Vector Mechanics for Engineers: Statics, 11th Edition
Vector Mechanics for Engineers: Statics, 11th Edition
11th Edition
ISBN: 9780077687304
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek
Publisher: McGraw-Hill Education
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Chapter 7.3, Problem 7.76P

(a)

To determine

Draw the shear force and bending moment diagrams.

(a)

Expert Solution
Check Mark

Explanation of Solution

Assumption:

Apply the sign convention for calculating the equations of equilibrium as below:

  • For the horizontal forces equilibrium condition, take the force acting towards right side as positive (+) and the force acting towards left side as negative ().
  • For the vertical forces equilibrium condition, take the upward force as positive (+) and downward force as negative ().
  • For moment equilibrium condition, take the clockwise moment as negative and counter clockwise moment as positive.

Apply the following sign convention for calculating the bending moment at any section x-x while approaching from the left hand side.

  • Take clockwise moment as positive and anticlockwise moment as negative

Apply the following sign convention for calculating the shear force at any section x-x while approaching from the left hand side.

  • Take downward force as negative and upward force as positive.

Calculation:

Show the free-body diagram of the beam as in Figure 1.

Vector Mechanics for Engineers: Statics, 11th Edition, Chapter 7.3, Problem 7.76P , additional homework tip  1

Refer to Figure 1:

Find the vertical reaction at point G by taking moment about point C.

MC=016×10×102100(6)150(12)100(18)+Gy(24)16×10×(24+102)=08006001,8001,800+24Gy4,640=0Gy=335lb()

Find the vertical reaction at point C by resolving the vertical component of forces.

Fy=016×10+Cy100150100+Gy16×10=0160+Cy350+335160=0Cy=335lb()

Find the horizontal reaction at point C by resolving the horizontal component of forces.

Fx=0Cx=0

Show the calculation of shear force as follows;

Shear force at x=0;

V|x=0=0

Shear force at x=10in.;

V|x=10in.(Justleft)=16×10=160lbV|x=10in.(Justright)=160+335=175lb

Shear force at x=16in.;

V|x=10in.(Justleft)=175lbV|x=10in.(Justright)=175100=75lb

Shear force at x=22in.;

V|x=22in.(Justleft)=75lbV|x=22in.(Justright)=75150=75lb

Shear force at x=28in.;

V|x=28in.(Justleft)=75lbV|x=28in.(Justright)=75100=175lb

Shear force at x=34in.;

V|x=34in.(Justleft)=175lbV|x=34in.(Justright)=175+Gy=175+335=160lb

Shear force at x=44in.;

V|x=44in.=16016×10=0

Tabulate the calculated shear force values as in Table 1.

Distance, x (in.)Shear force, V (lb)
00
10 (Just left)–160
10 (Just right)175
16 (Just left)175
16 (Just right)75
22 (Just left)75
22 (Just right)–75
28 (Just left)–75
28 (Just right)–175
34 (Just left)–175
34 (Just right)160
440

Plot the shear force diagram as in Figure 2.

Vector Mechanics for Engineers: Statics, 11th Edition, Chapter 7.3, Problem 7.76P , additional homework tip  2

Show the calculation of bending moment as follows;

Bending moment at x=0;

M|x=0=0

Bending moment at x=10in.;

M|x=10in.=16×10×102=800lb-in.

Bending moment at x=16in.

M|x=16in.=16×10×(102+6)+Ay(6)=1,760+335(6)=250lb-in.

Bending moment at x=22in.

M|x=22in.=16×10×(102+12)+Ay(12)100(6)=2,720+335(12)600=700lb-in.

Bending moment at x=28in.

M|x=28in.=16×10×(102+18)+Ay(18)100(12)150(6)=3,680+335(18)1,200900=250lb-in.

Bending moment at x=34in.

M|x=34in.=16×10×(102+24)+Ay(24)100(18)150(12)100(6)=4,640+335(24)1,8001,800600=800lb-in.

Bending moment at x=44in.

M|x=44in.=(16×10×(102+34)+Ay(34)100(28)150(22)100(16)+Gy(10)16×10×102)=6,240+335(34)2,8003,3001,600+335(10)800=0

Tabulate the calculated bending moment values as in Table 2.

Distance, x (in.)Bending moment, M (lb-in.)
00
10–800
16250
22700
28250
34–800
440

Plot the bending moment diagram as in Figure 3.

Vector Mechanics for Engineers: Statics, 11th Edition, Chapter 7.3, Problem 7.76P , additional homework tip  3

(b)

To determine

Find the maximum absolute values of the shear force and bending moment.

(b)

Expert Solution
Check Mark

Answer to Problem 7.76P

The maximum absolute shear force is |Vmax|=175lb_.

The maximum absolute bending moment is |Mmax|=800lb-in._

Explanation of Solution

Refer to the Figure (2);

The maximum absolute shear force is |Vmax|=175lb_.

Refer to the Figure (3);

The maximum absolute bending moment is |Mmax|=800lb-in._

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Chapter 7 Solutions

Vector Mechanics for Engineers: Statics, 11th Edition

Ch. 7.1 - A semicircular rod is loaded as shown. Determine...Ch. 7.1 - Fig. P7.11 and P7.12 7.12 A semicircular rod is...Ch. 7.1 - The axis of the curved member AB is a parabola...Ch. 7.1 - Knowing that the axis of the curved member AB is a...Ch. 7.1 - Prob. 7.15PCh. 7.1 - 7.16 Knowing that the radius of each pulley is 200...Ch. 7.1 - A 5-in.-diameter pipe is supported every 9 ft by a...Ch. 7.1 - For the frame of Prob. 7.17, determine the...Ch. 7.1 - Knowing that the radius of each pulley is 200 mm...Ch. 7.1 - Fig. P7.19 and P7.20 7.20 Knowing that the radius...Ch. 7.1 - and 7.22 A force P is applied to a bent rod that...Ch. 7.1 - and 7.22 A force P is applied to a bent rod that...Ch. 7.1 - A quarter-circular rod of weight W and uniform...Ch. 7.1 - For the rod of Prob. 7.23, determine the magnitude...Ch. 7.1 - A semicircular rod of weight W and uniform cross...Ch. 7.1 - A semicircular rod of weight W and uniform cross...Ch. 7.1 - 7.27 and 7.28 A half section of pipe rests on a...Ch. 7.1 - 7.27 and 7.28 A half section of pipe rests on a...Ch. 7.2 - Prob. 7.29PCh. 7.2 - Prob. 7.30PCh. 7.2 - 7.29 through 7.32 For the beam and loading shown,...Ch. 7.2 - 7.29 through 7.32 For the beam and loading shown,...Ch. 7.2 - 7.33 and 7.34 For the beam and loading shown, (a)...Ch. 7.2 - 7.33 and 7.34 For the beam and loading shown, (a)...Ch. 7.2 - 7.35 and 7.36 For the beam and loading shown, (a)...Ch. 7.2 - 7.35 and 7.36 For the beam and loading shown, (a)...Ch. 7.2 - 7.37 and 7.38 For the beam and loading shown, (a)...Ch. 7.2 - 7.37 and 7.38 For the beam and loading shown, (a)...Ch. 7.2 - For the beam and loading shown, (a) draw the shear...Ch. 7.2 - 7.39 through 7.42 For the beam and loading shown,...Ch. 7.2 - For the beam and loading shown, (a) draw the shear...Ch. 7.2 - Prob. 7.42PCh. 7.2 - Assuming the upward reaction of the ground on beam...Ch. 7.2 - Solve Problem 7.43 knowing that P = 3wa. PROBLEM...Ch. 7.2 - Assuming the upward reaction of the ground on beam...Ch. 7.2 - Solve Prob. 7.45 assuming that the 12-kip load has...Ch. 7.2 - Prob. 7.47PCh. 7.2 - Prob. 7.48PCh. 7.2 - Prob. 7.49PCh. 7.2 - Prob. 7.50PCh. 7.2 - Prob. 7.51PCh. 7.2 - Prob. 7.52PCh. 7.2 - Two small channel sections DF and EH have been...Ch. 7.2 - Solve Prob. 7.53 when = 60. PROBLEM 7.53 Two...Ch. 7.2 - For the structural member of Prob. 7.53, determine...Ch. 7.2 - For the beam of Prob. 7.43, determine (a) the...Ch. 7.2 - Determine (a) the distance a for which the maximum...Ch. 7.2 - For the beam and loading shown, determine (a) the...Ch. 7.2 - A uniform beam is to be picked up by crane cables...Ch. 7.2 - Knowing that P = Q = 150 lb, determine (a) the...Ch. 7.2 - Knowing that P = Q = 150 lb, determine (a) the...Ch. 7.2 - In order to reduce the bending moment in the...Ch. 7.3 - 7.63 Using the method of Sec. 7.3, solve Prob....Ch. 7.3 - Prob. 7.64PCh. 7.3 - 7.65 Using the method of Sec. 7.3, solve Prob....Ch. 7.3 - Prob. 7.66PCh. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.33....Ch. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.34....Ch. 7.3 - Prob. 7.69PCh. 7.3 - Prob. 7.70PCh. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.39....Ch. 7.3 - Prob. 7.72PCh. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.41....Ch. 7.3 - Prob. 7.74PCh. 7.3 - Prob. 7.75PCh. 7.3 - Prob. 7.76PCh. 7.3 - 7.77 and 7.78 For the beam and loading shown, (a)...Ch. 7.3 - Prob. 7.78PCh. 7.3 - Prob. 7.79PCh. 7.3 - For the beam and loading shown, (a) draw the shear...Ch. 7.3 - Prob. 7.81PCh. 7.3 - For the beam and loading shown, (a) draw the shear...Ch. 7.3 - (a) Draw the shear and bending-moment diagrams for...Ch. 7.3 - Solve Prob. 7.83 assuming that the 300-lb force...Ch. 7.3 - For the beam and loading shown, (a) write the...Ch. 7.3 - 7.85 and 7.86 For the beam and loading shown, (a)...Ch. 7.3 - For the beam and loading shown, (a) write the...Ch. 7.3 - For the beam and loading shown, (a) write the...Ch. 7.3 - *7.89 The beam AB is subjected to the uniformly...Ch. 7.3 - Prob. 7.90PCh. 7.3 - Prob. 7.91PCh. 7.3 - Prob. 7.92PCh. 7.4 - Three loads are suspended as shown from the cable...Ch. 7.4 - Knowing that the maximum tension in cable ABCDE is...Ch. 7.4 - Prob. 7.95PCh. 7.4 - Prob. 7.96PCh. 7.4 - Prob. 7.97PCh. 7.4 - Prob. 7.98PCh. 7.4 - Prob. 7.99PCh. 7.4 - Prob. 7.100PCh. 7.4 - Knowing that mB = 70 kg and mC = 25 kg, determine...Ch. 7.4 - Fig. P7.101 and P7.102 7.102 Knowing that mB = 18...Ch. 7.4 - Cable ABC supports two loads as shown. Knowing...Ch. 7.4 - Prob. 7.104PCh. 7.4 - If a = 3 m, determine the magnitudes of P and Q...Ch. 7.4 - If a = 4 m, determine the magnitudes of P and Q...Ch. 7.4 - An electric wire having a mass per unit length of...Ch. 7.4 - The total mass of cable ACB is 20 kg. Assuming...Ch. 7.4 - The center span of the George Washington Bridge,...Ch. 7.4 - The center span of the Verrazano-Narrows Bridge...Ch. 7.4 - Each cable of the Golden Gate Bridge supports a...Ch. 7.4 - Two cables of the same gauge are attached to a...Ch. 7.4 - A 76-m length of wire having a mass per unit...Ch. 7.4 - A cable of length L + is suspended between two...Ch. 7.4 - The total mass of cable AC is 25 kg. Assuming that...Ch. 7.4 - Cable ACB supports a load uniformly distributed...Ch. 7.4 - Each cable of the side spans of the Golden Gate...Ch. 7.4 - A steam pipe weighing 45 lb/ft that passes between...Ch. 7.4 - A cable AB of span L and a simple beam AB of the...Ch. 7.4 - Making use of the property established in Prob....Ch. 7.4 - Prob. 7.121PCh. 7.4 - 7.120 through 7.123 Making use of the property...Ch. 7.4 - Prob. 7.123PCh. 7.4 - Prob. 7.124PCh. 7.4 - Using the property indicated in Prob. 7.124,...Ch. 7.4 - If the weight per unit length of the cable AB is...Ch. 7.5 - A 25-ft chain with a weight of 30 lb is suspended...Ch. 7.5 - A 500-ft-long aerial tramway cable having a weight...Ch. 7.5 - A 40-m cable is strung as shown between two...Ch. 7.5 - A 50-m steel surveying tape has a mass of 1.6 kg....Ch. 7.5 - Prob. 7.131PCh. 7.5 - Prob. 7.132PCh. 7.5 - A 20-m length of wire having a mass per unit...Ch. 7.5 - Determine the sag of a 30-ft chain that is...Ch. 7.5 - Prob. 7.135PCh. 7.5 - Prob. 7.136PCh. 7.5 - A cable weighing 2 lb/ft is suspended between two...Ch. 7.5 - Prob. 7.138PCh. 7.5 - Prob. 7.139PCh. 7.5 - Fig. P7.139 and P7.140 7.140 A motor M is used to...Ch. 7.5 - Prob. 7.141PCh. 7.5 - Prob. 7.142PCh. 7.5 - Prob. 7.143PCh. 7.5 - Prob. 7.144PCh. 7.5 - To the left of point B, the long cable ABDE rests...Ch. 7.5 - Fig. P7.145 and P7.146 7.146 To the left of point...Ch. 7.5 - The 10-ft cable AB is attached to two collars as...Ch. 7.5 - Prob. 7.148PCh. 7.5 - Prob. 7.149PCh. 7.5 - (a) Determine the maximum allowable horizontal...Ch. 7.5 - A cable has a mass per unit length of 3 kg/m and...Ch. 7.5 - Determine the sag-to-span ratio for which the...Ch. 7.5 - Prob. 7.153PCh. 7 - Knowing that the turnbuckle has been tightened...Ch. 7 - Knowing that the turnbuckle has been tightened...Ch. 7 - Two members, each consisting of a straight and a...Ch. 7 - Knowing that the radius of each pulley is 150 mm,...Ch. 7 - For the beam shown, determine (a) the magnitude P...Ch. 7 - For the beam and loading shown, (a) draw the shear...Ch. 7 - For the beam and loading shown, (a) draw the shear...Ch. 7 - For the beam shown, draw the shear and...Ch. 7 - The beam AB, which lies on the ground, supports...Ch. 7 - Two loads are suspended as shown from the cable...Ch. 7 - A wire having a mass per unit length of 0.65 kg/m...Ch. 7 - A 10-ft rope is attached to two supports A and B...
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