The composite bar BCD in the figure is composed of an inner aluminum cylindrical core of length 2l=2m and radius R=1cm and a sleeve of steel of length L=1m and thickness R=1cm surrounding the aluminum core in the CD section of the bar. The Young’s moduli are:Eal= 70Gpa = , andEsteel=210GPa . The bar is fixed at B and a concentrated tensile load F is applied at the free end D . The resulting total elongation of bar BCD , is 1cm . Determine the normal stress in the steel sleeve.
0.4 mm for last problem.
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First par please and the others?
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Determine the normal stress in the steel sleeve.
plz help?
-86.8 MPa
thanhs Pa.
To determine the normal stress in the steel sleeve of the composite bar BCD, we can follow these steps:
1. Calculate the total elongation of the composite bar BCD:
The total elongation of the bar is given as 1 cm. Since both the aluminum core and the steel sleeve elongate together, the total elongation is the sum of the elongations in each material.
2. Find the elongation of the aluminum core:
The elongation of a cylindrical bar, such as the aluminum core in this case, can be calculated using the formula:
ΔL = (F * L) / (A * E)
where ΔL is the elongation, F is the applied load, L is the length of the bar, A is the cross-sectional area of the bar, and E is the Young's modulus of the material.
The cross-sectional area of the aluminum core can be calculated using the formula:
A = π * R^2
where R is the radius of the core.
3. Find the elongation of the steel sleeve:
Since the aluminum core and the steel sleeve are in series, they experience the same elongation. The elongation of the steel sleeve is given as the total elongation of the composite bar minus the elongation of the aluminum core.
4. Calculate the normal stress in the steel sleeve:
The normal stress in a cylindrical bar can be calculated using the formula:
σ = F / A
where σ is the stress, F is the applied load, and A is the cross-sectional area of the bar.
By following these steps and using the given values for the lengths, radii, Young's moduli, and the applied load, you can calculate the normal stress in the steel sleeve of the composite bar BCD.