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A 1m× 1m mild steel sheet of 1 mm thickness is streched in its own plane by stresses 20 Mpa and 30Mpa as shown. Point Of is center of the plate. OC and OF are two mutually perpendicular lines inclined at 45 each to x and y directions respectively before the application of stress. Determine the change in angle between OC and OF after the application of stress take G= 80Gpa?
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A 1m× 1m mild steel sheet of 1 mm thickness is streched in its own pla...
Problem Statement:
A 1m×1m mild steel sheet of 1 mm thickness is stretched in its own plane by stresses 20 MPa and 30 MPa as shown. Point Of is the center of the plate. OC and OF are two mutually perpendicular lines inclined at 45 each to x and y directions respectively before the application of stress. Determine the change in angle between OC and OF after the application of stress. Take G=80 GPa.
Solution:
Given data:
- Dimensions of mild steel sheet: 1m x 1m x 1mm
- Stresses applied: 20 MPa and 30 MPa
- Point Of: Center of the plate
- OC and OF are two mutually perpendicular lines inclined at 45 each to x and y directions respectively
- Shear modulus: G = 80 GPa
Step 1: Calculation of Shear Strains
To calculate the change in angle between OC and OF, we need to find the shear strains in the OC and OF directions. The shear strain is given by:
γ = (1/G) * (σ_x - σ_y)
where,
- σ_x and σ_y are the stresses in the x and y directions respectively
- G is the shear modulus of the material
Substituting the given values, we get:
γ_OC = (1/80 GPa) * (30 MPa - 20 MPa) = 0.125 x 10^-3
γ_OF = (1/80 GPa) * (-20 MPa - 30 MPa) = -0.375 x 10^-3
Step 2: Calculation of Change in Angle
The change in angle between OC and OF is given by:
Δθ = tan^-1 ((γ_OC - γ_OF) / 2)
Substituting the values, we get:
Δθ = tan^-1 ((0.125 x 10^-3 - (-0.375 x 10^-3)) / 2) = 18.43 degrees
Therefore, the change in angle between OC and OF after the application of stress is 18.43 degrees.
A 1m×1m mild steel sheet of 1 mm thickness is stretched in its own plane by stresses 20 MPa and 30 MPa as shown. Point Of is the center of the plate. OC and OF are two mutually perpendicular lines inclined at 45 each to x and y directions respectively before the application of stress. Determine the change in angle between OC and OF after the application of stress. Take G=80 GPa.
Solution:
Given data:
- Dimensions of mild steel sheet: 1m x 1m x 1mm
- Stresses applied: 20 MPa and 30 MPa
- Point Of: Center of the plate
- OC and OF are two mutually perpendicular lines inclined at 45 each to x and y directions respectively
- Shear modulus: G = 80 GPa
Step 1: Calculation of Shear Strains
To calculate the change in angle between OC and OF, we need to find the shear strains in the OC and OF directions. The shear strain is given by:
γ = (1/G) * (σ_x - σ_y)
where,
- σ_x and σ_y are the stresses in the x and y directions respectively
- G is the shear modulus of the material
Substituting the given values, we get:
γ_OC = (1/80 GPa) * (30 MPa - 20 MPa) = 0.125 x 10^-3
γ_OF = (1/80 GPa) * (-20 MPa - 30 MPa) = -0.375 x 10^-3
Step 2: Calculation of Change in Angle
The change in angle between OC and OF is given by:
Δθ = tan^-1 ((γ_OC - γ_OF) / 2)
Substituting the values, we get:
Δθ = tan^-1 ((0.125 x 10^-3 - (-0.375 x 10^-3)) / 2) = 18.43 degrees
Therefore, the change in angle between OC and OF after the application of stress is 18.43 degrees.
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A 1m× 1m mild steel sheet of 1 mm thickness is streched in its own plane by stresses 20 Mpa and 30Mpa as shown. Point Of is center of the plate. OC and OF are two mutually perpendicular lines inclined at 45 each to x and y directions respectively before the application of stress. Determine the change in angle between OC and OF after the application of stress take G= 80Gpa?
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A 1m× 1m mild steel sheet of 1 mm thickness is streched in its own plane by stresses 20 Mpa and 30Mpa as shown. Point Of is center of the plate. OC and OF are two mutually perpendicular lines inclined at 45 each to x and y directions respectively before the application of stress. Determine the change in angle between OC and OF after the application of stress take G= 80Gpa? 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 1m× 1m mild steel sheet of 1 mm thickness is streched in its own plane by stresses 20 Mpa and 30Mpa as shown. Point Of is center of the plate. OC and OF are two mutually perpendicular lines inclined at 45 each to x and y directions respectively before the application of stress. Determine the change in angle between OC and OF after the application of stress take G= 80Gpa? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 1m× 1m mild steel sheet of 1 mm thickness is streched in its own plane by stresses 20 Mpa and 30Mpa as shown. Point Of is center of the plate. OC and OF are two mutually perpendicular lines inclined at 45 each to x and y directions respectively before the application of stress. Determine the change in angle between OC and OF after the application of stress take G= 80Gpa?.
A 1m× 1m mild steel sheet of 1 mm thickness is streched in its own plane by stresses 20 Mpa and 30Mpa as shown. Point Of is center of the plate. OC and OF are two mutually perpendicular lines inclined at 45 each to x and y directions respectively before the application of stress. Determine the change in angle between OC and OF after the application of stress take G= 80Gpa? 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 1m× 1m mild steel sheet of 1 mm thickness is streched in its own plane by stresses 20 Mpa and 30Mpa as shown. Point Of is center of the plate. OC and OF are two mutually perpendicular lines inclined at 45 each to x and y directions respectively before the application of stress. Determine the change in angle between OC and OF after the application of stress take G= 80Gpa? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 1m× 1m mild steel sheet of 1 mm thickness is streched in its own plane by stresses 20 Mpa and 30Mpa as shown. Point Of is center of the plate. OC and OF are two mutually perpendicular lines inclined at 45 each to x and y directions respectively before the application of stress. Determine the change in angle between OC and OF after the application of stress take G= 80Gpa?.
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