at the point located 4.50 m to the left of point C. The ground reactions and shear-force diagram are shown. 65.60 kN Units: KN 40.0 KN 3 m B 65.60 65.60 25,60 -31.0 KN -26.9 KN -34.9 KN -28.4 KN O -17.3 kN 7.0 kN/m 12 m @x=6.66 m 58.40 KN -58.40arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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