Convert 103.69 kN to TN.

The solid aluminum shaft has a diameter of 50 mm. Determine the absolute maximum shear stress in the shaft and sketch the shear-

jarptica [38.1K]

Answer:

Max shear = 8.15 x 10^7 N/m2

Explanation:

In order to find the maximum stress for a solid shaft having radius r, we will be applying the Torsion formula which can be written as;

Allowable Shear Stress = Torque x Radius / pi/2 x radius^4

Putting the values we have;

T = 2000 N/m

Radius = Diameter/2 = 0.05 / 2 = 0.025 m

Putting values in formula;

Max shear = 2000 x 0.025 / 3.14/2 x (0.025)^4

Max shear = 8.15 x 10^7 N/m2

5 0

3 years ago

The bar DA is rigid and is originally held in the horizontal position when the weight W is supported from C. The wires are made

Rom4ik [11]

Answer:

W = 112 lb

Explanation:

Given:

- δb = 0.025 in

- E = 29000 ksi (A-36)

- Area A_de = 0.002 in^2

Find:

Compute Weight W attached at C

Solution:

- Use proportion to determine δd:

δd/5 = δb/3

δd = (5/3) * 0.025

δd = 0.0417 in

- Compute εde i.e strain in DE:

εde = δd / Lde

εde = 0.0417 / 3*12

εde = 0.00116

- Compute stress in DE, σde:

σde = E*εde

σde = 29000*0.00116

σde = 33.56 ksi

- Compute the Force F_de:

F_de = σde *A_de

F_de = 33.56*0.002

F_de = 0.0672 kips

- Equilibrium conditions apply:

(M)_a = 0

3*W - 5*F_de = 0

W = (5/3)*F_de

W = (5/3)* 0.0672 = 112 lb

4 0

3 years ago

I. The time till failure of an electronic component has an Exponential distribution and it is known that 10% of components have

drek231 [11]

Answer:

(a) The mean time to fail is 9491.22 hours

The standard deviation time to fail is 9491.22 hours

(b) 0.5905

(c) 3.915 × 10⁻¹²

(d) 2.63 × 10⁻⁵

Explanation:

(a) We put time to fail = t

∴ For an exponential distribution, we have f(t) = $\lambda e^{-\lambda t}$

Where we have a failure rate = 10% for 1000 hours, we have(based on online resource);

$P(t \leq 1000) = \int\limits^{1000}_0 {\lambda e^{-\lambda t}} \, dt = \dfrac{e^{1000\lambda}-1}{e^{1000\lambda}} = 0.1$

e^(1000·λ) - 0.1·e^(1000·λ) = 1

0.9·e^(1000·λ) = 1

1000·λ = ㏑(1/0.9)

λ = 1.054 × 10⁻⁴

Hence the mean time to fail, E = 1/λ = 1/(1.054 × 10⁻⁴) = 9491.22 hours

The standard deviation = √(1/λ)² = √(1/(1.054 × 10⁻⁴)²)) = 9491.22 hours

b) Here we have to integrate from 5000 to ∞ as follows;

$p(t>5000) = \int\limits^{\infty}_{5000} {\lambda e^{-\lambda t}} \, dt =\left [ -e^{\lambda t}\right ]_{5000}^{\infty} = e^{5000 \lambda} = 0.5905$

(c) The Poisson distribution is presented as follows;

$P(x = 3) = \dfrac{\lambda ^x e^{-x}}{x!} = \frac{(1.0532 \times 10^{-4})^3 e^{-3} }{3!} = 3.915\times 10^{-12}$

p(x = 3) = 3.915 × 10⁻¹²

d) Where at least 2 components fail in one half hour, then 1 component is expected to fail in 15 minutes or 1/4 hours

The Cumulative Distribution Function is given as follows;

p( t ≤ 1/4) $CDF = 1 - e^{-\lambda \times t} = 1 - e^{-1.054 \times 10 ^{-4} \times 1/4} = 2.63 \times 10 ^{-5}$ .

4 0

3 years ago

Need help fast 50 points Project: Creating a Morphological Matrix

Leokris [45]

Answer:

The fundamental difference between effective and less effective matrix organizations is whether the tension between different perspectives is creative or destructive. While various processes, systems and tools can help, what matters most is what top leadership says and does and how that flows through the organization in shared targets, clear accountabilities, live team interactions and team-building transparency and behaviors.

Getting matrix management right is linked inextricably to an organization’s culture - the only sustainable competitive advantage. Key components of a culture can be grouped into behaviors, relationships, attitudes, values and the environment.

Environment and values: Each organization has its own environment, context and bedrock values. Everyone needs to know what matters and why. Don’t try to do anything else until you’ve got that set.

Attitude is about choices: An organization’s overall strategy drives choices about which of its parts will be best in class (superior), world class (parity), strong (above average), or simplified/outsourced to be good enough. These choices help determine the need for a matrix and how best to design it.

Relationships and behaviors: This is why organizations have matrices. The most effective of them best balance focus and collaboration. They allow leaders and teams to build differential strengths and then work together to make the best possible decisions and scale enterprises with a creative tension that they could not do on their own.

My colleague Joe Durrett has worked all sides of matrix organizations in marketing at Procter & Gamble, sales and general management at Kraft General Foods and CEO of Information Resources, Broderbund Software and Advo. He has seen matrices at their best and at their worst and offered his perspective for this article along with his partners John Lawler and Linda Hlavac. The 12 ways to make matrix organizations more effective were built on their ideas.

Explanation:

7 0

3 years ago

A flow field is characterized by the stream function ψ= 3x2y−y3. Demonstrate thatthe flow field represents a two-dimensional inc

boyakko [2]

Answer:

δu/δx+δu/δy = 6x-6x =0

9r^2

Explanation:

The flow is obviously two-dimensional, since the stream function depends only on the x and y coordinate. We can find the x and y velocity components by using the following relations:

u =δψ/δy = 3x^2-3y^2

v =-δψ/δx = -6xy

Now, since:

δu/δx+δu/δy = 6x-6x =0

we conclude that this flow satisfies the continuity equation for a 2D incompressible flow. Therefore, the flow is indeed a two-dimensional incompressible one.

The magnitude of velocity is given by:

|V| = u^2+v^2

=(3x^2-3y^2)^2+(-6xy)^2

=9x^4+18x^2y^2+9y^2

=(3x^2+3y^2)^2

=9r^2

where r is the distance from the origin of the coordinates, and we have used that r^2 = x^2 + y^2.

The streamline ψ = 2 is given by the following equation:

3x^2y — y^3 = 2,

which is most easily plotted by solving it for x:

x =±√2-y^3/y

Plot of the streamline is given in the graph below.

Explanation for the plot: the two x(y) functions (with minus and plus signs) given in the equation above were plotted as functions of y, after which the graph was rotated to obtain a standard coordinate diagram. The "+" and "-" parts are given in different colors, but keep in mind that these are actually "parts" of the same streamline.

8 0

3 years ago