aluminum

Problem 274

At what temperature will the aluminum and steel segments in Prob. 273 have numerically equal stress?

Solution 274

\sigma_{al} = \sigma_{st}
\dfrac{R_1}{2} = \dfrac{(50\,000 − R_1)}{3}
3R_1 = 100\,000 – 2R_1
R_1 = 20\,000 \, \text{lbs}

Problem 269

As shown in Fig. P-269, there is a gap between the aluminum bar and the rigid slab that is supported by two copper bars. At 10°C, Δ = 0.18 mm. Neglecting the mass of the slab, calculate the stress in each rod when the temperature in the assembly is increased to 95°C. For each copper bar, A = 500 mm², E = 120 GPa, and α = 16.8 µm/(m·°C). For the aluminum bar, A = 400 mm², E = 70 GPa, and α = 23.1 µm/(m·°C).

Problem 257

Three bars AB, AC, and AD are pinned together as shown in Fig. P-257. Initially, the assembly is stress free. Horizontal movement of the joint at A is prevented by a short horizontal strut AE. Calculate the stress in each bar and the force in the strut AE when the assembly is used to support the load W = 10 kips. For each steel bar, A = 0.3 in.² and E = 29 × 10⁶ psi. For the aluminum bar, A = 0.6 in.² and E = 10 × 10⁶ psi.

Problem 242

The assembly in Fig. P-242 consists of a light rigid bar AB, pinned at O, that is attached to the steel and aluminum rods. In the position shown, bar AB is horizontal and there is a gap, Δ = 5 mm, between the lower end of the steel rod and its pin support at C. Compute the stress in the aluminum rod when the lower end of the steel rod is attached to its support.