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A circular nylon pipe supports a downward load P_A = 10 kN, which is uniformly distributed around a cap plate at the top of the lower pipe. A second load P_B = 20 kN is applied upward at the top. The inner and outer diameters of the upper and lower parts of the pipe are d₁ = 50 mm, d₂ = 60 mm, d₃ = 55 mm, and d₄ = 65 mm, respectively. The bottom pipe has length 400 mm and the upper pipe has length 300 mm.

(a) Calculate the axial normal stress in each pipe segment.

(b) Calculate the strain in each pipe segment if the elongation of the upper pipe is 3.29 mm and the elongation of the bottom part is 1.25 mm.

A symmetrical framework consisting of three pinconnected bars is loaded by a force P (see figure). The angle between the inclined bars and the horizontal is α = 52⁰. The axial strain in the middle bar is measured as 0.027.

Determine the tensile stress in the outer bars if they are constructed of a copper alloy having the following stress-strain relationship:

σ=124,020ε1+300ε0≤ε≤0.03(σ=MPa) σ=124,020ε1+300ε0≤ε≤0.03(σ=MPa)

A round bar of 10 mm diameter is made of aluminum alloy 7075-T6. When the bar is stretched by axial forces P, its diameter decreases by 0.016 mm. Find the magnitude of the load P. (Obtain the material properties from Appendix F.)

A ship’s spar is attached at the base of a mast by a pin connection (see figure). The spar is a steel tube of outer diameter d₂ = 80 mm. and inner diameter d₁ = 70 mm. The steel pin has diameter d = 25 mm., and the two plates connecting the spar to the pin have thickness t = 12 mm. The allowable stresses are as follows: compressive stress in the spar, 75 MPa; shear stress in the pin, 50 MPa; and bearing stress between the pin and the connecting plates, 120 MPa.

Determine the allowable compressive force P_allow in the spar.

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