Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Textbook Question
Chapter 6, Problem 8RP
A wooden beam has a square cross section as shown Determine which orientation of the beam provides the greatest strength at resisting the moment M. What is the difference in the resulting maximum stress in both cases?
R6–8
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You are working as an engineer in a bearing systems design company. The flow of
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The top plate, representing the moving part of the bearing, travels at a constant speed,
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y = +h
I
2h = 1 cm
x1
y = -h
u(y)
1 dP
2μ dx
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moving plate
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U
2
I2
L = 10 cm
Figure Q1: Flow in a hydrodynamic bearing. The plates extend a width, W = 20 cm,
into the page.
Question 1
You are working as an engineer in a bearing systems design company. The flow of
lubricant inside a hydrodynamic bearing (µ = 0.001 kg m¯¹ s¯¹) can be approximated
as a parallel, steady, two-dimensional, incompressible flow between two parallel plates.
The top plate, representing the moving part of the bearing, travels at a constant speed,
U, while the bottom plate remains stationary (Figure Q1). The plates are separated by
a distance of 2h = 1 cm and are W = 20 cm wide. Their length is L = 10 cm. By
applying the above approximations to the Navier-Stokes equations and assuming that
end effects can be neglected, the horizontal velocity profile can be shown to be
1 dP
u(y)
=
2μ dx
-y² + Ay + B
y= +h
Ꮖ
2h=1 cm
1
x1
y = −h
moving plate
stationary plate
2
X2
L = 10 cm
Figure Q1: Flow in a hydrodynamic bearing. The plates extend a width, W = 20 cm,
into the page.
(a) By considering the appropriate boundary conditions, show that the constants take
the following forms:
U
U
1 dP
A =…
Question 2
You are an engineer working in the propulsion team for a supersonic civil transport
aircraft driven by a turbojet engine, where you have oversight of the design for the
engine intake and the exhaust nozzle, indicated in Figure Q2a. The turbojet engine can
operate when provided with air flow in the Mach number range, 0.60 to 0.80. You are
asked to analyse a condition where the aircraft is flying at 472 m/s at an altitude of
14,000 m. For all parts of the question, you can assume that the flow path of air through
the engine has a circular cross section.
(a)
← intake
normal
shock
472 m/s
A B
(b)
50 m/s
H
472 m/s
B
engine
altitude: 14,000 m
exhaust nozzle
E
F
exit to
atmosphere
diameter: DE = 0.30 m
E
F
diameter: DF = 0.66 m
Figure Q2: Propulsion system for a supersonic aircraft.
a) When the aircraft is at an altitude of 14,000 m, use the International Standard
Atmosphere in the Module Data Book to state the local air pressure and tempera-
ture. Thus show that the aircraft speed…
Chapter 6 Solutions
Mechanics of Materials
Ch. 6.2 - and then draw the shear and moment diagrams for...Ch. 6.2 - In each case, express the shear and moment...Ch. 6.2 - In each case, express the shear and moment...Ch. 6.2 - In each case, express the shear and moment...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - Prob. 1PCh. 6.2 - Prob. 2P
Ch. 6.2 - Prob. 3PCh. 6.2 - Express the shear and moment in terms of x for 0 ...Ch. 6.2 - Express the internal shear and moment in the...Ch. 6.2 - Draw the shear and moment diagrams for the shaft....Ch. 6.2 - Determine the shear and moment as functions of x,...Ch. 6.2 - Determine the shear and moment as functions of x,...Ch. 6.2 - Determine the shear and moment as functions of x,...Ch. 6.2 - Determine the shear and moment in the double...Ch. 6.2 - Draw the shear and moment diagrams for the...Ch. 6.2 - Draw the shear and moment diagrams for the shaft....Ch. 6.2 - Draw the shear and moment diagrams for the...Ch. 6.2 - Draw the shear and moment diagrams for the...Ch. 6.2 - Draw the shear and moment diagrams for the...Ch. 6.2 - Prob. 16PCh. 6.2 - Draw the shear and moment diagrams for the simply...Ch. 6.2 - Prob. 19PCh. 6.2 - Draw the shear and moment diagrams for the beam.Ch. 6.2 - Draw the shear and moment diagrams for the...Ch. 6.2 - The 150-lb man sits in the center of the boat,...Ch. 6.2 - Prob. 24PCh. 6.2 - Draw the shear and moment diagrams for the beam.Ch. 6.2 - Prob. 26PCh. 6.2 - Draw the shear and moment diagrams for the beam....Ch. 6.2 - Prob. 29PCh. 6.2 - Prob. 30PCh. 6.2 - Prob. 31PCh. 6.2 - Prob. 34PCh. 6.2 - Prob. 35PCh. 6.2 - The beam is used to support a uniform load along...Ch. 6.2 - Prob. 39PCh. 6.2 - Prob. 42PCh. 6.2 - Prob. 43PCh. 6.2 - Prob. 44PCh. 6.2 - Prob. 45PCh. 6.2 - The truck is to be used to transport the concrete...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - Determine the moment M that will produce a maximum...Ch. 6.4 - Determine the maximum tensile and compressive...Ch. 6.4 - The beam is constructed from four pieces of wood,...Ch. 6.4 - The beam is constructed from four pieces of wood,...Ch. 6.4 - The beam is made from three boards nailed together...Ch. 6.4 - The beam is made from three boards nailed together...Ch. 6.4 - Prob. 54PCh. 6.4 - The tubular shaft is supported by a smooth thrust...Ch. 6.4 - Prob. 57PCh. 6.4 - If the beam is subjected to an internal moment or...Ch. 6.4 - If the beam is made of material having an...Ch. 6.4 - Prob. 60PCh. 6.4 - Prob. 61PCh. 6.4 - The beam is subjected to a moment of M = 40 kN m....Ch. 6.4 - The steel shaft has a diameter of 2 in. It is...Ch. 6.4 - Determine the dimension a of a beam having a...Ch. 6.4 - A shaft is made of a polymer having an elliptical...Ch. 6.4 - Solve Prob. 6-65 if the moment M = 50 N m is...Ch. 6.4 - Prob. 67PCh. 6.4 - If M=4kipft , determine the resultant force the...Ch. 6.4 - The strut on the utility pole supports the cable...Ch. 6.4 - The pin is used to connect the three links...Ch. 6.4 - Prob. 75PCh. 6.4 - A timber beam has a cross section which is...Ch. 6.4 - If the beam is subjected to an internal moment of...Ch. 6.4 - If the allowable tensile and compressive stress...Ch. 6.4 - If the beam is subjected to an internal moment of...Ch. 6.4 - Prob. 80PCh. 6.4 - Prob. 81PCh. 6.4 - Prob. 82PCh. 6.4 - Prob. 83PCh. 6.4 - If the intensity of the load w=15kN/m , determine...Ch. 6.4 - Prob. 85PCh. 6.4 - Determine the absolute maximum bending stress in...Ch. 6.4 - Prob. 87PCh. 6.4 - Prob. 88PCh. 6.4 - If the compound beam in Prob. 642 has a square...Ch. 6.4 - If the beam in Prob. 628 has a rectangular cross...Ch. 6.4 - Determine the absolute maximum bending stress in...Ch. 6.4 - Determine, to the nearest millimeter, the smallest...Ch. 6.4 - If the beam in Prob.63 has a rectangular cross...Ch. 6.4 - The simply supported truss is subjected to the...Ch. 6.4 - If d = 450 mm, determine the absolute maximum...Ch. 6.4 - If the allowable bending stress is allow = 6 MPa,...Ch. 6.4 - Prob. 102PCh. 6.4 - Prob. 103PCh. 6.5 - Determine the bending stress at corners A and B....Ch. 6.5 - Determine the maximum bending stress in the beams...Ch. 6.5 - The member has a square cross section and is...Ch. 6.5 - The member has a square cross section and is...Ch. 6.5 - Consider the general case of a prismatic beam...Ch. 6.5 - The steel shaft is subjected to the two loads. If...Ch. 6.5 - The 65-mm-diameter steel shaft is subjected to the...Ch. 6.5 - For the section, lz = 31.7(10-5) m4, lY =...Ch. 6.5 - For the section, lz, = 31.7(10-5) m4, lY =...Ch. 6.9 - The composite beam is made of steel (A) bonded to...Ch. 6.9 - The composite beam is made of steel (A) bonded to...Ch. 6.9 - Segment A of the composite beam is made from...Ch. 6.9 - Segment A of the composite beam is made from...Ch. 6.9 - A wood beam is reinforced with steel straps at its...Ch. 6.9 - The composite beam is made of A-36 steel (A)...Ch. 6.9 - The composite beam is made of A-36 steel (A)...Ch. 6.9 - If the beam is subjected to a moment of M = 45 kN...Ch. 6.9 - The Douglas Fir beam is reinforced with A-36 steel...Ch. 6.9 - For the curved beam in Fig. 640a, show that when...Ch. 6.9 - The curved member is subjected to the moment of M...Ch. 6.9 - The curved member is made from material having an...Ch. 6.9 - If P = 3 kN, determine the bending stress at...Ch. 6.9 - If the maximum bending stress at section a-a is...Ch. 6.9 - The elbow of the pipe has an outer radius of 0.75...Ch. 6.9 - The curved bar used on a machine has a rectangular...Ch. 6.9 - The steel rod has a circular cross section. If it...Ch. 6.9 - Prob. 150PCh. 6.9 - Prob. 151PCh. 6.9 - The bar has a thickness of 1 in. and the allowable...Ch. 6.9 - The bar has a thickness of 1 in. and is subjected...Ch. 6.9 - Prob. 154PCh. 6.9 - The bar is subjected to a moment of M=17.5Nm If...Ch. 6.9 - Prob. 156PCh. 6.9 - Prob. 157PCh. 6.10 - The beam is made of an elastic plastic material...Ch. 6.10 - The wide-flange member is made from an elastic...Ch. 6.10 - The rod has a circular cross section. If it is...Ch. 6.10 - The rod has a circular cross section. If it is...Ch. 6.10 - The beam is made of an elastic perfectly plastic...Ch. 6.10 - Determine the plastic moment Mp that can be...Ch. 6.10 - Prob. 164PCh. 6.10 - Prob. 166PCh. 6.10 - Prob. 170PCh. 6.10 - Prob. 171PCh. 6.10 - The box beam is made of an elastic perfectly...Ch. 6.10 - The plexiglass bar has a stress-strain curve that...Ch. 6 - Determine the shape factor for the wide-flange...Ch. 6 - The compound beam consists of two segments that...Ch. 6 - The composite beam consists of a wood core and two...Ch. 6 - If it resists a moment of M = 125 N m, determine...Ch. 6 - Determine the maximum bending stress in the handle...Ch. 6 - The curved beam is subjected to a bending moment...Ch. 6 - Determine the shear and moment in the beam as...Ch. 6 - A wooden beam has a square cross section as shown...Ch. 6 - Draw the shear and moment diagrams for the shaft...Ch. 6 - The strut has a square cross section a by a and is...
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