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Determine the width of the cotter used in cotter joint connecting two rods subjected to axial load of 50kN and permissible shear stress in cotter is 50N/(mm² ). Given thickness of cotter=10mm. Also check cotter pin for induced bending stress?
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Determine the width of the cotter used in cotter joint connecting two ...
Determining the Width of Cotter Joint
In order to determine the width of the cotter joint connecting two rods subjected to an axial load of 50kN and a permissible shear stress in cotter of 50N/(mm²), the following steps can be taken:
Step 1: Calculate the Shear Stress
Using the formula for shear stress, we can calculate the maximum shear stress that the cotter joint can handle:
Maximum Shear Stress (τ) = Applied Load / Area of Cross Section
τ = 50kN / (10mm x Width)
τ = 5N/mm² x (1,000,000mm²/m²)
τ = 5MPa
Step 2: Determine the Width of Cotter Joint
Now that we have calculated the maximum shear stress, we can use the permissible shear stress to determine the width of the cotter joint:
Permissible Shear Stress = 50N/mm²
50N/mm² = 5MPa
Width = Applied Load / (Permissible Shear Stress x Thickness of Cotter)
Width = 50kN / (50N/mm² x 10mm)
Width = 100mm
Therefore, the width of the cotter joint is 100mm.
Step 3: Check the Cotter Pin for Induced Bending Stress
Since the cotter pin is a part of the cotter joint, it is important to check it for induced bending stress. This can be done using the formula for bending stress:
Bending Stress (σ) = (Applied Load x Distance from Neutral Axis) / (Moment of Inertia x Section Modulus)
Assuming the cotter pin is made of steel:
Modulus of Elasticity (E) = 200GPa
Moment of Inertia (I) = (π/64) x (Diameter)⁴
Section Modulus (Z) = (π/32) x (Diameter)³
Maximum Permissible Bending Stress (σ) = 165N/mm²
Using these values, we can determine the diameter of the cotter pin that can handle the induced bending stress:
σ = (50kN x (Thickness of Cotter + Width/2)) / (I x Z)
165N/mm² = (50kN x (10mm + 100mm/2)) / (I x Z)
I = (π/64) x (Diameter)⁴
Z = (π/32) x (Diameter)³
Substituting the values and solving for Diameter:
Diameter = 30mm
Therefore, the cotter pin should have a diameter of 30mm to handle the induced bending stress.
Conclusion
The width of the
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Determine the width of the cotter used in cotter joint connecting two rods subjected to axial load of 50kN and permissible shear stress in cotter is 50N/(mm² ). Given thickness of cotter=10mm. Also check cotter pin for induced bending stress?
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Determine the width of the cotter used in cotter joint connecting two rods subjected to axial load of 50kN and permissible shear stress in cotter is 50N/(mm² ). Given thickness of cotter=10mm. Also check cotter pin for induced bending stress? 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 Determine the width of the cotter used in cotter joint connecting two rods subjected to axial load of 50kN and permissible shear stress in cotter is 50N/(mm² ). Given thickness of cotter=10mm. Also check cotter pin for induced bending stress? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the width of the cotter used in cotter joint connecting two rods subjected to axial load of 50kN and permissible shear stress in cotter is 50N/(mm² ). Given thickness of cotter=10mm. Also check cotter pin for induced bending stress?.
Determine the width of the cotter used in cotter joint connecting two rods subjected to axial load of 50kN and permissible shear stress in cotter is 50N/(mm² ). Given thickness of cotter=10mm. Also check cotter pin for induced bending stress? 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 Determine the width of the cotter used in cotter joint connecting two rods subjected to axial load of 50kN and permissible shear stress in cotter is 50N/(mm² ). Given thickness of cotter=10mm. Also check cotter pin for induced bending stress? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the width of the cotter used in cotter joint connecting two rods subjected to axial load of 50kN and permissible shear stress in cotter is 50N/(mm² ). Given thickness of cotter=10mm. Also check cotter pin for induced bending stress?.
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