Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Chapter 4, Problem 4.3.27P
The centrifuge shown in the figure rotates in a horizontal plane (the x-y plane) on a smooth surface about the z axis (which is vertical) with an angular acceleration a. Each of the two arms has a weight w per unit length and supports a weight W = 2B/L at its end.
Derive formulas for the maximum shear force and maximum bending moment in the arms, assuming b = L/9 and c = L/10.
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The figure below depicts the tire, axle, and gear of a large tractor. The entire structure is in mechanical
equilibrium. Bearings support the rotating axle at points A and C attached to the tractor's frame. A
force FD = 5000 lb is applied in the -z direction at point G of a gear with a 3-in radius. The force W
= 1000 lb in the +z direction represents a normal force resulting from the weight of the tractor. The
force Q acting in the +x direction, represents the traction force between the tire and the ground. The
wheel, axle, and gear assembly weigh 150 lb with center of gravity at point D, which lies on the y axis
with coordinate yp = -18 in. Points A, C, D (not seen in the figure), and E lie in the yz plane. Point
G lies in the xy plane.
Questions & Analysis:
(a) Draw the FBD for the wheel, axle, and gear assembly if the bearings at A and B resist moments and
the bearing at A is a thrust bearing. Label all unknowns.
(b) Is the assembly statically determinate or statically…
points A, B and D, respectively, as shown in the figure. A uniformly distributed loac
of 4 kN/m acting vertically downwards extends for a length of 4 m between point
A and C.
Page 3 of 6
5 kN
10 kN
4 kN/m
A
2 m
2 m
1 m
2 m
30 kN
Figure Q2: A cantilever beam
2.1.
Calculate the magnitudes and directions of the support reaction force RE
and bending moment ME and at point E.
2.2.
Establish the equations of shear forces (SF) and bending moments (BM)
for each span of the beam.
2.3.
On the basis of the established equations for SF and BM for the
cantilever beam, construct the shear force and bending moment
diagrams along the entire span of the beam.
2.4. Determine the magnitude and position of the maximum bending moment
acting on the beam.
2.5.
Calculate and show the positions of the points of contra-flexure (PCE)
1. The side rod of the engine in the figure is 8ft long and weighs 100lb. the cranks AD
and BC are of length r=18in. and rotate at 300 rpm. Determine the maximum
bending moment M in the rod if M=wL/8, where w is the total distributed load and L
is the length of the rod.
B
Chapter 4 Solutions
Mechanics of Materials (MindTap Course List)
Ch. 4 - Calculate the shear force V and bending moment...Ch. 4 - Determine the shear force V and bending moment M...Ch. 4 - Determine the shear force V and bending moment M...Ch. 4 - Calculate the shear force V and bending moment M...Ch. 4 - Consider the beam with an overhang shown in the...Ch. 4 - The beam ABC shown in the figure is simply...Ch. 4 - The beam ABCD shown in the figure has overhangs at...Ch. 4 - At a full d raw, an archer applies a pull of 130 N...Ch. 4 - A curved bar ABC is subjected to loads in the form...Ch. 4 - Under cruising conditions, the distributed load...
Ch. 4 - A beam ABCD with a vertical arm CE is supported as...Ch. 4 - A simply supported beam AB supports a trapezoid...Ch. 4 - Beam ABCD represents a reinforced-concrete...Ch. 4 - Find shear (V) and moment (M) at x = 3L/4 for the...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - Find expressions for shear force V and moment Mat...Ch. 4 - Find expressions for shear force V and moment Mat...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - A cable with force P is attached to a frame at A...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - A cable with force P is attached to a frame at D...Ch. 4 - Frame ABCD carries two concentrated loads (2P at T...Ch. 4 - Frame ABC has a moment release just left of joint...Ch. 4 - The simply supported beam ABCD is loaded by a...Ch. 4 - The centrifuge shown in the figure rotates in a...Ch. 4 - Draw the shear-Force and bending-moment diagrams...Ch. 4 - A simple beam AB is subjected to a counter...Ch. 4 - Draw the shear-force and bending-moment diagrams...Ch. 4 - The cantilever beam AB shown in the figure is...Ch. 4 - Cantilever beam AB carries an upward uniform load...Ch. 4 - The simple beam AB shown in the figure is...Ch. 4 - A simple beam AB subjected to couples M1and 3M2...Ch. 4 - A simply supported beam ABC is loaded by a...Ch. 4 - A simply supported beam ABC is loaded at the end...Ch. 4 - A beam ABC is simply supported at A and B and has...Ch. 4 - Beam ABCD is simply supported at B and C and has...Ch. 4 - Draw the shear-force and bending-moment diagrams...Ch. 4 - The simple beam AB supports a triangular load of...Ch. 4 - The beam AB shown in the figure supports a uniform...Ch. 4 - A cantilever beam AB supports a couple and a...Ch. 4 - The cantilever beam A B shown in the figure is...Ch. 4 - Beam ABC has simple supports at .A and B. an...Ch. 4 - Beam ABC with an overhang at one end supports a...Ch. 4 - Consider the two beams shown in the figures. Which...Ch. 4 - The three beams in the figure have the same...Ch. 4 - The beam ABC shown in the figure is simply...Ch. 4 - A simple beam AB is loaded by two segments of...Ch. 4 - Two beams (see figure) are loaded the same and...Ch. 4 - The beam A BCD shown in the figure has overhangs...Ch. 4 - A beam ABCD with a vertical arm CE is supported as...Ch. 4 - Beams ABC and CD are supported at A,C, and D and...Ch. 4 - The simple beam ACE shown in the figure is...Ch. 4 - A beam with simple supports is subjected to a...Ch. 4 - A beam of length L is designed to support a...Ch. 4 - The compound beam ABCDE shown in the figure...Ch. 4 - Draw the shear-force and bending-moment diagrams...Ch. 4 - The shear-force diagram for a simple beam is shown...Ch. 4 - The shear-force diagram for a beam is shown in the...Ch. 4 - A compound beam (see figure) has an internal...Ch. 4 - A compound beam (see figure) has an shear release...Ch. 4 - A simple beam AB supports two connected wheel...Ch. 4 - The inclined beam represents a ladder with the...Ch. 4 - Beam ABC is supported by a tie rod CD as shown....Ch. 4 - A plane frame (see figure) consists of column AB...Ch. 4 - The plane frame shown in the figure is part of an...
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