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A 700 mm length of aluminium alloy bar is suspended from the ceiling so as to provide a clearance of 0.3 mm between it and a 250 mm length of steel bar as shown in Fig. 14.32. Aal = 1250 mm2, Eal = 70 GN/m2, As = 2500 mm2, Es = 210 GN/m2. Determine the stress in the aluminium and in the steel due to a 300kN load applied 500 mm from the ceiling.?
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A 700 mm length of aluminium alloy bar is suspended from the ceiling s...
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A 700 mm length of aluminium alloy bar is suspended from the ceiling s...
Given:
- Length of aluminium alloy bar (Lal) = 700 mm
- Clearance between aluminium and steel bar (c) = 0.3 mm
- Length of steel bar (Ls) = 250 mm
- Cross-sectional area of aluminium bar (Aal) = 1250 mm²
- Young's modulus of aluminium (Eal) = 70 GN/m²
- Cross-sectional area of steel bar (As) = 2500 mm²
- Young's modulus of steel (Es) = 210 GN/m²
- Load applied (F) = 300 kN
- Distance of load from the ceiling (d) = 500 mm
Calculating Stress in Aluminium:
- The elongation (∆l) of the aluminium bar can be calculated using the formula:
∆l = (F * d) / (Aal * Eal)
where F is the load applied, d is the distance of the load from the ceiling, Aal is the cross-sectional area of aluminium, and Eal is the Young's modulus of aluminium.
- Substituting the given values:
∆l = (300 kN * 500 mm) / (1250 mm² * 70 GN/m²)
= 0.02143 mm
- The stress (σal) in the aluminium bar can be calculated using the formula:
σal = (∆l / Lal) * 1000
where ∆l is the elongation of the aluminium bar and Lal is the length of the aluminium bar.
- Substituting the given values:
σal = (0.02143 mm / 700 mm) * 1000
= 30.61 MPa
Calculating Stress in Steel:
- Since there is a clearance of 0.3 mm between the aluminium and steel bars, the elongation of the steel bar (∆ls) will be equal to the elongation of the aluminium bar (∆l) plus the clearance (c).
∆ls = ∆l + c
= 0.02143 mm + 0.3 mm
= 0.32143 mm
- The stress (σs) in the steel bar can be calculated using the formula:
σs = (∆ls / Ls) * 1000
where ∆ls is the elongation of the steel bar and Ls is the length of the steel bar.
- Substituting the given values:
σs = (0.32143 mm / 250 mm) * 1000
= 1.29 MPa
Summary:
- The stress in the aluminium bar due to the applied load of 300 kN is 30.61 MPa.
- The stress in the steel bar due to the applied load of 300 kN is 1.29 MPa.
- Length of aluminium alloy bar (Lal) = 700 mm
- Clearance between aluminium and steel bar (c) = 0.3 mm
- Length of steel bar (Ls) = 250 mm
- Cross-sectional area of aluminium bar (Aal) = 1250 mm²
- Young's modulus of aluminium (Eal) = 70 GN/m²
- Cross-sectional area of steel bar (As) = 2500 mm²
- Young's modulus of steel (Es) = 210 GN/m²
- Load applied (F) = 300 kN
- Distance of load from the ceiling (d) = 500 mm
Calculating Stress in Aluminium:
- The elongation (∆l) of the aluminium bar can be calculated using the formula:
∆l = (F * d) / (Aal * Eal)
where F is the load applied, d is the distance of the load from the ceiling, Aal is the cross-sectional area of aluminium, and Eal is the Young's modulus of aluminium.
- Substituting the given values:
∆l = (300 kN * 500 mm) / (1250 mm² * 70 GN/m²)
= 0.02143 mm
- The stress (σal) in the aluminium bar can be calculated using the formula:
σal = (∆l / Lal) * 1000
where ∆l is the elongation of the aluminium bar and Lal is the length of the aluminium bar.
- Substituting the given values:
σal = (0.02143 mm / 700 mm) * 1000
= 30.61 MPa
Calculating Stress in Steel:
- Since there is a clearance of 0.3 mm between the aluminium and steel bars, the elongation of the steel bar (∆ls) will be equal to the elongation of the aluminium bar (∆l) plus the clearance (c).
∆ls = ∆l + c
= 0.02143 mm + 0.3 mm
= 0.32143 mm
- The stress (σs) in the steel bar can be calculated using the formula:
σs = (∆ls / Ls) * 1000
where ∆ls is the elongation of the steel bar and Ls is the length of the steel bar.
- Substituting the given values:
σs = (0.32143 mm / 250 mm) * 1000
= 1.29 MPa
Summary:
- The stress in the aluminium bar due to the applied load of 300 kN is 30.61 MPa.
- The stress in the steel bar due to the applied load of 300 kN is 1.29 MPa.
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A 700 mm length of aluminium alloy bar is suspended from the ceiling so as to provide a clearance of 0.3 mm between it and a 250 mm length of steel bar as shown in Fig. 14.32. Aal = 1250 mm2, Eal = 70 GN/m2, As = 2500 mm2, Es = 210 GN/m2. Determine the stress in the aluminium and in the steel due to a 300kN load applied 500 mm from the ceiling.?
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A 700 mm length of aluminium alloy bar is suspended from the ceiling so as to provide a clearance of 0.3 mm between it and a 250 mm length of steel bar as shown in Fig. 14.32. Aal = 1250 mm2, Eal = 70 GN/m2, As = 2500 mm2, Es = 210 GN/m2. Determine the stress in the aluminium and in the steel due to a 300kN load applied 500 mm from the ceiling.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A 700 mm length of aluminium alloy bar is suspended from the ceiling so as to provide a clearance of 0.3 mm between it and a 250 mm length of steel bar as shown in Fig. 14.32. Aal = 1250 mm2, Eal = 70 GN/m2, As = 2500 mm2, Es = 210 GN/m2. Determine the stress in the aluminium and in the steel due to a 300kN load applied 500 mm from the ceiling.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 700 mm length of aluminium alloy bar is suspended from the ceiling so as to provide a clearance of 0.3 mm between it and a 250 mm length of steel bar as shown in Fig. 14.32. Aal = 1250 mm2, Eal = 70 GN/m2, As = 2500 mm2, Es = 210 GN/m2. Determine the stress in the aluminium and in the steel due to a 300kN load applied 500 mm from the ceiling.?.
A 700 mm length of aluminium alloy bar is suspended from the ceiling so as to provide a clearance of 0.3 mm between it and a 250 mm length of steel bar as shown in Fig. 14.32. Aal = 1250 mm2, Eal = 70 GN/m2, As = 2500 mm2, Es = 210 GN/m2. Determine the stress in the aluminium and in the steel due to a 300kN load applied 500 mm from the ceiling.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A 700 mm length of aluminium alloy bar is suspended from the ceiling so as to provide a clearance of 0.3 mm between it and a 250 mm length of steel bar as shown in Fig. 14.32. Aal = 1250 mm2, Eal = 70 GN/m2, As = 2500 mm2, Es = 210 GN/m2. Determine the stress in the aluminium and in the steel due to a 300kN load applied 500 mm from the ceiling.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 700 mm length of aluminium alloy bar is suspended from the ceiling so as to provide a clearance of 0.3 mm between it and a 250 mm length of steel bar as shown in Fig. 14.32. Aal = 1250 mm2, Eal = 70 GN/m2, As = 2500 mm2, Es = 210 GN/m2. Determine the stress in the aluminium and in the steel due to a 300kN load applied 500 mm from the ceiling.?.
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A 700 mm length of aluminium alloy bar is suspended from the ceiling so as to provide a clearance of 0.3 mm between it and a 250 mm length of steel bar as shown in Fig. 14.32. Aal = 1250 mm2, Eal = 70 GN/m2, As = 2500 mm2, Es = 210 GN/m2. Determine the stress in the aluminium and in the steel due to a 300kN load applied 500 mm from the ceiling.?, a detailed solution for A 700 mm length of aluminium alloy bar is suspended from the ceiling so as to provide a clearance of 0.3 mm between it and a 250 mm length of steel bar as shown in Fig. 14.32. Aal = 1250 mm2, Eal = 70 GN/m2, As = 2500 mm2, Es = 210 GN/m2. Determine the stress in the aluminium and in the steel due to a 300kN load applied 500 mm from the ceiling.? has been provided alongside types of A 700 mm length of aluminium alloy bar is suspended from the ceiling so as to provide a clearance of 0.3 mm between it and a 250 mm length of steel bar as shown in Fig. 14.32. Aal = 1250 mm2, Eal = 70 GN/m2, As = 2500 mm2, Es = 210 GN/m2. Determine the stress in the aluminium and in the steel due to a 300kN load applied 500 mm from the ceiling.? theory, EduRev gives you an
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