Knowing that the allowable stress in section ABD is $10\ \text{ksi}$, determine the largest force P that can be applied to the bracket shown.

An offset $h$ must be introduced into a solid circular rod of diameter $d$. Knowing that the maximum stress after the offset is introduced must not exceed 5 times the stress in the rod when it is straight, determine the largest offset that can be used.

A bar having the cross section shown has been formed by securely bonding brass and aluminum stock. Using the data given below, find the largest permissible bending moment when the composite bar is bent about a horizontal axis.

A bar having the cross section shown has been formed by securely bonding brass and aluminum stock. Using the data given in the table, determine the largest permissible bending moment when the composite bar is bent about a horizontal axis.

A bar having the cross section shown has been formed by securely bonding brass and aluminum stock. Using the data given below, determine the largest permissible bending moment when the composite bar is bent about a horizontal axis.

Knowing that the allowable stress for the steel used is 24 ksi, choose the most economical wide-flange beam to support the loading shown.

The allowable shearing stress is $15\ \text{ksi}$ in the steel rod AB and 8 ksi in the brass rod BC. Knowing that a torque of magnitude T=10 kip - in. is applied at A and neglecting the effect of stress concentrations, determine the required diameter of (a) rod AB, (b) rod BC.

Knowing that for the extruded beam shown the allowable stress is 12 ksi in tension and 16 ksi in compression, find the largest couple M that can be applied.

Knowing that for the beam shown the allowable stress is $12 \mathrm{~ksi}$ in tension and $16 \mathrm{~ksi}$ in compression, determine the largest couple $\mathbf{M}$ that can be applied.

Knowing that for the beam shown the allowable stress is 12 ksi in tension and 16 ksi in compression, find the largest couple that can be applied.

Two equal and opposite couples of magnitude $M=15 \mathrm{~kN} \cdot \mathrm{m}$ are applied to the channel-shaped beam $AB$. Observing that the couples cause the beam to bend in a horizontal plane, determine the stress (a) at point $C,(b)$ at point $D,(c)$ at point $E$.

Using the isothermal transformation diagram for an iron–carbon alloy of eutectoid composition, specify the nature of the final microstructure (in terms of microconstituents present and approximate percentages of each) of a small specimen that has been subjected to the following time–temperature treatments. In each case assume that the specimen begins at $760^{\circ} \mathrm{C}$ $\left(1400^{\circ} \mathrm{F}\right)$ and that it has been held at this temperature long enough to have achieved a complete and homogeneous austenitic structure. (a) Cool rapidly to $350^{\circ} \mathrm{C}\left(660^{\circ} \mathrm{F}\right)$, hold for $10^{3}$ s, then quench to room temperature. (b) Rapidly cool to $625^{\circ} \mathrm{C}\left(1160^{\circ} \mathrm{F}\right)$, hold for 10 s, then quench to room temperature. (c) Rapidly cool to $600^{\circ} \mathrm{C}\left(1110^{\circ} \mathrm{F}\right)$, hold for 4 s, rapidly cool to $450^{\circ} \mathrm{C}\left(840^{\circ} \mathrm{F}\right)$, hold for 10 s, then quench to room temperature. (d) Reheat the specimen in part (c) to $700^{\circ} \mathrm{C}\left(1290^{\circ} \mathrm{F}\right)$ for 20 h. (e) Rapidly cool to $300^{\circ} \mathrm{C}\left(570^{\circ} \mathrm{F}\right)$, hold for 20 s, then quench to room temperature in water. Reheat to $425^{\circ} \mathrm{C}\left(800^{\circ} \mathrm{F}\right)$ for $10^{3}$ s and slowly cool to room temperature. (f) Cool rapidly to $665^{\circ} \mathrm{C}\left(1230^{\circ} \mathrm{F}\right)$, hold for $10^{3}$ s, then quench to room temperature. (g) Rapidly cool to $575^{\circ} \mathrm{C}\left(1065^{\circ} \mathrm{F}\right)$, hold for 20 s, rapidly cool to $350^{\circ} \mathrm{C}\left(660^{\circ} \mathrm{F}\right)$, hold for 100 s, then quench to room temperature. (h) Rapidly cool to $350^{\circ} \mathrm{C}\left(660^{\circ} \mathrm{F}\right)$, hold for 150 s, then quench to room temperature.

Compute the mass fraction of eutectoid ferrite in an iron–carbon alloy that contains 0.43 wt% C

Consider 2.0 kg of a 99.6 wt% Fe–0.4 wt% C alloy that is cooled to a temperature just below the eutectoid.

(a) How many kilograms of proeutectoid ferrite form?

(b) How many kilograms of eutectoid ferrite form?

(c) How many kilograms of cementite form?