Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > A cantilever beam of length 2 m with a square...
Start Learning for Free
A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver is
- a)20.0 MPa
- b)37.5 MPa
- c)60.0 MPa
- d)75.0 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 cantilever beam of length 2 m with a square section of side length 0...
Deflection
Most Upvoted Answer
A cantilever beam of length 2 m with a square section of side length 0...
's modulus of 200 GPa. The moment of inertia for a square section is (1/12) * a^4, where 'a' is the side length of the square.
To find the vertical displacement at the free end of the cantilever beam, we can use the formula for deflection in a cantilever beam under a point load:
δ = (F * L^3) / (3 * E * I)
Where:
δ = vertical displacement at the free end
F = load applied at the free end
L = length of the cantilever beam
E = Young's modulus
I = moment of inertia
In this case, F = mg, where m is the mass and g is the acceleration due to gravity. Since the load is applied vertically, F = mg.
Given:
L = 2 m
a = 0.1 m
δ = 5 mm = 0.005 m
E = 200 GPa = 200 * 10^9 Pa
First, let's calculate the moment of inertia for the square section:
I = (1/12) * a^4
I = (1/12) * (0.1^4)
I = 0.0000083333 m^4
Next, we need to convert the load into force:
F = mg
To calculate the mass, we need to find the volume of the square section:
Volume = a^2 * L
Volume = 0.1^2 * 2
Volume = 0.02 m^3
The mass can be calculated using the density of steel, which is approximately 7850 kg/m^3:
m = density * volume
m = 7850 * 0.02
m = 157 kg
Now, we can calculate the force:
F = mg
F = 157 * 9.8
F = 1538.6 N
Finally, we can substitute the values into the formula for deflection:
δ = (F * L^3) / (3 * E * I)
0.005 = (1538.6 * 2^3) / (3 * 200 * 10^9 * 0.0000083333)
0.005 = 6154.4 / (0.05 * 10^9 * 0.0000083333)
0.005 = 6154.4 / (4.1667 * 10^-6)
0.005 = 1476614400
Therefore, the vertical displacement at the free end of the cantilever beam is approximately 1476614400 mm.
To find the vertical displacement at the free end of the cantilever beam, we can use the formula for deflection in a cantilever beam under a point load:
δ = (F * L^3) / (3 * E * I)
Where:
δ = vertical displacement at the free end
F = load applied at the free end
L = length of the cantilever beam
E = Young's modulus
I = moment of inertia
In this case, F = mg, where m is the mass and g is the acceleration due to gravity. Since the load is applied vertically, F = mg.
Given:
L = 2 m
a = 0.1 m
δ = 5 mm = 0.005 m
E = 200 GPa = 200 * 10^9 Pa
First, let's calculate the moment of inertia for the square section:
I = (1/12) * a^4
I = (1/12) * (0.1^4)
I = 0.0000083333 m^4
Next, we need to convert the load into force:
F = mg
To calculate the mass, we need to find the volume of the square section:
Volume = a^2 * L
Volume = 0.1^2 * 2
Volume = 0.02 m^3
The mass can be calculated using the density of steel, which is approximately 7850 kg/m^3:
m = density * volume
m = 7850 * 0.02
m = 157 kg
Now, we can calculate the force:
F = mg
F = 157 * 9.8
F = 1538.6 N
Finally, we can substitute the values into the formula for deflection:
δ = (F * L^3) / (3 * E * I)
0.005 = (1538.6 * 2^3) / (3 * 200 * 10^9 * 0.0000083333)
0.005 = 6154.4 / (0.05 * 10^9 * 0.0000083333)
0.005 = 6154.4 / (4.1667 * 10^-6)
0.005 = 1476614400
Therefore, the vertical displacement at the free end of the cantilever beam is approximately 1476614400 mm.
Attention Civil Engineering (CE) Students!
To make sure you are not studying endlessly, EduRev has designed Civil Engineering (CE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Civil Engineering (CE).
|
Explore Courses for Civil Engineering (CE) exam
|
|
Top Courses for Civil Engineering (CE)View all
A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver isa)20.0 MPab)37.5 MPac)60.0 MPad)75.0 MPaCorrect answer is option 'B'. Can you explain this answer?
Question Description
A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver isa)20.0 MPab)37.5 MPac)60.0 MPad)75.0 MPaCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver isa)20.0 MPab)37.5 MPac)60.0 MPad)75.0 MPaCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver isa)20.0 MPab)37.5 MPac)60.0 MPad)75.0 MPaCorrect answer is option 'B'. Can you explain this answer?.
A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver isa)20.0 MPab)37.5 MPac)60.0 MPad)75.0 MPaCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver isa)20.0 MPab)37.5 MPac)60.0 MPad)75.0 MPaCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver isa)20.0 MPab)37.5 MPac)60.0 MPad)75.0 MPaCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver isa)20.0 MPab)37.5 MPac)60.0 MPad)75.0 MPaCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver isa)20.0 MPab)37.5 MPac)60.0 MPad)75.0 MPaCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver isa)20.0 MPab)37.5 MPac)60.0 MPad)75.0 MPaCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver isa)20.0 MPab)37.5 MPac)60.0 MPad)75.0 MPaCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver isa)20.0 MPab)37.5 MPac)60.0 MPad)75.0 MPaCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver isa)20.0 MPab)37.5 MPac)60.0 MPad)75.0 MPaCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) 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