Answer:
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Answer:
a) 53 MPa, 14.87 degree
b) 60.5 MPa
Average shear = -7.5 MPa
Explanation:
Given
A = 45
B = -60
C = 30
a) stress P1 = (A+B)/2 + Sqrt ({(A-B)/2}^2 + C)
Substituting the given values, we get -
P1 = (45-60)/2 + Sqrt ({(45-(-60))/2}^2 + 30)
P1 = 53 MPa
Likewise P2 = (A+B)/2 - Sqrt ({(A-B)/2}^2 + C)
Substituting the given values, we get -
P1 = (45-60)/2 - Sqrt ({(45-(-60))/2}^2 + 30)
P1 = -68 MPa
Tan 2a = C/{(A-B)/2}
Tan 2a = 30/(45+60)/2
a = 14.87 degree
Principal stress
p1 = (45+60)/2 + (45-60)/2 cos 2a + 30 sin2a = 53 MPa
b) Shear stress in plane
Sqrt ({(45-(-60))/2}^2 + 30) = 60.5 MPa
Average = (45-(-60))/2 = -7.5 MPa
Answer:
#See solution for details.
Explanation:
#The commutative property of multiplication tells us that it doesn't matter in what order you multiply numbers. The formula for this property is a * b = b * a:
![40\times32\times10\times 25=320,000\\\\25\times10\times32\times 40=320,000\\\\10\times32\times25\times 40=320,000\\\\32\times25\times40\times 10=320,000](https://tex.z-dn.net/?f=40%5Ctimes32%5Ctimes10%5Ctimes%2025%3D320%2C000%5C%5C%5C%5C25%5Ctimes10%5Ctimes32%5Ctimes%2040%3D320%2C000%5C%5C%5C%5C10%5Ctimes32%5Ctimes25%5Ctimes%2040%3D320%2C000%5C%5C%5C%5C32%5Ctimes25%5Ctimes40%5Ctimes%2010%3D320%2C000)
Hence, the product of the four numbers remains 320,000 irrespective of their order.
Answer:
maximum isolator stiffness k =1764 kN-m
Explanation:
mean speed of rotation ![=\frac{N_1 +N_2}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7BN_1%20%2BN_2%7D%7B2%7D)
![Nm = \frac{500+750}{2} = 625 rpm](https://tex.z-dn.net/?f=Nm%20%3D%20%5Cfrac%7B500%2B750%7D%7B2%7D%20%3D%20625%20rpm)
![w =\frac{2\pi Nm}{60}](https://tex.z-dn.net/?f=w%20%3D%5Cfrac%7B2%5Cpi%20Nm%7D%7B60%7D)
=65.44 rad/sec
![F_T = mw^2 e](https://tex.z-dn.net/?f=F_T%20%3D%20mw%5E2%20e)
![F_T = mew^2](https://tex.z-dn.net/?f=F_T%20%3D%20mew%5E2)
= 0.1*(65.44)^2
F_T =428.36 N
Transmission ratio ![=\frac{300}{428.36} = 0.7](https://tex.z-dn.net/?f=%3D%5Cfrac%7B300%7D%7B428.36%7D%20%3D%200.7)
also
transmission ratio ![= \frac{1}{[\frac{w}{w_n}]^{2} -1}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%7D%7B%5B%5Cfrac%7Bw%7D%7Bw_n%7D%5D%5E%7B2%7D%20-1%7D)
![0.7 =\frac{1}{[\frac{65.44}{w_n}]^2 -1}](https://tex.z-dn.net/?f=0.7%20%3D%5Cfrac%7B1%7D%7B%5B%5Cfrac%7B65.44%7D%7Bw_n%7D%5D%5E2%20-1%7D)
SOLVING FOR Wn
Wn = 42 rad/sec
![Wn = \sqrt {\frac{k}{m}](https://tex.z-dn.net/?f=Wn%20%3D%20%5Csqrt%20%7B%5Cfrac%7Bk%7D%7Bm%7D)
k = m*W^2_n
k = 1000*42^2 = 1764 kN-m
k =1764 kN-m