The 10-mm-diameter steel bolt is surrounded by a bronze sleeve. The outer diameter of this sleeve is 20 mm, and its inner diameter is 10 mm. If the yield stress for the steel is

$$(σ_γ)_{st} = 640 MPa,$$

and for the bronze

$$(σ_γ)_{br} = 520 MPa,$$

determine the magnitude of the largest elastic load P that can be applied to the assembly.

$$E_{st} = 200 GPa, E_{br} = 100 GPa.$$

Two steel plates are to be held together by means of 16-mm-diameter high-strength steel bolts fitting snugly inside cylindrical brass spacers. Knowing that the average normal stress must not exceed 200 MPa in the bolts and 130 MPa in the spacers, determine the outer diameter of the spacers that yields the most economical and safe design.

A steel wire and a copper wire have equal lengths and support equal loads P. The moduli of elasticity for the steel and copper are $E_{s}=30,000\ \mathrm{ksi}$ and $E_{c}=18,000\ \mathrm{ksi}$, respectively. (a) If the wires have the same diameters, what is the ratio of the elongation of the copper wire to the elongation of the steel wire? (b) If the wires stretch the same amount, what is the ratio of the diameter of the copper wire to the diameter of the steel wire?

The load of 2000 lb is to be supported by the two vertical steel wires for which

$$σ_γ = 70 ksi.$$

Originally wire AB is 60 in. long and wire AC is 60.04 in. long. Determine the cross-sectional area of AB if the load is to be shared equally between both wires. Wire AC has a cross-sectional area of 0.02 in². Eₛₜ = 29.0(10³) ksi.

The elastic portion of the stress-strain diagram for an aluminum alloy is shown in the figure. The specimen from which it was obtained has an origunal diameter of $12.7$ mm and a gage length of $50.8$ mm . When the applied load on the specimen is $50$ kN the diameter is $12.67494$mm . Determine Poisson's ratio for the material.

The load of 2000 lb is to be supported by the two vertical steel wires for which

$$σ_γ = 70 ksi.$$

Originally wire AB is 60 in. long and wire AC is 60.04 in. long. Determine the force developed in each wire after the load is suspended. Each wire has a cross-sectional area of 0.02 in². Eₛₜ = 29.0(10³) ksi.