Mechanics of Materials
9th Edition
ISBN: 9780133254426
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Textbook Question
Chapter 10, Problem 10.95RP
The plate is made of material having a modulus of elasticity E = 200 GPa and Poisson’s ratio v =
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Example-1:
l
D
A uniform rotor of length 0.6 m and diameter 0.4 m is made of steel (density 7810 kg/m³)
is supported by identical short bearings of stiffness 1 MN/m in the horizontal and vertical
directions. If the distance between the bearings is 0.7 m, determine the natural frequencies
and plot whirl speed map.
Solution:
B
find the laplace transform for the
flowing function
2(1-e)
Ans. F(s)=-
S
12)
k
0
Ans. F(s)=
k
s(1+e)
0 a
2a 3a 4a
13)
2+
Ans. F(s)=
1
s(1+e")
3
14) f(t)=1, 0
Find the solution of the following Differential Equations
Using Laplace Transforms
1) 4y+2y=0.
y(0)=2.
y'(0)=0.
2) y+w²y=0,
(0)=A,
y'(0)=B.
3) +2y-8y 0.
y(0)=1.
y'(0)-8.
4)-2-3y=0,
y(0)=1.
y'(0)=7.
5) y-ky'=0,
y(0)=2,
y'(0)=k.
6) y+ky'-2k²y=0,
y(0)=2,
y'(0) = 2k.
7) '+4y=0,
y(0)=2.8
8) y+y=17 sin(21),
y(0)=-1.
9) y-y-6y=0,
y(0)=6,
y'(0)=13.
10) y=0.
y(0)=4,
y' (0)=0.
11) -4y+4y-0,
y(0)=2.1.
y'(0)=3.9
12) y+2y'+2y=0,
y(0)=1,
y'(0)=-3.
13) +7y+12y=21e".
y(0)=3.5.
y'(0)=-10.
14) "+9y=10e".
y(0)=0,
y'(0)=0.
15) +3y+2.25y=91' +64.
y(0)=1.
y'(0) = 31.5
16)
-6y+5y-29 cos(2t).
y(0)=3.2,
y'(0)=6.2
17) y+2y+2y=0,
y(0)=0.
y'(0)=1.
18) y+2y+17y=0,
y(0)=0.
y'(0)=12.
19) y"-4y+5y=0,
y(0)=1,
y'(0)=2.
20) 9y-6y+y=0,
(0)-3,
y'(0)=1.
21) -2y+10y=0,
y(0)=3,
y'(0)=3.
22) 4y-4y+37y=0,
y(0)=3.
y'(0)=1.5
23) 4y-8y+5y=0,
y(0)=0,
y'(0)=1.
24)
++1.25y-0,
y(0)=1,
y'(0)=-0.5
25) y 2 cos(r).
y(0)=2.
y'(0) = 0.
26)
-4y+3y-0,
y(0)=3,
y(0) 7.
27) y+2y+y=e
y(0)=0.
y'(0)=0.
28) y+2y-3y=10sinh(27),
y(0)=0.
y'(0)=4.
29)…
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 - Prob. 10.3PCh. 10.3 - Prob. 10.4PCh. 10.3 - 10-5. The state of strain at the point on the gear...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Prob. 10.8PCh. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Use the strain- transformation equations to...
Ch. 10.3 - 10–11. The state of strain on an element has...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 - Prob. 10.17PCh. 10.3 - Prob. 10.18PCh. 10.3 - 10–19. Solve part (a) of Prob. 10–4 using Mohr’s...Ch. 10.3 - *10–20. Solve part (a) of Prob. 10–5 using Mohr’s...Ch. 10.3 - using Mohrs circle. 106. The state of strain at a...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. 10.5 - Prob. 10.24PCh. 10.5 - Prob. 10.25PCh. 10.5 - 10–26. The 60° strain rosette is attached to point...Ch. 10.5 - 10–27. The strain rosette is attached at the point...Ch. 10.5 - Prob. 10.28PCh. 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 modulus of elasticity and Polssons...Ch. 10.6 - If it is subjected to an axial load of 15 N such...Ch. 10.6 - If it has the original dimensions shown, determine...Ch. 10.6 - If it has the original dimensions shown, determine...Ch. 10.6 - A strain gage having a length of 20 mm Is attached...Ch. 10.6 - Determine the bulk modulus for each of the...Ch. 10.6 - The strain gage is placed on the surface of the...Ch. 10.6 - 10–39. The strain in the x direction at point A on...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. 10.6 - The cube of aluminum is subjected to the three...Ch. 10.6 - Prob. 10.43PCh. 10.6 - *10–44. Strain gauge b is attached to the surface...Ch. 10.6 - Prob. 10.45PCh. 10.6 - 10?46. The principal strains in a plane, measured...Ch. 10.6 - 10–47. The principal stresses at a point are shown...Ch. 10.6 - *10–48. The 6061-T6 aluminum alloy plate fits...Ch. 10.6 - Determine the normal stresses x and y in the plate...Ch. 10.6 - The steel shaft has a radius of 15 mm. Determine...Ch. 10.6 - Prob. 10.51PCh. 10.6 - Prob. 10.52PCh. 10.6 - Air is pumped into the steel thin-walled pressure...Ch. 10.6 - Air is pumped into the steel thin-walled pressure...Ch. 10.6 - Prob. 10.55PCh. 10.6 - The thin-walled cylindrical pressure vessel of...Ch. 10.6 - The thin-walled cylindrical pressure vessel of...Ch. 10.6 - Prob. 10.58PCh. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - The yield stress for a zirconium-magnesium alloy...Ch. 10.7 - Solve Prob. 1061 using the maximum distortion...Ch. 10.7 - Prob. 10.63PCh. 10.7 - Prob. 10.64PCh. 10.7 - Prob. 10.65PCh. 10.7 - Prob. 10.66PCh. 10.7 - Prob. 10.67PCh. 10.7 - If the material is machine steel having a yield...Ch. 10.7 - The short concrete cylinder having a diameter of...Ch. 10.7 - 10–70. Derive an expression for an equivalent...Ch. 10.7 - Prob. 10.71PCh. 10.7 - Prob. 10.72PCh. 10.7 - If the 2-in diameter shaft is made from brittle...Ch. 10.7 - If the 2-in diameter shaft is made from cast iron...Ch. 10.7 - 10–75. The components of plane stress at a...Ch. 10.7 - Prob. 10.76PCh. 10.7 - 10–77. If the A-36 steel pipe has outer and inner...Ch. 10.7 - Prob. 10.78PCh. 10.7 - Prob. 10.79PCh. 10.7 - Prob. 10.80PCh. 10.7 - Prob. 10.81PCh. 10.7 - Prob. 10.82PCh. 10.7 - Prob. 10.83PCh. 10.7 - Prob. 10.84PCh. 10.7 - 10–85. The state of stress acting at a critical...Ch. 10.7 - The shaft consists of a solid segment AB and a...Ch. 10.7 - Prob. 10.87PCh. 10.7 - Prob. 10.88PCh. 10.7 - 10–89. The gas tank has an inner diameter of 1.50...Ch. 10.7 - The gas tank is made from A-36 steel and has an...Ch. 10.7 - The internal loadings at a critical section along...Ch. 10.7 - *10–92. The shaft consists of a solid segment AB...Ch. 10.7 - Prob. 10.93PCh. 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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