Chapter $7$

Locate the $x-x$ and $Y-Y$ centroidal axes for the areas shown.

Problem $1$

Problem $2$

Chapter $8$

Calculate the moments of inertia with respect to both centroidal axes for the areas shown.

Problem $1$

Problem $2$

$q,$

Chapter $9$

Problem $1$

A bin weighing $8$ tons is supported by three steel tension rods. Each rod is $\frac{5}{8}in.$ in diameter. Assume that the rods support equal loads. Find the stress in the rods.

Problem$2$

A titanium alloy bar elongates $0\mathrm{.}500$ in $.$ when subjected to an axial tensile load of $100$ k $.$ The bar is $16$ ft long and has a cross$-$sectional area of $2\mathrm{.}25i{n}^2.$ Compute the modulus of elasticity E$.$ Use a proportional limit of $125$ ksi $.$

Chapter $10$

Problem $1$

An $18-$in$.-$long titanium alloy rod is subjected to a tensile load of $24,000lb.$ If the allowable tensile stress is $60$ ksi and the allowable total elongation is not to exceed $0\mathrm{.}05$ in $.,$ compute the required rod diameter. Assume the proportional limit to be $120$ ksi $.$

Problem $2$

Test results of a steel specimen indicated an ultimate tensile strength of $827$ MPa and a yield stress of $350$ MPa $.$ If the tensile allowable stress per design specifications is $210$ MPa $,$ compute the factor of safety based on

$($a$)$ yield stress

$($b$)$ tensile strength

Chapter $11$

Problem $1$

$11\mathrm{.}2$ A rectangular ASTM A$36$ steel bar $2$ in$.$ by $6$ in$.$ in cross section is subjected to an axial tensile load of $300,000lb.$ The proportional limit of the steel is $34,000.$ Compute the change in the transverse $6-in.$ dimension.

Problem $2$

$11\mathrm{.}4$ Modulus of elasticity, modulus of rigidity, and Poisson's ratio are interrelated.

$($a$)$ Calculate $G$ for $E=30,000,000$ psi and $=0\mathrm{.}30.$

$($b$)$ Calculate $$ for $E=16,000,000$ psi and $G=5,800,000.$