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A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The material has yield strength of 240 MPa and endurance limit in reversed bending is 160 MPa. According to the Soderberg principle, the area of cross-section in mm2 of the bar for a factor of safety of 2 is
- a)400
- b)600
- c)750
- d)1000
Correct answer is option 'D'. Can you explain this answer?
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A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. T...
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Solution:
Given data:
Fluctuating tensile load = 20 kN to 100 kN
Yield strength = 240 MPa
Endurance limit in reversed bending = 160 MPa
Factor of safety = 2
Soderberg principle:
According to the Soderberg principle, the material should withstand the combined effect of fluctuating stresses and steady stresses. The principle states that the product of the steady stress and the reciprocal of the steady stress factor should be added to the product of the alternating stress and the reciprocal of the alternating stress factor. This sum should be less than or equal to the material's endurance limit in reversed bending.
Calculation:
The maximum alternating stress on the bar can be calculated as follows:
Maximum alternating stress = Maximum fluctuating load / Area
= 100 kN / (π/4) d^2
where d is the diameter of the bar.
The maximum steady stress on the bar can be calculated as follows:
Maximum steady stress = Yield strength / Factor of safety
= 240 MPa / 2
The alternating stress factor can be calculated as follows:
Alternating stress factor = 0.5 (240 / 160) = 0.75
The steady stress factor can be taken as 1.
Now, applying the Soderberg principle, we get:
(240 / 2) + [(100 / (π/4) d^2) / 0.75] ≤ 160
Solving for d, we get:
d = 11.32 mm
The area of cross-section of the bar can be calculated as follows:
Area = (π/4) d^2 = (π/4) (11.32)^2 = 1000 mm^2
Therefore, the correct answer is option D, i.e., 1000 mm^2.
Given data:
Fluctuating tensile load = 20 kN to 100 kN
Yield strength = 240 MPa
Endurance limit in reversed bending = 160 MPa
Factor of safety = 2
Soderberg principle:
According to the Soderberg principle, the material should withstand the combined effect of fluctuating stresses and steady stresses. The principle states that the product of the steady stress and the reciprocal of the steady stress factor should be added to the product of the alternating stress and the reciprocal of the alternating stress factor. This sum should be less than or equal to the material's endurance limit in reversed bending.
Calculation:
The maximum alternating stress on the bar can be calculated as follows:
Maximum alternating stress = Maximum fluctuating load / Area
= 100 kN / (π/4) d^2
where d is the diameter of the bar.
The maximum steady stress on the bar can be calculated as follows:
Maximum steady stress = Yield strength / Factor of safety
= 240 MPa / 2
The alternating stress factor can be calculated as follows:
Alternating stress factor = 0.5 (240 / 160) = 0.75
The steady stress factor can be taken as 1.
Now, applying the Soderberg principle, we get:
(240 / 2) + [(100 / (π/4) d^2) / 0.75] ≤ 160
Solving for d, we get:
d = 11.32 mm
The area of cross-section of the bar can be calculated as follows:
Area = (π/4) d^2 = (π/4) (11.32)^2 = 1000 mm^2
Therefore, the correct answer is option D, i.e., 1000 mm^2.
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A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The materialhas yield strength of 240 MPa and endurance limit in reversed bending is 160MPa. According to the Soderberg principle, the area of cross-section in mm2 ofthe bar for a factor of safety of 2 isa)400b)600c)750d)1000Correct answer is option 'D'. Can you explain this answer?
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A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The materialhas yield strength of 240 MPa and endurance limit in reversed bending is 160MPa. According to the Soderberg principle, the area of cross-section in mm2 ofthe bar for a factor of safety of 2 isa)400b)600c)750d)1000Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The materialhas yield strength of 240 MPa and endurance limit in reversed bending is 160MPa. According to the Soderberg principle, the area of cross-section in mm2 ofthe bar for a factor of safety of 2 isa)400b)600c)750d)1000Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The materialhas yield strength of 240 MPa and endurance limit in reversed bending is 160MPa. According to the Soderberg principle, the area of cross-section in mm2 ofthe bar for a factor of safety of 2 isa)400b)600c)750d)1000Correct answer is option 'D'. Can you explain this answer?.
A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The materialhas yield strength of 240 MPa and endurance limit in reversed bending is 160MPa. According to the Soderberg principle, the area of cross-section in mm2 ofthe bar for a factor of safety of 2 isa)400b)600c)750d)1000Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The materialhas yield strength of 240 MPa and endurance limit in reversed bending is 160MPa. According to the Soderberg principle, the area of cross-section in mm2 ofthe bar for a factor of safety of 2 isa)400b)600c)750d)1000Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The materialhas yield strength of 240 MPa and endurance limit in reversed bending is 160MPa. According to the Soderberg principle, the area of cross-section in mm2 ofthe bar for a factor of safety of 2 isa)400b)600c)750d)1000Correct answer is option 'D'. Can you explain this answer?.
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A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The materialhas yield strength of 240 MPa and endurance limit in reversed bending is 160MPa. According to the Soderberg principle, the area of cross-section in mm2 ofthe bar for a factor of safety of 2 isa)400b)600c)750d)1000Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The materialhas yield strength of 240 MPa and endurance limit in reversed bending is 160MPa. According to the Soderberg principle, the area of cross-section in mm2 ofthe bar for a factor of safety of 2 isa)400b)600c)750d)1000Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The materialhas yield strength of 240 MPa and endurance limit in reversed bending is 160MPa. According to the Soderberg principle, the area of cross-section in mm2 ofthe bar for a factor of safety of 2 isa)400b)600c)750d)1000Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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