A milling operation was used to remove a portion of a solid bar of square cross section. Knowing that $a=1.2 \mathrm{~in}$, $d=0.8 \mathrm{~in}$, and $\sigma_{all}=8\mathrm{~ksi}$, determine the magnitude P of the largest forces that can be safely applied at the centers of the ends of the bar.

An offset $h$ must be introduced into a metal tube of $18-\mathrm{mm}$ outer diameter and $2-\mathrm{mm}$ wall thickness. Knowing that the maximum stress after the offset is introduced must not exceed four times the stress in the tube when it was straight, determine the largest offset that can be used.

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 four times the stress in the rod when it was straight, determine the largest offset that can be used.

Determine the stress at points $A$ and $B(a)$ for the loading shown, (b) if the $60-\mathrm{kN}$ loads applied at points $2$ and $3$ are removed.

Determine the stress at points $A$ and $B(a)$ for the loading shown, $(b)$ if the $60-\mathrm{kN}$ loads are applied at points $1$ and $2$ only.

Solve the vertical portion of the press shown consists of a rectangular tube having a wall thickness $t=\frac{1}{2}$ $\mathrm{in}$. Knowing that the press has been tightened on wooden planks being glued together until $P=$ 6 $\mathrm{kips}$, determine the stress (a) at point $A,(b)$ point $B$. assuming that $t=\frac{3}{8}$ $\mathrm{in}$.

The vertical portion of the press shown consists of a rectangular tube having a wall thickness $t=\frac{1}{2}$ $\mathrm{in}$. Knowing that the press has been tightened on wooden planks being glued together until $P=$ 6 $\mathrm{kips}$, determine the stress (a) at point $A,(b)$ point $B$.

Knowing that the magnitude of the horizontal force P is $8 \mathrm{~kN}$, determine the stress at

(a) point A,

(b) point B.

As many as three axial loads each of magnitude $P=10$ $\mathrm{kips}$ can be applied to the end of a $W8$ $\times 21$ rolled-steel shape. Determine the stress at point $A(a)$ for the loading shown, (b) if loads are applied at points $2$ and $3$ only.

As many as three axial loads each of magnitude $P=10 \mathrm{~kips}$ can be applied to the end of a $\mathrm{W}8$ $\times 21$ rolled-steel shape. Detertnine the stress at point $A(a)$ for the loading shown, $(b)$ if loads are applied at points $1$ and $2$ only.

A nylon spacing bar has the cross section shown. Knowing that the allowable stress for the grade of nylon used is $24 \mathrm{~MPa}$, determine the largest couple $\mathbf{M}_{2}$ that can be applied to the bar.

Two forces P can be applied separately or at the same time to a plate that is welded to a solid circular bar of radius r. Determine the largest compressive stress in the circular bar (a) when both forces are applied, (b) when only one of the forces is applied.

Five metal strips, each of $0.5 \times 1.5-\text{in.}$ cross section, are bonded together to form the composite beam shown. The modulus of elasticity is $30 \times 10^6$ psi for the steel, $15 \times 10^6 \mathrm{psi}$ for the brass, and $10 \times 10^6\ \mathrm{psi}$ for the aluminum. Knowing that the beam is bent about a horizontal axis by a couple of moment $12\ \text{kip.in}$ determine (a) the maximum stress in each of the three metals, (b) the radius of curvature of the composite beam.

Five metal strips, each of $0.5 \times 1.5-\text{in.}$ cross section, are bonded together to form the composite beam shown. The modulus of elasticity is $30 \times 10^6$ psi for the steel, $15 \times 10^6\ \mathrm{psi}$ for the brass, and $10 \times 10^6 \mathrm{psi}$ for the aluminum. Knowing that the beam is bent about a horizontal axis by a couple of moment $12\ \text{kip.in}$ determine (a) the maximum stress in each of the three metals, (b) the radius of curvature of the composite beam.