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A couple of 25 kN/m is acting at one end of a simply supported beam. The maximum slope occuring on the beam is _______________ × 10-5 radian. Take E = 250 GPa and I = 10,00,000 mm4. (Answer up to one decimal place)
Correct answer is '3.3'. Can you explain this answer?
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A couple of 25 kN/m is acting at one end of a simply supported beam. ...
Consider the diagram,
M = 25000 N/m, E = 250 x 109 Pa, I = 0.001 m4
Maximum slope is
= 3.3 × 10-5
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A couple of 25 kN/m is acting at one end of a simply supported beam. ...
To find the maximum slope occurring on the beam, we can use the equation for slope:
θ = (Mx * L^2) / (2 * E * I)
Where:
θ = maximum slope (in radians)
Mx = maximum moment at the location of interest (in Nm)
L = length of the beam (in meters)
E = modulus of elasticity (in N/m^2)
I = moment of inertia of the beam (in mm^4)
Given:
Couple = 25 kN/m = 25,000 N/m
E = 250 GPa = 250,000 N/mm^2
I = 1,000,000 mm^4
- Identify the given values and convert them if necessary.
Couple = 25,000 N/m
E = 250,000 N/mm^2
I = 1,000,000 mm^4
- Calculate the maximum moment at the location of interest.
The couple acting on the beam creates a bending moment. The maximum moment occurs at the supports and is equal to the product of the couple and the distance to the support.
Maximum moment = Couple * L
Given that the beam is simply supported, the maximum moment occurs at the support, which is at a distance of L/2 from the location of interest.
Maximum moment = Couple * (L/2)
Substituting the given values:
Maximum moment = 25,000 * (L/2)
- Substitute the values into the equation for slope.
θ = (Mx * L^2) / (2 * E * I)
Substituting the maximum moment:
θ = (25,000 * (L/2) * L^2) / (2 * 250,000 * 1,000,000)
Simplifying:
θ = (12,500 * L^3) / (500,000,000)
θ = 25 * L^3 / 1,000,000,000
- Substitute the length of the beam and calculate the maximum slope.
Given that the length of the beam is not provided in the question, we cannot calculate the exact maximum slope. However, if we assume a length of 1 meter for the beam, the calculation becomes:
θ = 25 * (1^3) / 1,000,000,000
θ = 25 / 1,000,000,000
Converting the slope from radian to the requested format (× 10^-5 radian):
θ = 25 / 1,000,000,000 * 10^5
θ ≈ 2.5 × 10^-5 radian
Therefore, the maximum slope occurring on the beam is approximately 2.5 × 10^-5 radian, not 3.3 as stated in the answer.
θ = (Mx * L^2) / (2 * E * I)
Where:
θ = maximum slope (in radians)
Mx = maximum moment at the location of interest (in Nm)
L = length of the beam (in meters)
E = modulus of elasticity (in N/m^2)
I = moment of inertia of the beam (in mm^4)
Given:
Couple = 25 kN/m = 25,000 N/m
E = 250 GPa = 250,000 N/mm^2
I = 1,000,000 mm^4
- Identify the given values and convert them if necessary.
Couple = 25,000 N/m
E = 250,000 N/mm^2
I = 1,000,000 mm^4
- Calculate the maximum moment at the location of interest.
The couple acting on the beam creates a bending moment. The maximum moment occurs at the supports and is equal to the product of the couple and the distance to the support.
Maximum moment = Couple * L
Given that the beam is simply supported, the maximum moment occurs at the support, which is at a distance of L/2 from the location of interest.
Maximum moment = Couple * (L/2)
Substituting the given values:
Maximum moment = 25,000 * (L/2)
- Substitute the values into the equation for slope.
θ = (Mx * L^2) / (2 * E * I)
Substituting the maximum moment:
θ = (25,000 * (L/2) * L^2) / (2 * 250,000 * 1,000,000)
Simplifying:
θ = (12,500 * L^3) / (500,000,000)
θ = 25 * L^3 / 1,000,000,000
- Substitute the length of the beam and calculate the maximum slope.
Given that the length of the beam is not provided in the question, we cannot calculate the exact maximum slope. However, if we assume a length of 1 meter for the beam, the calculation becomes:
θ = 25 * (1^3) / 1,000,000,000
θ = 25 / 1,000,000,000
Converting the slope from radian to the requested format (× 10^-5 radian):
θ = 25 / 1,000,000,000 * 10^5
θ ≈ 2.5 × 10^-5 radian
Therefore, the maximum slope occurring on the beam is approximately 2.5 × 10^-5 radian, not 3.3 as stated in the answer.
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A couple of 25 kN/m is acting at one end of a simply supported beam. The maximum slope occuring on the beam is _______________ × 10-5 radian. Take E = 250 GPa and I = 10,00,000 mm4. (Answer up to one decimal place)Correct answer is '3.3'. Can you explain this answer?
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A couple of 25 kN/m is acting at one end of a simply supported beam. The maximum slope occuring on the beam is _______________ × 10-5 radian. Take E = 250 GPa and I = 10,00,000 mm4. (Answer up to one decimal place)Correct answer is '3.3'. 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 couple of 25 kN/m is acting at one end of a simply supported beam. The maximum slope occuring on the beam is _______________ × 10-5 radian. Take E = 250 GPa and I = 10,00,000 mm4. (Answer up to one decimal place)Correct answer is '3.3'. 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 couple of 25 kN/m is acting at one end of a simply supported beam. The maximum slope occuring on the beam is _______________ × 10-5 radian. Take E = 250 GPa and I = 10,00,000 mm4. (Answer up to one decimal place)Correct answer is '3.3'. Can you explain this answer?.
A couple of 25 kN/m is acting at one end of a simply supported beam. The maximum slope occuring on the beam is _______________ × 10-5 radian. Take E = 250 GPa and I = 10,00,000 mm4. (Answer up to one decimal place)Correct answer is '3.3'. 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 couple of 25 kN/m is acting at one end of a simply supported beam. The maximum slope occuring on the beam is _______________ × 10-5 radian. Take E = 250 GPa and I = 10,00,000 mm4. (Answer up to one decimal place)Correct answer is '3.3'. 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 couple of 25 kN/m is acting at one end of a simply supported beam. The maximum slope occuring on the beam is _______________ × 10-5 radian. Take E = 250 GPa and I = 10,00,000 mm4. (Answer up to one decimal place)Correct answer is '3.3'. Can you explain this answer?.
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