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.

A concrete beam is reinforced by three steel rods placed as shown. The modulus of elasticity is $3 \times 10^6 \mathrm{psi}$ for the concrete and $30 \times$ $10^6 \mathrm{psi}$ for the steel. Using an allowable stress of $1350\ \text{psi}$ for the concrete and $20\ \text{ksi}$ for the steel, determine the largest permissible positive bending moment in the beam.

Knowing that the bending moment in the reinforced concrete beam is $+150 \mathrm{~kip} \cdot \mathrm{ft}$ and that the modulus of elasticity is $3.75 \times$ $10^{6}$ $\mathrm{psi}$ for the concrete and $30 \times 10^{6}$ $\mathrm{psi}$ for the steel, determine (a) the stress in the steel, (b) the maximum stress in the concrete.

Solve a concrete slab is reinforced by $16 -\mathrm{mm}$-diameter steel rods placed on $180-\mathrm{mm}$ centers as shown. The modulus of elasticity is $20 \mathrm{~GPa}$ for the concrete and $200 \mathrm{~GPa}$ for the steel. Using an allowable stress of $9 \mathrm{~MPa}$ for the concrete and $120 \mathrm{~MPa}$ for the steel, determine the largest allowable positive bending moment in a portion of the slab $1 \mathrm{~m}$ wide. assuming that the spacing of the $16-\mathrm{mm}$-diameter rods is increased to $225 \mathrm{~mm}$ on centers.

A concrete slab is reinforced by $16 -\mathrm{mm}$-diameter steel rods placed on $180-\mathrm{mm}$ centers as shown. The modulus of elasticity is $20 \mathrm{~GPa}$ for the concrete and $200 \mathrm{~GPa}$ for the steel. Using an allowable stress of $9 \mathrm{~MPa}$ for the concrete and $120 \mathrm{~MPa}$ for the steel, determine the largest allowable positive bending moment in a portion of the slab $1 \mathrm{~m}$ wide.

Solve the reinforced concrete beam shown is subjected to a positive bending moment of $175 \mathrm{~kN} \cdot \mathrm{m}$. Knowing that the modulus of elasticity is $25 \mathrm{~GPa}$ for the concrete and $200 \mathrm{~GPa}$ for the steel, determine (a) the stress in the steel, (b) the maximum stress in the concrete. assuming that the $450-\mathrm{mm}$ depth of the beam is increased to $500 \mathrm{~mm}$.

Solve earlier problem by assuming that the wide-flange beam is bent about the y axis by a couple of moment $M_y$.

For the composite bar indicated, determine the radius of curvature caused by the couple of moment $450\ \text{kip - in}$.

For the composite bar indicated, determine the radius of curvature caused by the couple of moment $450\ \text{kip - in}$.

The reinforced concrete beam shown is subjected to a positive bending moment of $175 \mathrm{~kN} \cdot \mathrm{m}$. Knowing that the modulus of elasticity is $25 \mathrm{~GPa}$ for the concrete and $200 \mathrm{~GPa}$ for the steel, determine (a) the stress in the steel, (b) the maximum stress in the concrete.

The $6 \times 12-\text{in}$. timber beam has been strengthened by bolting to it the steel reinforcement shown. The modulus of elasticity for wood is $1.8 \times 10^6 \mathrm{psi}$ and for steel $29 \times 10^6 \mathrm{psi}$. Knowing that the beam is bent about a horizontal axis by a couple of moment 450 kip. in., determine the maximum stress in (a) the wood, (b) the steel.

The $6 \times 12-\text{in}$. timber beam has been strengthened by bolting to it the steel reinforcement shown. The modulus of elasticity for wood is $1.8 \times 10^6 \mathrm{psi}$ and for steel $29 \times 10^6 \mathrm{psi}$. Knowing that the beam is bent about a horizontal axis by a couple of moment $450\ \text{kip. in.}$, determine the maximum stress in (a) the wood, (b) the steel.

For the composite bar indicated, determine the radius of curvature caused by the couple of moment $35 \mathrm{~N} \cdot \mathrm{m}$.

For the composite bar indicated, find the radius of curvature caused by the couple of moment $35 \mathrm{~N} \cdot \mathrm{m}$.