Mechanical Engineering Exam > Mechanical Engineering Questions > A beam of rectangular section (12cm wide × 2...
Start Learning for Free
A beam of rectangular section (12cm wide × 20cm deep) is simply supported over a span of 12m. It is acted upon by a concentrated load of 80 kN at the mid span. The maximum bending stress induced is
- a)40 MPa
- b)300 MPa
- c)200 MPa
- d)100 MPa
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A beam of rectangular section (12cm wide × 20cm deep) is simply suppo...
The cross-section of beam,
View all questions of this test
Moment of inertia of cross-section
= 8 x 103cm4
Maximum moment under given loading,
Maximum bending stress
= 300 MPa
Most Upvoted Answer
A beam of rectangular section (12cm wide × 20cm deep) is simply suppo...
To determine the maximum bending stress induced in the beam, we can use the formula for the bending stress:
σ = (M * c) / I
Where:
σ is the bending stress
M is the bending moment
c is the distance from the neutral axis to the point of interest
I is the second moment of area (also known as the moment of inertia)
First, let's calculate the bending moment at the mid span of the beam. Since the beam is simply supported, the bending moment at the mid span can be calculated as half of the concentrated load multiplied by the span:
M = (80 kN * 12m) / 2 = 480 kNm
Next, we need to determine the distance from the neutral axis to the point of interest. In a rectangular section, the neutral axis is located at the centroid, which is half the depth of the section. Therefore, c = 20cm / 2 = 10cm = 0.1m.
Now, we need to calculate the second moment of area. For a rectangular section, the second moment of area about the horizontal axis is given by the formula:
I = (b * h^3) / 12
Where:
b is the width of the section
h is the depth of the section
Plugging in the values, we get:
I = (12cm * (20cm)^3) / 12 = 3200 cm^4 = 0.00032 m^4
Finally, we can substitute the values into the bending stress formula:
σ = (480 kNm * 0.1m) / 0.00032 m^4 = 150 MPa
Therefore, the maximum bending stress induced in the beam is 150 MPa.
σ = (M * c) / I
Where:
σ is the bending stress
M is the bending moment
c is the distance from the neutral axis to the point of interest
I is the second moment of area (also known as the moment of inertia)
First, let's calculate the bending moment at the mid span of the beam. Since the beam is simply supported, the bending moment at the mid span can be calculated as half of the concentrated load multiplied by the span:
M = (80 kN * 12m) / 2 = 480 kNm
Next, we need to determine the distance from the neutral axis to the point of interest. In a rectangular section, the neutral axis is located at the centroid, which is half the depth of the section. Therefore, c = 20cm / 2 = 10cm = 0.1m.
Now, we need to calculate the second moment of area. For a rectangular section, the second moment of area about the horizontal axis is given by the formula:
I = (b * h^3) / 12
Where:
b is the width of the section
h is the depth of the section
Plugging in the values, we get:
I = (12cm * (20cm)^3) / 12 = 3200 cm^4 = 0.00032 m^4
Finally, we can substitute the values into the bending stress formula:
σ = (480 kNm * 0.1m) / 0.00032 m^4 = 150 MPa
Therefore, the maximum bending stress induced in the beam is 150 MPa.
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 rectangular section (12cm wide × 20cm deep) is simply supported over a span of 12m. It is acted upon by a concentrated load of 80 kN at the mid span. The maximum bending stress induced isa) 40 MPab) 300 MPac) 200 MPad) 100 MPaCorrect answer is option 'B'. Can you explain this answer?
Question Description
A beam of rectangular section (12cm wide × 20cm deep) is simply supported over a span of 12m. It is acted upon by a concentrated load of 80 kN at the mid span. The maximum bending stress induced isa) 40 MPab) 300 MPac) 200 MPad) 100 MPaCorrect answer is option 'B'. 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 A beam of rectangular section (12cm wide × 20cm deep) is simply supported over a span of 12m. It is acted upon by a concentrated load of 80 kN at the mid span. The maximum bending stress induced isa) 40 MPab) 300 MPac) 200 MPad) 100 MPaCorrect answer is option 'B'. 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 A beam of rectangular section (12cm wide × 20cm deep) is simply supported over a span of 12m. It is acted upon by a concentrated load of 80 kN at the mid span. The maximum bending stress induced isa) 40 MPab) 300 MPac) 200 MPad) 100 MPaCorrect answer is option 'B'. Can you explain this answer?.
A beam of rectangular section (12cm wide × 20cm deep) is simply supported over a span of 12m. It is acted upon by a concentrated load of 80 kN at the mid span. The maximum bending stress induced isa) 40 MPab) 300 MPac) 200 MPad) 100 MPaCorrect answer is option 'B'. 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 A beam of rectangular section (12cm wide × 20cm deep) is simply supported over a span of 12m. It is acted upon by a concentrated load of 80 kN at the mid span. The maximum bending stress induced isa) 40 MPab) 300 MPac) 200 MPad) 100 MPaCorrect answer is option 'B'. 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 A beam of rectangular section (12cm wide × 20cm deep) is simply supported over a span of 12m. It is acted upon by a concentrated load of 80 kN at the mid span. The maximum bending stress induced isa) 40 MPab) 300 MPac) 200 MPad) 100 MPaCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A beam of rectangular section (12cm wide × 20cm deep) is simply supported over a span of 12m. It is acted upon by a concentrated load of 80 kN at the mid span. The maximum bending stress induced isa) 40 MPab) 300 MPac) 200 MPad) 100 MPaCorrect answer is option 'B'. 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 A beam of rectangular section (12cm wide × 20cm deep) is simply supported over a span of 12m. It is acted upon by a concentrated load of 80 kN at the mid span. The maximum bending stress induced isa) 40 MPab) 300 MPac) 200 MPad) 100 MPaCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A beam of rectangular section (12cm wide × 20cm deep) is simply supported over a span of 12m. It is acted upon by a concentrated load of 80 kN at the mid span. The maximum bending stress induced isa) 40 MPab) 300 MPac) 200 MPad) 100 MPaCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A beam of rectangular section (12cm wide × 20cm deep) is simply supported over a span of 12m. It is acted upon by a concentrated load of 80 kN at the mid span. The maximum bending stress induced isa) 40 MPab) 300 MPac) 200 MPad) 100 MPaCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A beam of rectangular section (12cm wide × 20cm deep) is simply supported over a span of 12m. It is acted upon by a concentrated load of 80 kN at the mid span. The maximum bending stress induced isa) 40 MPab) 300 MPac) 200 MPad) 100 MPaCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A beam of rectangular section (12cm wide × 20cm deep) is simply supported over a span of 12m. It is acted upon by a concentrated load of 80 kN at the mid span. The maximum bending stress induced isa) 40 MPab) 300 MPac) 200 MPad) 100 MPaCorrect answer is option 'B'. 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