EBK MECHANICS OF MATERIALS
7th Edition
ISBN: 8220100257063
Author: BEER
Publisher: YUZU
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Chapter 6.5, Problem 55P
To determine
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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.
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
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.
Chapter 6 Solutions
EBK MECHANICS OF MATERIALS
Ch. 6.2 - Three full-size 50 100-mm boards are nailed...Ch. 6.2 - For the built-up beam of Prob. 6.1, determine the...Ch. 6.2 - Three boards, each 2 in. thick, are nailed...Ch. 6.2 - A square box beam is made of two 20 80-mm planks...Ch. 6.2 - The American Standard rolled-steel beam shown has...Ch. 6.2 - The beam shown is fabricated by connecting two...Ch. 6.2 - A column is fabricated by connecting the...Ch. 6.2 - The composite beam shown is fabricated by...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...
Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.13 and 6.14 For a beam having the cross section...Ch. 6.2 - 6.13 and 6.14 For a beam having the cross section...Ch. 6.2 - For a timber beam having the cross section shown,...Ch. 6.2 - Two steel plates of 12 220-mm rectangular cross...Ch. 6.2 - Two W8 31 rolled sections may be welded at A and...Ch. 6.2 - For the beam and. loading shown, determine the...Ch. 6.2 - Fig. P6.19 6.19 A timber beam AB of length L and...Ch. 6.2 - A timber beam AB of Length L and rectangular cross...Ch. 6.2 - 6.21 and 6.22 For the beam and loading shown,...Ch. 6.2 - 6.21 and 6.22 For the beam and loading shown,...Ch. 6.2 - 6.23 and 6.24 For the beam and loading shown,...Ch. 6.2 - 6.23 and 6.24 For the beam and loading shown,...Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.2 - Prob. 27PCh. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.5 - The built-up timber beam shown is subjected to a...Ch. 6.5 - The built-up beam shown is made by gluing together...Ch. 6.5 - The built-up beam was made by gluing together...Ch. 6.5 - Several wooden planks are glued together to form...Ch. 6.5 - The built-up wooden beam shown is subjected to a...Ch. 6.5 - Knowing that a W360 122 rolled-steel beam is...Ch. 6.5 - 6.35 and 6.36 An extruded aluminum beam has the...Ch. 6.5 - 6.35 and 6.36 An extruded aluminum beam has the...Ch. 6.5 - Knowing that a given vertical shear V causes a...Ch. 6.5 - The vertical shear is 1200 lb in a beam having the...Ch. 6.5 - The vertical shear is 1200 lb in a beam having the...Ch. 6.5 - 6.40 and 6.47 The extruded aluminum beam has a...Ch. 6.5 - Prob. 41PCh. 6.5 - Prob. 42PCh. 6.5 - Three planks are connected as shown by bolts of...Ch. 6.5 - A beam consists of three planks connected as shown...Ch. 6.5 - A beam consists of five planks of 1.5 6-in. cross...Ch. 6.5 - Four L102 102 9.5 steel angle shapes and a 12 ...Ch. 6.5 - A plate of 14-in. thickness is corrugated as shown...Ch. 6.5 - Prob. 48PCh. 6.5 - An extruded beam has the cross section shown and a...Ch. 6.5 - Prob. 50PCh. 6.5 - The design of a beam calls for connecting two...Ch. 6.5 - The cross section of an extruded beam is a hollow...Ch. 6.5 - Prob. 53PCh. 6.5 - Prob. 54PCh. 6.5 - Prob. 55PCh. 6.5 - 6.56 and 6.57 A composite beam is made by...Ch. 6.5 - 6.56 and 6.57 A composite beam is made by...Ch. 6.5 - Prob. 58PCh. 6.5 - Prob. 59PCh. 6.5 - Prob. 60PCh. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - Prob. 64PCh. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.69 through 6.74 Determine the location of the...Ch. 6.6 - Prob. 70PCh. 6.6 - Prob. 71PCh. 6.6 - Prob. 72PCh. 6.6 - Prob. 73PCh. 6.6 - Prob. 74PCh. 6.6 - Prob. 75PCh. 6.6 - 6.75 and 6.76 A thin-walled beam has the cross...Ch. 6.6 - 6.77 and 6.78 A thin-walled beam of uniform...Ch. 6.6 - Prob. 78PCh. 6.6 - Prob. 79PCh. 6.6 - Prob. 80PCh. 6.6 - Prob. 81PCh. 6.6 - Prob. 82PCh. 6.6 - Prob. 83PCh. 6.6 - Prob. 84PCh. 6.6 - Prob. 85PCh. 6.6 - Solve Prob. 6.85, assuming that the thickness of...Ch. 6.6 - Prob. 87PCh. 6.6 - Prob. 88PCh. 6 - Three boards are nailed together to form the beam...Ch. 6 - For the beam and loading shown, consider section...Ch. 6 - For the wide-flange beam with the loading shown,...Ch. 6 - For the beam and loading shown, consider section...Ch. 6 - The built-up timber beam is subjected to a 1500-lb...Ch. 6 - Knowing that a given vertical shear V causes a...Ch. 6 - Three planks are connected as shown by bolts of...Ch. 6 - Three 1 18-in. steel plates are bolted to four L6...Ch. 6 - The composite beam shown is made by welding C200 ...Ch. 6 - Prob. 98RPCh. 6 - A thin-walled beam of uniform thickness has the...Ch. 6 - Determine the location of the shear center O of a...
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- ]: A horizontal beam with a length of 4.5 m is subjected to the shown loading. The forces are vertical and the couple moment is applied at point D. The figure is not to scale. 3 kN/ m 1 kN/ m 3 kNm A В C D E 1 т 1.5 m 0.5m 1.5m 0.6 KN 1.35KN (a) Motivate with substantiating explanations and clear and applicable calculations why the beam is in equilibrium. (b) Draw the shear force and bending moment diagrams for the beam. Calculate all local maxima and minima, zeros and points where the diagrams change shape, and show these values and points on the diagrams.arrow_forwardsolve the question provided in the image completely.arrow_forward2. The simply supported wood beam ABC in Fig. (a) has the rectangular cross section shown. The beam supports a concentrated load of 300 N located 2 m from the left support. Determine the maximum displacement and maximum slope angle of the beam at 1.7 m from A. Use E = 12 GPa for the modulus of elasticity. Neglect the weight of the beam. |300 N В C A 80 mm 40 mm 2 m 1.0 m→ Rc RA (a)arrow_forward
- Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Leta = 5.2 ft, w = 235 Ib/ft, Mp = 7000 lb-ft, and P = 11001b. 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. Mp Determine the bending moment acting at each of the following locations: (a) x = 5.2 ft (i.e., at point B) (b) x = 10.4 ft (i.e., at point C) (c) x = 15.6 – ft (i.e., just to the left of point D) (d) x = 15.6 + ft (i.e., just to the right of point D) (e) x = 20.8 ft (i.e., at point E) When entering your answers, use the bending moment sign convention.arrow_forward| 5 kips 30 kip • ft I = 90 in.“. 6 in. |B D NA 2 in. 4 ft 4 ft- FIG. P5.36arrow_forwardfind second moment of area for cases 4-7arrow_forward
- For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the location of the maximum deflection, and (c) the maximum beam deflection. Assume that El is constant for the beam. Let w = 13 kN/m, L = 4.0 m, E = 180 GPa, and I = 130 x 106 mm“. B L Answer: (b) х %3 m (c) Vmax mmarrow_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_forwardStrength of Materialsarrow_forward
- For the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let w = 20.0 kips/ft, a=6.0 ft, and b=20.5 ft. 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 A A Answers: By a = Calculate the reaction forces By and Cy 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 Bx = O, it has been omitted from the free-body diagram.) = a i B Cy i = W B b W b kips X kips Xarrow_forwardGraph the shear and bending momentarrow_forward1. From the given figures below, write the shear and moment equation of each segment of the beam. Use the left portion of the beam and use point A as reference of 'x'. Figure1.1 40 kN 32 kN / m B C 4 m 4 m 4 m Figure 1.2 30 kN 20 kN 16 k N / m 10 k N / m 40 kN-m A B |C E OF 3 m 3 m - 2 m 8 m 2 m -arrow_forward
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