MECHANICS OF MATERIALS
11th Edition
ISBN: 9780137605521
Author: HIBBELER
Publisher: RENT PEARS
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Chapter 3, Problem 7RP
The stress-strain diagram for polyethylene, which is used to sheath coaxial cables, is determined from testing a specimen that has a gage length of 10 in. If a load P on the specimen develops a strain of ε = 0.024 in./in., determine the approximate length of the specimen, measured between the gage points, when the load is removed. Assume the specimen recovers elastically.
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(I) [40 Points] Using centered finite difference approximations as done in class, solve the equation for O:
d20
dx²
+ 0.010+ Q=0
subject to the boundary conditions shown in the stencil below. Do this for two values of Q: (a) Q = 0.3,
and (b) Q= √(0.5 + 2x)e-sinx (cos(5x)+x-0.5√1.006-x| + e −43*|1+.001+x* | * sin (1.5 − x) +
(cosx+0.001 + ex-1250+ sin (1-0.9x)|) * x - 4.68x4. For Case (a) (that is, Q = 0.3), use the stencil in Fig.
1. For Case (b), calculate with both the stencils in Fig. 1 and Fig 2. For all the three cases, show a table as
well as a plot of O versus x. Discuss your results. Use MATLAB and hand in the MATLAB codes.
1
0=0
x=0
2
3
4
0=1
x=1
Fig 1
1 2 3 4 5 6 7 8 9 10
11
0=0
x=0
0=1
x=1
Fig 2
Fig 2
(II) [60 Points] Using centered finite difference approximation as done in class, solve the equation:
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+
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subject to the boundary conditions shown in the stencils below. Do this for two values of Q: (a) Q = 0.3,
and (b) Q = 10.5x² + 1.26 * 1.5 x 0.002 0.008. For Case (a) (that is, Q = 0.3) use Fig 3. For Case (b),
use both Fig. 3 and Fig 4. For all the three cases, show a table as well as the contour plots of versus
(x, y), and the (x, y) heat flux values at all the nodes on the boundaries x = 1 and y = 1. Discuss your
results. Use MATLAB and hand in the MATLAB codes. (Note that the domain is (x, y)e[0,1] x [0,1].)
0=0
0=0
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5
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Textbook: Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, McGraw-Hill, Eighth
Edition (2021).
Ship construction question. Sketch and describe the forward arrangements of a ship. Include componets of the structure and a explanation of each part/ term.
Ive attached a general fore end arrangement. Simplfy construction and give a brief describion of the terms.
Chapter 3 Solutions
MECHANICS OF MATERIALS
Ch. 3.4 - Define a homogeneous material.Ch. 3.4 - Indicate the points on the stress-strain diagram...Ch. 3.4 - Define the modulus of elasticity E.Ch. 3.4 - At room temperature, mild steel is a ductile...Ch. 3.4 - Engineering stress and strain are calculated using...Ch. 3.4 - As the temperature increases the modulus of...Ch. 3.4 - A 100-mm-long rod has a diameter of 15 mm. If an...Ch. 3.4 - A bar has a length of 8 in. and cross-sectional...Ch. 3.4 - A 10-mm-diameter rod has a modulus of elasticity...Ch. 3.4 - The material for the 50-mm-long specimen has the...
Ch. 3.4 - The material for the 50-mm-long specimen has the...Ch. 3.4 - If the elongation of wire BC is 0.2 mm after the...Ch. 3.4 - Data taken from a stress-strain test for a ceramic...Ch. 3.4 - The stress-strain diagram for a steel alloy having...Ch. 3.4 - The stress-strain diagram for a steel alloy having...Ch. 3.4 - The stress-strain diagram for a steel alloy having...Ch. 3.4 - Determine the elongation of the square hollow bar...Ch. 3.4 - The stress-strain diagram for an aluminum alloy...Ch. 3.4 - The stress-strain diagram for an aluminum alloy...Ch. 3.4 - The stress-strain diagram for an aluminum alloy...Ch. 3.4 - A structural member in a nuclear reactor is made...Ch. 3.4 - The rigid pipe is supported by a pin at A and an...Ch. 3.4 - The rigid pipe is supported by a pin at A and an...Ch. 3.4 - Direct tension indicators are sometimes used...Ch. 3.4 - A tension test was performed on a magnesium alloy...Ch. 3.4 - The stress-strain diagram for a bone is shown and...Ch. 3.4 - The two bars are made of a material that has the...Ch. 3.4 - The two bars are made of a material that has the...Ch. 3.7 - A 100-mm-long rod has a diameter of 15 mm. If an...Ch. 3.7 - A solid circular rod that is 600 mm long and 20 mm...Ch. 3.7 - A 20-mm-wide block is firmly bonded to rigid...Ch. 3.7 - A 20-mm-wide block is bonded to rigid plates at...Ch. 3.7 - The acrylic plastic rod is 400mm long and 20mm in...Ch. 3.7 - The elastic portion of the stress-strain diagram...Ch. 3.7 - The elastic portion of the stress-strain diagram...Ch. 3.7 - The lap joint is connected together using a 1.25...Ch. 3.7 - The lap joint is connected together using a 1.25...Ch. 3.7 - Prob. 32PCh. 3.7 - The thin-walled tube is subjected to an axial...Ch. 3 - The elastic portion of the tension stress-strain...Ch. 3 - The elastic portion of the tension stress-strain...Ch. 3 - The rigid beam rests in the horizontal position on...Ch. 3 - The wires each have a diameter of 12 in., length...Ch. 3 - Prob. 5RPCh. 3 - diameter steel bolts. If the clamping force in...Ch. 3 - The stress-strain diagram for polyethylene, which...Ch. 3 - The pipe with two rigid caps attached to its ends...Ch. 3 - The 8-mm-diameter bolt is made of an aluminum...Ch. 3 - An acetal polymer block is fixed to the rigid...
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