Mechanical Engineering Exam > Mechanical Engineering Questions > A beam of square cross section is subjected t...
Start Learning for Free
A beam of square cross section is subjected to a bending moment m and the max stress developed is 100 mpa if the diagonal of the section take vertical and horizontal direction bending moment remaining the same the max stress developed will become?
Most Upvoted Answer
A beam of square cross section is subjected to a bending moment m and ...
Cross Section of the Beam
The cross section of the beam is square in shape, which means all sides of the square are equal in length. Let's assume the length of each side of the square cross section is 'a'.
Bending Moment and Maximum Stress
When a beam is subjected to a bending moment, it experiences a variation of stress across its cross section. The maximum stress developed in the beam occurs at the furthest point from the neutral axis, which in this case is at the corners of the square cross section.
Given that the maximum stress developed is 100 MPa, we can use this information to determine the moment of inertia of the square cross section. The moment of inertia, denoted by 'I', is a property of the cross section that influences its resistance to bending.
Diagonal Direction Bending Moment
Now, let's consider the scenario where the diagonal of the square cross section takes a vertical and horizontal direction while the bending moment remains the same.
In this case, the diagonal of the square cross section divides it into two right-angled triangles. Each triangle has a base of 'a' and a height of 'a'.
Effect on Moment of Inertia
When the diagonal is vertical and horizontal, the centroid of the cross section shifts. The new centroid position is at the intersection of the diagonals, which is at a distance of 'a/2' from each side.
The moment of inertia of the square cross section in this case can be calculated using the parallel axis theorem. It is given by the sum of the moments of inertia of the two right-angled triangles formed by the diagonal.
The moment of inertia of a right-angled triangle about its centroid is given by (base^3 * height)/12. Since there are two triangles, the total moment of inertia is 2 * [(a^3 * a)/12].
Calculating the New Maximum Stress
The maximum stress developed in the beam can be calculated by dividing the bending moment (m) by the moment of inertia (I).
So, when the diagonal of the square cross section takes a vertical and horizontal direction, the new maximum stress can be calculated using the equation:
New Maximum Stress = m / [2 * (a^4 / 12)]
Now, you can calculate the new maximum stress using the given bending moment (m) and the length of each side of the square cross section (a).
The cross section of the beam is square in shape, which means all sides of the square are equal in length. Let's assume the length of each side of the square cross section is 'a'.
Bending Moment and Maximum Stress
When a beam is subjected to a bending moment, it experiences a variation of stress across its cross section. The maximum stress developed in the beam occurs at the furthest point from the neutral axis, which in this case is at the corners of the square cross section.
Given that the maximum stress developed is 100 MPa, we can use this information to determine the moment of inertia of the square cross section. The moment of inertia, denoted by 'I', is a property of the cross section that influences its resistance to bending.
Diagonal Direction Bending Moment
Now, let's consider the scenario where the diagonal of the square cross section takes a vertical and horizontal direction while the bending moment remains the same.
In this case, the diagonal of the square cross section divides it into two right-angled triangles. Each triangle has a base of 'a' and a height of 'a'.
Effect on Moment of Inertia
When the diagonal is vertical and horizontal, the centroid of the cross section shifts. The new centroid position is at the intersection of the diagonals, which is at a distance of 'a/2' from each side.
The moment of inertia of the square cross section in this case can be calculated using the parallel axis theorem. It is given by the sum of the moments of inertia of the two right-angled triangles formed by the diagonal.
The moment of inertia of a right-angled triangle about its centroid is given by (base^3 * height)/12. Since there are two triangles, the total moment of inertia is 2 * [(a^3 * a)/12].
Calculating the New Maximum Stress
The maximum stress developed in the beam can be calculated by dividing the bending moment (m) by the moment of inertia (I).
So, when the diagonal of the square cross section takes a vertical and horizontal direction, the new maximum stress can be calculated using the equation:
New Maximum Stress = m / [2 * (a^4 / 12)]
Now, you can calculate the new maximum stress using the given bending moment (m) and the length of each side of the square cross section (a).
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
A beam of square cross section is subjected to a bending moment m and the max stress developed is 100 mpa if the diagonal of the section take vertical and horizontal direction bending moment remaining the same the max stress developed will become?
Question Description
A beam of square cross section is subjected to a bending moment m and the max stress developed is 100 mpa if the diagonal of the section take vertical and horizontal direction bending moment remaining the same the max stress developed will become? 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 A beam of square cross section is subjected to a bending moment m and the max stress developed is 100 mpa if the diagonal of the section take vertical and horizontal direction bending moment remaining the same the max stress developed will become? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A beam of square cross section is subjected to a bending moment m and the max stress developed is 100 mpa if the diagonal of the section take vertical and horizontal direction bending moment remaining the same the max stress developed will become?.
A beam of square cross section is subjected to a bending moment m and the max stress developed is 100 mpa if the diagonal of the section take vertical and horizontal direction bending moment remaining the same the max stress developed will become? 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 A beam of square cross section is subjected to a bending moment m and the max stress developed is 100 mpa if the diagonal of the section take vertical and horizontal direction bending moment remaining the same the max stress developed will become? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A beam of square cross section is subjected to a bending moment m and the max stress developed is 100 mpa if the diagonal of the section take vertical and horizontal direction bending moment remaining the same the max stress developed will become?.
Solutions for A beam of square cross section is subjected to a bending moment m and the max stress developed is 100 mpa if the diagonal of the section take vertical and horizontal direction bending moment remaining the same the max stress developed will become? 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 A beam of square cross section is subjected to a bending moment m and the max stress developed is 100 mpa if the diagonal of the section take vertical and horizontal direction bending moment remaining the same the max stress developed will become? defined & explained in the simplest way possible. Besides giving the explanation of
A beam of square cross section is subjected to a bending moment m and the max stress developed is 100 mpa if the diagonal of the section take vertical and horizontal direction bending moment remaining the same the max stress developed will become?, a detailed solution for A beam of square cross section is subjected to a bending moment m and the max stress developed is 100 mpa if the diagonal of the section take vertical and horizontal direction bending moment remaining the same the max stress developed will become? has been provided alongside types of A beam of square cross section is subjected to a bending moment m and the max stress developed is 100 mpa if the diagonal of the section take vertical and horizontal direction bending moment remaining the same the max stress developed will become? theory, EduRev gives you an
ample number of questions to practice A beam of square cross section is subjected to a bending moment m and the max stress developed is 100 mpa if the diagonal of the section take vertical and horizontal direction bending moment remaining the same the max stress developed will become? 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