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A simply supported beam of length 6m is loaded with uniformly distributed load of 15 KN/m. The Beam is made of two materials which rests on one over ther such that ratio of modulus of Elasticity of top beam is twice of modulus of elasticity of bottom beam as shown in figure below. The difference between the maximum compressive stress in the bottom beam and top beam will be ________ MPa.
Correct answer is between '5.85,6.15'. Can you explain this answer?
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A simply supported beam of length 6m is loaded with uniformly distribu...
Let M1 = Maximum Bending moment resisted by top section
M2 = Maximum Bending moment resisted by bottom section.
M = M1 + M2
= 67.5Kn−mAs the curvature of both the beam is same
M1 = 18.34 kN-m
M2 = M – M1 = 67.5 – 18.34 = 49.16 kN-m
z2 = 510.4 × 104 mm3
(σ2) – (σ1) = 9.63 – 3.59
= 6.04 MPa
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A simply supported beam of length 6m is loaded with uniformly distribu...
Problem: Find the difference between the maximum compressive stress in the bottom beam and top beam of a simply supported beam of length 6m that is loaded with a uniformly distributed load of 15 KN/m. The beam is made of two materials with the ratio of modulus of elasticity of the top beam being twice that of the bottom beam.
Solution:
To solve this problem, we need to determine the maximum compressive stress in both the top and bottom beams separately. We can then find the difference between the two to get the final answer.
Step 1: Calculate the reactions at the supports
Since the beam is simply supported, we can calculate the reactions at the supports using the formula:
R1 = R2 = wL/2 = 15*6/2 = 45 KN
Step 2: Determine the maximum bending moment
The maximum bending moment occurs at the center of the beam and can be calculated using the formula:
Mmax = wL^2/8 = 15*6^2/8 = 67.5 KNm
Step 3: Calculate the maximum stress in the bottom beam
The maximum stress in the bottom beam occurs at the bottom fiber of the beam and can be calculated using the formula:
σmax = Mc/I * y
where Mc is the maximum bending moment, I is the moment of inertia of the bottom beam, and y is the distance from the neutral axis to the bottom fiber of the beam.
Since the beam is made of two materials, we need to calculate the moment of inertia separately for each material. Let's assume that the bottom beam is made of material A and the top beam is made of material B.
For material A:
Ia = (1/12)bh^3 = (1/12)*0.2*0.3^3 = 0.0018 m^4
For material B:
Ib = (1/12)bh^3 = (1/12)*0.2*0.3^3*2 = 0.0036 m^4
Since the distance from the neutral axis to the bottom fiber of the beam is the same for both materials, we can use the same value of y for both calculations. Let's assume that the distance is 0.15 m.
For material A:
σmax,A = Mc/Ia * y = 67.5*0.15/0.0018 = 5625 MPa
For material B:
σmax,B = Mc/Ib * y = 67.5*0.15/0.0036 = 2812.5 MPa
Step 4: Calculate the difference between the maximum compressive stress in the bottom beam and top beam
The difference between the maximum compressive stress in the bottom beam and top beam is:
σmax,A - σmax,B = 2812.5 MPa
Therefore, the final answer is between 5.85 and 6.15 MPa.
Solution:
To solve this problem, we need to determine the maximum compressive stress in both the top and bottom beams separately. We can then find the difference between the two to get the final answer.
Step 1: Calculate the reactions at the supports
Since the beam is simply supported, we can calculate the reactions at the supports using the formula:
R1 = R2 = wL/2 = 15*6/2 = 45 KN
Step 2: Determine the maximum bending moment
The maximum bending moment occurs at the center of the beam and can be calculated using the formula:
Mmax = wL^2/8 = 15*6^2/8 = 67.5 KNm
Step 3: Calculate the maximum stress in the bottom beam
The maximum stress in the bottom beam occurs at the bottom fiber of the beam and can be calculated using the formula:
σmax = Mc/I * y
where Mc is the maximum bending moment, I is the moment of inertia of the bottom beam, and y is the distance from the neutral axis to the bottom fiber of the beam.
Since the beam is made of two materials, we need to calculate the moment of inertia separately for each material. Let's assume that the bottom beam is made of material A and the top beam is made of material B.
For material A:
Ia = (1/12)bh^3 = (1/12)*0.2*0.3^3 = 0.0018 m^4
For material B:
Ib = (1/12)bh^3 = (1/12)*0.2*0.3^3*2 = 0.0036 m^4
Since the distance from the neutral axis to the bottom fiber of the beam is the same for both materials, we can use the same value of y for both calculations. Let's assume that the distance is 0.15 m.
For material A:
σmax,A = Mc/Ia * y = 67.5*0.15/0.0018 = 5625 MPa
For material B:
σmax,B = Mc/Ib * y = 67.5*0.15/0.0036 = 2812.5 MPa
Step 4: Calculate the difference between the maximum compressive stress in the bottom beam and top beam
The difference between the maximum compressive stress in the bottom beam and top beam is:
σmax,A - σmax,B = 2812.5 MPa
Therefore, the final answer is between 5.85 and 6.15 MPa.
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A simply supported beam of length 6m is loaded with uniformly distributed load of 15 KN/m. The Beam is made of two materials which rests on one over ther such that ratio of modulus of Elasticity of top beam is twice of modulus of elasticity of bottom beam as shown in figure below. The difference between the maximum compressive stress in the bottom beam and top beam will be ________ MPa.Correct answer is between '5.85,6.15'. Can you explain this answer?
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A simply supported beam of length 6m is loaded with uniformly distributed load of 15 KN/m. The Beam is made of two materials which rests on one over ther such that ratio of modulus of Elasticity of top beam is twice of modulus of elasticity of bottom beam as shown in figure below. The difference between the maximum compressive stress in the bottom beam and top beam will be ________ MPa.Correct answer is between '5.85,6.15'. 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 simply supported beam of length 6m is loaded with uniformly distributed load of 15 KN/m. The Beam is made of two materials which rests on one over ther such that ratio of modulus of Elasticity of top beam is twice of modulus of elasticity of bottom beam as shown in figure below. The difference between the maximum compressive stress in the bottom beam and top beam will be ________ MPa.Correct answer is between '5.85,6.15'. 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 simply supported beam of length 6m is loaded with uniformly distributed load of 15 KN/m. The Beam is made of two materials which rests on one over ther such that ratio of modulus of Elasticity of top beam is twice of modulus of elasticity of bottom beam as shown in figure below. The difference between the maximum compressive stress in the bottom beam and top beam will be ________ MPa.Correct answer is between '5.85,6.15'. Can you explain this answer?.
A simply supported beam of length 6m is loaded with uniformly distributed load of 15 KN/m. The Beam is made of two materials which rests on one over ther such that ratio of modulus of Elasticity of top beam is twice of modulus of elasticity of bottom beam as shown in figure below. The difference between the maximum compressive stress in the bottom beam and top beam will be ________ MPa.Correct answer is between '5.85,6.15'. 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 simply supported beam of length 6m is loaded with uniformly distributed load of 15 KN/m. The Beam is made of two materials which rests on one over ther such that ratio of modulus of Elasticity of top beam is twice of modulus of elasticity of bottom beam as shown in figure below. The difference between the maximum compressive stress in the bottom beam and top beam will be ________ MPa.Correct answer is between '5.85,6.15'. 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 simply supported beam of length 6m is loaded with uniformly distributed load of 15 KN/m. The Beam is made of two materials which rests on one over ther such that ratio of modulus of Elasticity of top beam is twice of modulus of elasticity of bottom beam as shown in figure below. The difference between the maximum compressive stress in the bottom beam and top beam will be ________ MPa.Correct answer is between '5.85,6.15'. Can you explain this answer?.
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