Vector Mechanics for Engineers: Statics
12th Edition
ISBN: 9781259977244
Author: BEER
Publisher: MCG
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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
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Ch. 7.1 - A semicircular rod is loaded as shown. 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