Mechanical Engineering Exam > Mechanical Engineering Questions > At a certain point in a structural member, th...
Start Learning for Free
At a certain point in a structural member, there are perpendicular stresses 80 N/mm2 and 20 N/mm2, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)
- a)Zero
- b)20 N/mm2
- c)60 N/mm2
- d)75 N/mm2
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
At a certain point in a structural member, there are perpendicular str...
Most Upvoted Answer
At a certain point in a structural member, there are perpendicular str...
To determine the equivalent stress in simple tension using the maximum principal strain theory, we need to consider the given perpendicular stresses and Poisson's ratio.
Given:
Perpendicular tensile stress 1 (σ1) = 80 N/mm^2
Perpendicular tensile stress 2 (σ2) = 20 N/mm^2
Poisson's ratio (ν) = 0.25
Step 1: Calculate the principal stresses
The principal stresses can be calculated using the formula:
σ1' = (σ1 + σ2) / 2 + √[((σ1 - σ2) / 2)^2 + τ^2]
σ2' = (σ1 + σ2) / 2 - √[((σ1 - σ2) / 2)^2 + τ^2]
where τ is the shear stress, which is assumed to be zero in this case since only perpendicular stresses are given.
Substituting the given values into the formula, we get:
σ1' = (80 + 20) / 2 + √[((80 - 20) / 2)^2 + 0^2]
= 50 + √[30^2]
= 50 + 30
= 80 N/mm^2
σ2' = (80 + 20) / 2 - √[((80 - 20) / 2)^2 + 0^2]
= 50 - √[30^2]
= 50 - 30
= 20 N/mm^2
Step 2: Calculate the equivalent stress
The equivalent stress (σe) can be calculated using the formula:
σe = √(σ1'^2 - σ1'σ2' + σ2'^2)
Substituting the calculated values into the formula, we get:
σe = √(80^2 - 80*20 + 20^2)
= √(6400 - 1600 + 400)
= √(4400)
≈ 66.33 N/mm^2
Therefore, the equivalent stress in simple tension, according to the maximum principal strain theory, is approximately 66.33 N/mm^2. Since none of the given options match this value, it seems there might be an error in the question or the answer choices.
Given:
Perpendicular tensile stress 1 (σ1) = 80 N/mm^2
Perpendicular tensile stress 2 (σ2) = 20 N/mm^2
Poisson's ratio (ν) = 0.25
Step 1: Calculate the principal stresses
The principal stresses can be calculated using the formula:
σ1' = (σ1 + σ2) / 2 + √[((σ1 - σ2) / 2)^2 + τ^2]
σ2' = (σ1 + σ2) / 2 - √[((σ1 - σ2) / 2)^2 + τ^2]
where τ is the shear stress, which is assumed to be zero in this case since only perpendicular stresses are given.
Substituting the given values into the formula, we get:
σ1' = (80 + 20) / 2 + √[((80 - 20) / 2)^2 + 0^2]
= 50 + √[30^2]
= 50 + 30
= 80 N/mm^2
σ2' = (80 + 20) / 2 - √[((80 - 20) / 2)^2 + 0^2]
= 50 - √[30^2]
= 50 - 30
= 20 N/mm^2
Step 2: Calculate the equivalent stress
The equivalent stress (σe) can be calculated using the formula:
σe = √(σ1'^2 - σ1'σ2' + σ2'^2)
Substituting the calculated values into the formula, we get:
σe = √(80^2 - 80*20 + 20^2)
= √(6400 - 1600 + 400)
= √(4400)
≈ 66.33 N/mm^2
Therefore, the equivalent stress in simple tension, according to the maximum principal strain theory, is approximately 66.33 N/mm^2. Since none of the given options match this value, it seems there might be an error in the question or the answer choices.
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
At a certain point in a structural member, there are perpendicular stresses 80 N/mm2 and 20 N/mm2, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)a)Zero b)20 N/mm2c)60 N/mm2 d)75 N/mm2Correct answer is option 'D'. Can you explain this answer?
Question Description
At a certain point in a structural member, there are perpendicular stresses 80 N/mm2 and 20 N/mm2, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)a)Zero b)20 N/mm2c)60 N/mm2 d)75 N/mm2Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about At a certain point in a structural member, there are perpendicular stresses 80 N/mm2 and 20 N/mm2, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)a)Zero b)20 N/mm2c)60 N/mm2 d)75 N/mm2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At a certain point in a structural member, there are perpendicular stresses 80 N/mm2 and 20 N/mm2, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)a)Zero b)20 N/mm2c)60 N/mm2 d)75 N/mm2Correct answer is option 'D'. Can you explain this answer?.
At a certain point in a structural member, there are perpendicular stresses 80 N/mm2 and 20 N/mm2, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)a)Zero b)20 N/mm2c)60 N/mm2 d)75 N/mm2Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about At a certain point in a structural member, there are perpendicular stresses 80 N/mm2 and 20 N/mm2, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)a)Zero b)20 N/mm2c)60 N/mm2 d)75 N/mm2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At a certain point in a structural member, there are perpendicular stresses 80 N/mm2 and 20 N/mm2, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)a)Zero b)20 N/mm2c)60 N/mm2 d)75 N/mm2Correct answer is option 'D'. Can you explain this answer?.
Solutions for At a certain point in a structural member, there are perpendicular stresses 80 N/mm2 and 20 N/mm2, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)a)Zero b)20 N/mm2c)60 N/mm2 d)75 N/mm2Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of At a certain point in a structural member, there are perpendicular stresses 80 N/mm2 and 20 N/mm2, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)a)Zero b)20 N/mm2c)60 N/mm2 d)75 N/mm2Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
At a certain point in a structural member, there are perpendicular stresses 80 N/mm2 and 20 N/mm2, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)a)Zero b)20 N/mm2c)60 N/mm2 d)75 N/mm2Correct answer is option 'D'. Can you explain this answer?, a detailed solution for At a certain point in a structural member, there are perpendicular stresses 80 N/mm2 and 20 N/mm2, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)a)Zero b)20 N/mm2c)60 N/mm2 d)75 N/mm2Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of At a certain point in a structural member, there are perpendicular stresses 80 N/mm2 and 20 N/mm2, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)a)Zero b)20 N/mm2c)60 N/mm2 d)75 N/mm2Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice At a certain point in a structural member, there are perpendicular stresses 80 N/mm2 and 20 N/mm2, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)a)Zero b)20 N/mm2c)60 N/mm2 d)75 N/mm2Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup