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A component is loaded with normal and shear stresses as σx= 15 MPa ; σy = 5 MPa ; and τxy = 10 MPa. Find the maximum shear stress developed in the component.?
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A component is loaded with normal and shear stresses as σx= 15 MPa ; σ...
Maximum Shear Stress Calculation
To find the maximum shear stress developed in the component, we need to determine the principal stresses first. The principal stresses are the normal stresses on the planes where the shear stress is zero. From these principal stresses, we can then calculate the maximum shear stress.
Step 1: Calculate the average normal stress:
The average normal stress, σ_avg, can be calculated using the formula:
σ_avg = (σx + σy) / 2
Given:
σx = 15 MPa
σy = 5 MPa
Using the above formula, we can calculate:
σ_avg = (15 + 5) / 2 = 10 MPa
Step 2: Calculate the difference in normal stresses:
The difference in normal stresses, Δσ, can be calculated using the formula:
Δσ = (σx - σy) / 2
Using the given values:
Δσ = (15 - 5) / 2 = 5 MPa
Step 3: Calculate the maximum normal stress:
The maximum normal stress, σ_max, can be calculated using the formula:
σ_max = σ_avg ± Δσ
In this case, since Δσ is positive, we will use the plus sign.
σ_max = σ_avg + Δσ
σ_max = 10 + 5 = 15 MPa
Step 4: Calculate the maximum shear stress:
The maximum shear stress, τ_max, can be calculated using the formula:
τ_max = (σ_max - σ_min) / 2
In this case, σ_min is the minimum normal stress, which is the smaller of the two normal stresses (σx and σy).
Since σy is smaller, σ_min = σy = 5 MPa
Using the above formula, we can calculate:
τ_max = (σ_max - σ_min) / 2
τ_max = (15 - 5) / 2 = 5 MPa
Conclusion:
Therefore, the maximum shear stress developed in the component is 5 MPa.
To find the maximum shear stress developed in the component, we need to determine the principal stresses first. The principal stresses are the normal stresses on the planes where the shear stress is zero. From these principal stresses, we can then calculate the maximum shear stress.
Step 1: Calculate the average normal stress:
The average normal stress, σ_avg, can be calculated using the formula:
σ_avg = (σx + σy) / 2
Given:
σx = 15 MPa
σy = 5 MPa
Using the above formula, we can calculate:
σ_avg = (15 + 5) / 2 = 10 MPa
Step 2: Calculate the difference in normal stresses:
The difference in normal stresses, Δσ, can be calculated using the formula:
Δσ = (σx - σy) / 2
Using the given values:
Δσ = (15 - 5) / 2 = 5 MPa
Step 3: Calculate the maximum normal stress:
The maximum normal stress, σ_max, can be calculated using the formula:
σ_max = σ_avg ± Δσ
In this case, since Δσ is positive, we will use the plus sign.
σ_max = σ_avg + Δσ
σ_max = 10 + 5 = 15 MPa
Step 4: Calculate the maximum shear stress:
The maximum shear stress, τ_max, can be calculated using the formula:
τ_max = (σ_max - σ_min) / 2
In this case, σ_min is the minimum normal stress, which is the smaller of the two normal stresses (σx and σy).
Since σy is smaller, σ_min = σy = 5 MPa
Using the above formula, we can calculate:
τ_max = (σ_max - σ_min) / 2
τ_max = (15 - 5) / 2 = 5 MPa
Conclusion:
Therefore, the maximum shear stress developed in the component is 5 MPa.
Community Answer
A component is loaded with normal and shear stresses as σx= 15 MPa ; σ...
14.14 (N/mm^2)
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A component is loaded with normal and shear stresses as σx= 15 MPa ; σy = 5 MPa ; and τxy = 10 MPa. Find the maximum shear stress developed in the component.?
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A component is loaded with normal and shear stresses as σx= 15 MPa ; σy = 5 MPa ; and τxy = 10 MPa. Find the maximum shear stress developed in the component.? 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 component is loaded with normal and shear stresses as σx= 15 MPa ; σy = 5 MPa ; and τxy = 10 MPa. Find the maximum shear stress developed in the component.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A component is loaded with normal and shear stresses as σx= 15 MPa ; σy = 5 MPa ; and τxy = 10 MPa. Find the maximum shear stress developed in the component.?.
A component is loaded with normal and shear stresses as σx= 15 MPa ; σy = 5 MPa ; and τxy = 10 MPa. Find the maximum shear stress developed in the component.? 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 component is loaded with normal and shear stresses as σx= 15 MPa ; σy = 5 MPa ; and τxy = 10 MPa. Find the maximum shear stress developed in the component.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A component is loaded with normal and shear stresses as σx= 15 MPa ; σy = 5 MPa ; and τxy = 10 MPa. Find the maximum shear stress developed in the component.?.
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