1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lesya [120]
3 years ago
11

The aluminum rod (E1 = 68 GPa) is reinforced with the firmly bonded steel tube (E2 = 201 GPa). The diameter of the aluminum rod

is d = 25 mm and the outside diameter of the steel tube is D= 45 mm. The length of the composite column is L = 761 mm. A force P = 88 kN is applied at the top surface, distributed across both the rod and tube.
Required:
Determine the normal stress σ in the steel tube.
Engineering
1 answer:
Vsevolod [243]3 years ago
8 0

Answer:

Explanation:

From the information given:

E_1 = 68 \ GPa \\ \\ E_2 = 201 \ GPa  \\ \\ d = 25 \ mm \  \\ \\ D = 45 \ mm \ \\ \\ L   = 761 \ mm  \\ \\ P = -88 kN

The total load is distributed across both the rod and tube:

P = P_1+P_2 --- (1)

Since this is a composite column; the elongation of both aluminum rod & steel tube is equal.

\delta_1=\delta_2

\dfrac{P_1L}{A_1E_1}= \dfrac{P_2L}{A_2E_2}

\dfrac{P_1 \times 0.761}{(\dfrac{\pi}{4}\times .0025^2 ) \times 68\times 10^4}= \dfrac{P_2\times 0.761}{(\dfrac{\pi}{4}\times (0.045^2-0.025^2))\times 201 \times 10^9}

P_1(2.27984775\times 10^{-8}) = P_2(3.44326686\times 10^{-9})

P_2 = \dfrac{ (2.27984775\times 10^{-8}) P_1}{(3.44326686\times 10^{-9})}

P_2 = 6.6212 \ P_1

Replace P_2 into equation (1)

P= P_1 + 6.6212 \ P_1\\ \\ P= 7.6212\ P_1 \\ \\  -88 = 7.6212 \ P_1  \\ \\ P_1 = \dfrac{-88}{7.6212} \\ \\  P_1 = -11.547 \ kN

Finally, to determine the normal stress in aluminum rod:

\sigma _1 = \dfrac{P_1}{A_1} \\ \\  \sigma _1 = \dfrac{-11.547 \times 10^3}{\dfrac{\pi}{4} \times 25^2}

\sigma_1 = - 23.523 \ MPa}

Thus, the normal stress = 23.523 MPa in compression.

You might be interested in
One unethical decision won't cause any harm.( true) or (false)
konstantin123 [22]

Answer:

true

Explanation:

7 0
3 years ago
Read 2 more answers
In the video "Understanding Flight', What is the main benefit of flying to the people in the airport?
ivolga24 [154]

Answer:

a

Explanation:

common sense

6 0
3 years ago
Definition of ceramics
dezoksy [38]

Answer:

Ceramics are generally made by taking mixtures of clay, earthen elements, powders, and water and shaping them into desired forms. Once the ceramic has been shaped, it is fired in a high temperature oven known as a kiln. Often, ceramics are covered in decorative, waterproof, paint-like substances known as glazes.

Explanation:

3 0
3 years ago
Read 2 more answers
Paul is constructing an aquarium. The exterior of the aquarium in made of white marble. Which design principle element is being
sasho [114]

Answer:

B

Explanation:

because you can see in the text it is expressing that it is shape

7 0
3 years ago
When current flows through an electrical component due to a potential difference,
ira [324]

Answer:

Ohm, a german physicist, found experimentally that the current in a metal conductor is directly proportional to the potential difference across its ends

Explanation:

8 0
3 years ago
Other questions:
  • Find the mathematical equation for SF distribution and BM diagram for the beam shown in figure 1.​
    10·1 answer
  • / Air enters a 20-cm-diameter 12-m-long underwater duct at 50°C and 1 atm at a
    7·1 answer
  • Cavitation in pump assemblies can be avoided by decreasing tank pressure. a)-True b)-False
    10·1 answer
  • Can someone answer plz!! It’s 24 points
    15·2 answers
  • Can somebody help me
    9·1 answer
  • A college student volunteers with the elderly in a hospice program and discovers her clients complain of dry skin. She has an id
    13·2 answers
  • Hello it's my new id<br>I am numu ​
    15·1 answer
  • While reflecting on the solutions and the process of concept generation, the development team takes a look at some critical ques
    10·1 answer
  • Find the remaining trigonometric function of 0 if
    13·1 answer
  • How can I skip more helppppppppppppppppppppppp
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!