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 7.2, Problem 7.57P
Determine (a) the distance a for which the maximum absolute value of the bending moment in beam AB is as small as possible, (b) the corresponding value of |M|max. (See the hint for Prob. 7.55.)
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A uniform beam is to be picked up by crane cables attached at A and B. Determine the distance afrom the ends of the beam to the points where the cables should be attached if the maximum absolute value of the bending moment in the beam is to be as small as possible. (Hint: Draw the bending-moment diagram in terms of a, L, and the weight per unit length w , and then equate the absolute values of the largest positive and negative bending moments obtained.)
Draw the shearing-force and bending-moment diagrams for the following beams:
1. A cantilever of length 20 m carrying a load of 10 kN at a distance of 15 m from the supported end.
2. A cantilever of length 20 m carrying a load of 10 kN is uniformly distributed over the inner 15 m of its length.
3. A cantilever of length 12 m carrying a load of 8 kN, applied 5 m from the supported end, and a load of 2kNlm over its whole length.
Determine the bending moment acting at each of the following locations:(a) x = 13.5- ft (i.e., just to the left of point B)(b) x = 13.5+ ft(i.e., just to the right of point B)(c) x = 17.0 ft (i.e. at point C)(d) x = 23.0 ftNote that x = 0 at support A. When entering your answers, use the shear-force sign convention detailed in Section 7.2.Answers:
(a)
M =
kips-ft
(b)
M =
kips-ft
(c)
M =
kips-ft
(d)
M =
kips-ft
Use your shear-force and bending-moment diagrams to determine the maximum positive bending moment, Mmax, pos, the maximum negative bending moment, Mmax, neg, and their respective locations, xmax, pos and xmax, neg. When entering your answers for the maximum bending moments, use the shear-force and bending-moment sign conventions detailed in Section 7.2. The maximum negative bending moment is the negative moment with the largest absolute value. Enter the maximum negative bending moment as a negative value.Answers:
Mmax, pos =
kips-ft
xmax, pos =
ft
Mmax,…
Chapter 7 Solutions
Vector Mechanics for Engineers: Statics, 11th Edition
Ch. 7.1 - 7.1 and 7.2 Determine the internal forces (axial...Ch. 7.1 - Prob. 7.2PCh. 7.1 - 7.3 Determine the internal forces at point J when...Ch. 7.1 - Prob. 7.4PCh. 7.1 - Prob. 7.5PCh. 7.1 - Prob. 7.6PCh. 7.1 - An archer aiming at a target is pulling with a...Ch. 7.1 - For the bow of Prob. 7.7, determine the magnitude...Ch. 7.1 - A semicircular rod is loaded as shown. Determine...Ch. 7.1 - A semicircular rod is loaded as shown. Determine...
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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