Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 5, Problem 5.7.2P
.2 A ligmio.irc ii supported by two vorlical beams consistins: of thin-walled, tapered circular lubes (see ligure part at. for purposes of this analysis, each beam may be represented as a cantilever AB of length L = 8.0 m subjected to a lateral load P = 2.4 kN at the free end. The tubes have a constant thickness ; = 10.0 mm and average diameters dA = 90 mm and dB = 270 mm at ends A and B, re s pec lively.
Because the thickness is small compared to the diameters, the moment of inerlia at any cross section may be obtained from the formula / = jrrf3;/8 (see Case 22, Appendix E); therefore, the section modulus mav be obtained from the formula S = trdhlA.
(a) At what dislance A from the free end docs the maximum bending stress occur? What is the magnitude trllul of the maximum bending stress? What is the ratio of the maximum stress to the largest stress
(b) Repeat part (a) if concentrated load P is applied upward at A and downward uniform load q {-x) = 2PIL is applied over the entire beam as shown in the figure part b What is the ratio of the maximum stress to the stress at the location of maximum moment? 
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
1. Plot the moment (M), axial (N), and shear (S) diagrams as functions of z.
a)
b)
F₁ = 1250 N
F₁ = 600 N
M₁ = 350 000 N mm
F2 = 500 N
200 N
a = 600 mm
b=1000 mm
a=750 mm
b = 1000 mm
d)
M₁ = 350 000 N mm
F₁ = 600 N
F₂ =200 N
a = 600 mm
b = 1000 mm
M₁ 175 000 Nmm
F = 900 N
a-250 mm
b-1000 mm
-250 mm.
Figure 1: Schematics problem 1.
Given the following cross-sections (with units in mm):
b)
t=2
b=25
h=25
t = 1.5
b=20
b=25
t=2
I
t = 1.5
a=10
b=15
h-25
b=15
t=3
T
h=25
Figure 3: Cross-sections for problem 2.
1. For each of them, calculate the position of the centroid of area with respect to the given coordinate system
and report them in the table below.
2. For each of them, calculate the second moments of inertia I...
and I, around their respective centroid
of area and report them in the table below. Note: use the parallel axes theorem as much as possible to
minimize the need to solve integrals.
Centroid position
x
y
box
Moment of inertia
lyy
by
a)
b)
c)
d)
e)
Problem 1: Analyze the canard-wing combination shown in Fig. 1. The canard and wing are made
of the same airfoil section and have
AR AR, S = 0.25, and = 0.45%
1. Develop an expression for the moment coefficient about the center of gravity in terms of the
shown parameters (, and zg) and the three-dimensional aerodynamic characteristics of the
used wing/canard (CL C and CM).
2. What is the range of the cg location for this configuration to be statically stable?
You may simplify the problem by neglecting the upwash (downwash) effects between the lifting
surfaces and the drag contribution to the moment. You may also assume small angle approximation.
Figure 1: Canard-Wing Configuration.
Chapter 5 Solutions
Mechanics of Materials (MindTap Course List)
Ch. 5 - A steel wire with a diameter of d = 1/16 in. is...Ch. 5 - A copper wire having a diameter ofd = 4 mm is bent...Ch. 5 - A 4.75-in, outside diameter polyethylene pipe...Ch. 5 - A cantilever beam AB is loaded by a couple M0at...Ch. 5 - A thin strip of steel with a length of L =19 in....Ch. 5 - A bar of rectangular cross section is loaded and...Ch. 5 - A simply supported beam with a length L = 10 ft...Ch. 5 - A cantilever beam is subjected to a concentrated...Ch. 5 - A thin strip of hard copper (E = 16,000 ksi)...Ch. 5 - A steel wire (E = 200 GPa) of a diameter d = L25...
Ch. 5 - A thin, high-strength steel rule (E = 30 x 10ft...Ch. 5 - A simply supported wood beam AB with a span length...Ch. 5 - Beam ABC has simple supports at A and B and an...Ch. 5 - A simply supported beam is subjected to a in early...Ch. 5 - Each girder of the lift bridge (sec figure) is 180...Ch. 5 - A freight-car axle AS is loaded approximately as...Ch. 5 - A seesaw weighing 3 lb/ft of length is occupied by...Ch. 5 - During construction of a highway bridge, the main...Ch. 5 - The horizontal beam ABC of an oil-well pump has...Ch. 5 - A railroad tie (or sleeper) is subjected to two...Ch. 5 - A fiberglass pipe is lifted by a sling, as shown...Ch. 5 - A small dam of height h = 2.0 m is constructed of...Ch. 5 - Determine the maximum tensile stress (7, (due to...Ch. 5 - Determine the maximum bending stress emaxdue to...Ch. 5 - A simple beam A B of a span length L = 24 ft is...Ch. 5 - Determine the maximum tensile stress erand maximum...Ch. 5 - A cantilever beam A3, loaded by a uniform load and...Ch. 5 - A canti lever beam A B of a n isosceles t...Ch. 5 - A cantilever beam, a C12 x 30 section, is...Ch. 5 - A frame ABC travels horizontally with an...Ch. 5 - A beam ABC with an overhang from B to C supports a...Ch. 5 - A cantilever beam AB with a rectangular cross...Ch. 5 - A beam with a T-section is supported and loaded as...Ch. 5 - Consider the compound beam with segments AB and...Ch. 5 - A small dam of a height h = 6 ft is constructed of...Ch. 5 - A foot bridge on a hiking trail is constructed...Ch. 5 - A steel post (E=30×106) having thickness t = 1/8...Ch. 5 - Beam ABCDE has a moment release just right of...Ch. 5 - A simply supported wood beam having a span length...Ch. 5 - A simply supported beam (L = 4.5 m) must support...Ch. 5 - The cross section of a narrow-gage railway bridge...Ch. 5 - A fiberglass bracket A BCD with a solid circular...Ch. 5 - A cantilever beanie B is loaded by a uniform load...Ch. 5 - A simple beam of length L = 5 m carries a uniform...Ch. 5 - A simple beam AB is loaded as shown in the figure....Ch. 5 - A pontoon bridge (see figure) is constructed of...Ch. 5 - A floor system in a small building consists of...Ch. 5 - The wood joists supporting a plank Floor (see...Ch. 5 - A beam ABC with an overhang from B to C is...Ch. 5 - -12 A "trapeze bar" in a hospital room provides a...Ch. 5 - A two-axle carriage that is part of an over head...Ch. 5 - A cantilever beam AB with a circular cross section...Ch. 5 - A propped cantilever beam A BC (see figure) has a...Ch. 5 - A small balcony constructed of wood is supported...Ch. 5 - A beam having a cross section in the form of an un...Ch. 5 - A beam having a cross section in the form of a...Ch. 5 - Determine the ratios of the weights of four beams...Ch. 5 - Prob. 5.6.20PCh. 5 - A steel plate (called a cover ploie) having...Ch. 5 - A steel beam ABC is simply supported at A and...Ch. 5 - A retaining wall 6 ft high is constructed of...Ch. 5 - A retaining wall (Fig. a) is constructed using...Ch. 5 - A beam of square cross section (a = length of each...Ch. 5 - The cross section of a rectangular beam having a...Ch. 5 - A tapered cantilever beam A B of length L has...Ch. 5 - .2 A ligmio.irc ii supported by two vorlical beams...Ch. 5 - Prob. 5.7.3PCh. 5 - Prob. 5.7.4PCh. 5 - Prob. 5.7.5PCh. 5 - A cantilever beam AB with rectangular cross...Ch. 5 - A simple beam ABC having rectangular cross...Ch. 5 - A cantilever beam AB having rectangular cross...Ch. 5 - The shear stresses t in a rectangular beam arc...Ch. 5 - .2 Calculate the maximum shear stress tmaxand the...Ch. 5 - A simply supported wood beam is subjected to...Ch. 5 - A simply supported wood beam with overhang is...Ch. 5 - Two wood beams, each of rectangular cross section...Ch. 5 - A cantilever beam of length L = 2 m supports a...Ch. 5 - A steel beam of length L = 16 in. and...Ch. 5 - A beam of rectangular cross section (width/) and...Ch. 5 - A laminated wood beam on simple supports (figure...Ch. 5 - A laminated plastic beam of square cross section...Ch. 5 - A wood beam AB on simple supports with span length...Ch. 5 - A simply supported wood beam of rectangular cross...Ch. 5 - A square wood platform is 8 ft × 8 ft in area and...Ch. 5 - A wood beam ABC with simple supports at A and B...Ch. 5 - A wood pole with a solid circular cross section (d...Ch. 5 - A simple log bridge in a remote area consists of...Ch. 5 - A vertical pole consisting of a circular tube of...Ch. 5 - A circular pole is subjected to linearly varying...Ch. 5 - A sign for an automobile service station is...Ch. 5 - A steel pipe is subjected to a quadratic...Ch. 5 - -1 through 5.10-6 A wide-flange beam (see figure)...Ch. 5 - -1 through 5.10-6 A wide-flange beam (see figure)...Ch. 5 - -1 through 5.10-6 A wide-flange beam (see figure)...Ch. 5 - -1 through 5.10-6 A wide-flange beam (see figure)...Ch. 5 - -1 through 5.10-6 A wide-flange beam (see figure)...Ch. 5 - -1 through 5.10-6 A wide-flange beam (see figure)...Ch. 5 - A cantilever beam AB of length L = 6.5 ft supports...Ch. 5 - A bridge girder A B on a simple span of length L =...Ch. 5 - A simple beam with an overhang supports a uniform...Ch. 5 - A hollow steel box beam has the rectangular cross...Ch. 5 - A hollow aluminum box beam has the square cross...Ch. 5 - The T-beam shown in the figure has cross-sectional...Ch. 5 - Calculate the maximum shear stress tmax. in the...Ch. 5 - A prefabricated wood I-beam serving as a floor...Ch. 5 - A welded steel gird crhaving the erass section...Ch. 5 - A welded steel girder having the cross section...Ch. 5 - A wood box beam is constructed of two 260 mm × 50...Ch. 5 - A box beam is constructed of four wood boards as...Ch. 5 - Two wood box beams (beams A and B) have the same...Ch. 5 - A hollow wood beam with plywood webs has the...Ch. 5 - A beam of a T cross section is formed by nailing...Ch. 5 - The T-beam shown in the figure is fabricated by...Ch. 5 - A steel beam is built up from a W 410 × 85 wide...Ch. 5 - The three beams shown have approximately the same...Ch. 5 - Two W 310 × 74 Steel wide-flange beams are bolted...Ch. 5 - A pole is fixed at the base and is subjected to a...Ch. 5 - A solid circular pole is subjected to linearly...Ch. 5 - While drilling a hole with a brace and bit, you...Ch. 5 - An aluminum pole for a street light weighs 4600 N...Ch. 5 - A curved bar ABC having a circular axis (radius r...Ch. 5 - A rigid Trame ABC is formed by welding two steel...Ch. 5 - A palm tree weighing 1000 lb is inclined at an...Ch. 5 - A vertical pole of aluminum is fixed at the base...Ch. 5 - Because of foundation settlement, a circular tower...Ch. 5 - A steel bracket of solid circular cross section is...Ch. 5 - A cylindrical brick chimney of height H weighs w =...Ch. 5 - A flying but tress transmit s a load P = 25 kN,...Ch. 5 - A plain concrete wall (i.e., a wall with no steel...Ch. 5 - A circular post, a rectangular post, and a post of...Ch. 5 - Two cables, each carrying a tensile force P = 1200...Ch. 5 - Prob. 5.12.16PCh. 5 - A short column constructed of a W 12 × 35...Ch. 5 - A short column with a wide-flange shape is...Ch. 5 - A tension member constructed of an L inch angle...Ch. 5 - A short length of a C 200 × 17.1 channel is...Ch. 5 - The beams shown in the figure are subjected to...Ch. 5 - The beams shown in the figure are subjected to...Ch. 5 - A rectangular beam with semicircular notches, as...Ch. 5 - A rectangular beam with semicircular notches, as...Ch. 5 - A rectangular beam with notches and a hole (see...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Problem 2: Consider the Boeing 747 jet transport, whose layout is shown in Fig. 2 and has the following characteristics: xoa 0.25, 8 5500/2, b 195.68ft, 27.31ft, AR, 3.57, V = 0.887 Determine the wing and tail contributions to the CM-a curve. You may want to assume CM, reasonable assumptions (e.g., -0.09, 0, -4°. i=0.0°, and i = -2.0°. Make any other 0.9).arrow_forwardZ Fy = 100 N Fx = 100 N F₂ = 500 N a = 500 mm b = 1000 mm Figure 2: Schematics for problem 3. 1. Draw the moment (M), axial (N), and shear (S) diagrams. Please note that this is a 3D problem and you will have moment (M) and shear (S) along two different axes. That means that you will have a total of 5 diagrams.arrow_forwardAn ideal gas with MW of 29 g/mol, cp = 1.044 kJ/kgK and c₁ = 0.745 kJ/kgK contained in a cylinder-piston assembly initially has a pressure of 175 kPa, a temperature of 22°C, and a volume of 0.30 m³. It is heated slowly at constant volume (process 1-2) until the pressure is doubled. It is then expanded slowly at constant pressure (process 2-3) until the volume is doubled. Draw a figure of the system and the PV diagram showing each state and the path each process takes. Determine the total work done by the system and total heat added (J) in the combined process.arrow_forward
- please explain each method used, thank youarrow_forwardDetermine the resultant loadings acting on the cross sections at points D and E of the frame.arrow_forwardA spring of stiffness factor 98 N/m is pulled through 20 cm. Find the restoring force and compute the mass which should be attached so as to stretch in spring by same amount.arrow_forward
- please box out or highlight all the answersarrow_forwardWhat are some ways Historical Data can be used and applied to an estimate?arrow_forwardProblem 1. Rod OAB is rotating counterclockwise with the constant angular velocity of 5 rad/s. In the position shown, collar P is sliding toward A with the constant speed of 0.8 m/s relative to the rod. Find the velocity of P and the acceleration of P. y B 3 P 300 mm A - Answer: Up = -0.861 − 0.48ĵ™; ā₂ = 4.8î −1.1ĵ marrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Mechanics of Materials Lecture: Beam Design; Author: UWMC Engineering;https://www.youtube.com/watch?v=-wVs5pvQPm4;License: Standard Youtube License