Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Chapter 10.3, Problem 15P
Determine the equivalent state of strain, which represents (a) the principal strains, and (b) the maximum in-plane shear strain and the associated average normal strain. Specify the orientation of the corresponding elements for these states of strain with respect to the original element.
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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:
020 020
+
მx2 მy2
+0.0150+Q=0
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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8
12
16
10
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15
25
9
14
19
24
3
11
15
0=0
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0=0
3
8
13
18
23
2
6
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5
0=0
10
14
6
12
17
22
1
6
11
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Fig 3
Fig 4
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 10 Solutions
Mechanics of Materials
Ch. 10.3 - Prove that the sum of the normal strains in...Ch. 10.3 - The state of strain at the point on the arm has...Ch. 10.3 - The state of strain at the point on the leaf of...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Determine the equivalent state of strain on an...Ch. 10.3 - Determine the equivalent state of strain which...Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Determine the equivalent state of strain, which...Ch. 10.3 - Solve Prob.103 using Mohrs circle. 103. The state...Ch. 10.5 - The strain at point A on the bracket has...
Ch. 10.5 - Determine (a) the principal strains at A, (b) the...Ch. 10.6 - For the case of plane stress, show that Hookes law...Ch. 10.6 - to develop the strain tranformation equations....Ch. 10.6 - Determine the associated principal stresses at the...Ch. 10.6 - Determine the applied load P. What is the shear...Ch. 10.6 - If a load of P = 3 kip is applied to the A-36...Ch. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - Solve Prob. 1061 using the maximum distortion...Ch. 10.7 - Solve Prob.1063 using the maximum distortion...Ch. 10.7 - Prob. 70PCh. 10.7 - The plate is made of Tobin bronze, which yields at...Ch. 10.7 - If a machine part is made of titanium (TI-6A1-4V)...Ch. 10.7 - The components of plane stress at a critical point...Ch. 10.7 - If Y = 50 ksi, determine the factor of safety for...Ch. 10.7 - Prob. 82PCh. 10.7 - If the yield stress for steel is Y = 36 ksi,...Ch. 10.7 - Prob. 84PCh. 10.7 - The state of stress acting at a critical point on...Ch. 10.7 - The shaft consists of a solid segment AB and a...Ch. 10 - In the case of plane stress, where the in-plane...Ch. 10 - The plate is made of material having a modulus of...Ch. 10 - If the material is machine steel having a yield...Ch. 10 - Determine if yielding has occurred on the basis of...Ch. 10 - The 60 strain rosette is mounted on a beam. The...Ch. 10 - Use the strain transformation equations to...Ch. 10 - If the strain gages a and b at points give...Ch. 10 - Use the strain-transformation equations and...Ch. 10 - Use the strain transformation equations to...Ch. 10 - Specify the orientation of the corresponding...
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