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An aluminum wire having a diameter d = 2 mm and length L = 3.8 m is subjected to a tensile load P (see figure). The aluminum has modulus of elasticity E = 75 GPa.

If the maximum permissible elongation of the wire is 3.0 mm and the allowable stress in tension is 60 MPa, what is the allowable load P_max?

A hollow, circular, cast-iron pipe (E_c = 83 GPa) supports a brass rod (E_b = 96 GPa) and weight W = 9 kN, as shown. The outside diameter of the pipe is d_c = 150 mm.

(a) If the allowable compressive stress in the pipe is 35 MPa and the allowable shortening of the pipe is 0.5 mm, what is the minimum required wall thickness t_c,min? (Include the weights of the rod and steel cap in your calculations.)

(b) What is the elongation of the brass rod δ_r due to both load W and its own weight?

(c) What is the minimum required clearance h?

A bar ABC of length L consists of two parts of equal lengths but different diameters. Segment AB has diameter d₁ = 100 mm, and segment BC has diameter d₂ = 60 mm. Both segments have length L/2 = 0.6 m. A longitudinal hole of diameter d is drilled through segment AB for one-half of its length (distance L/4 = 0.3 m). The bar is made of plastic having modulus of elasticity

E = 4.0 GPa. Compressive loads P = 110 kN act at the ends of the bar.

(a) If the shortening of the bar is limited to 8.0 mm, what is the maximum allowable diameter d_max of the hole? (See figure part a.)

(b) Now, if d_max is instead set at d₂/2, at what distance b from end C should load P be applied to limit the bar shortening to 8.0 mm? (See figure part b.) (c) Finally, if loads P are applied at the ends and d_max = d₂/2, what is the permissible length x of the hole if shortening is to be limited to 8.0 mm? (See figure part c.)

Three prismatic bars, two of material A and one of material B, transmit a tensile load P. The two outer bars (material A) are identical. The cross-sectional area of the middle bar (material B) is 50% larger than the cross-sectional area of one of the outer bars. Also, the modulus of elasticity of material A is twice that of material B.

a. What fraction of the load P is transmitted by the middle bar?

b. What is the ratio of the stress in the middle bar to the stress in the outer bars?

c. What is the ratio of the strain in the middle bar to the strain in the outer bars?

An aluminum pipe has a length of 60 m at a temperature of 10°C. An adjacent steel pipe at the same temperature is 5 mm longer than the aluminum pipe.

At what temperature (degrees Celsius) will the aluminum pipe be 15 mm longer than the steel pipe? (Assume that the coefficients of thermal expansion of aluminum and steel are α_a = 23 × 10⁻⁶/°C and α_s = 12 × 10⁻⁶/°C, respectively.)

During a tension test of a mild-steel specimen (see figure), the extensometer shows an elongation of 0.004 mm. with a gage length of 50 mm. Assume that the steel is stressed below the proportional limit and that the modulus of elasticity E = 210 GPa.

(a) What is the maximum normal stress σ_max in the specimen?

(b) What is the maximum shear stress τ_max?

(c) Draw a stress element oriented at an angle of 45° to the axis of the bar and show all stresses acting on the faces of this element.

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