1. Engineering Mechanics

Mechanics Of Materials — Quiz

Test your understanding of mechanics of materials with 5 practice questions.

Practice Questions

Question 1

A prismatic steel bar of length \$L=2\,$\mathrm{m}$\$, cross-sectional area \$A=$5\times10^{-4}$\,$\mathrm{m^2}$\$, and Young’s modulus \$E=200\,$\mathrm{GPa}$\$ is subjected to a tensile load \$P=50\,$\mathrm{kN}$\$. Using the formula \$U=$\dfrac{P^2L}{2AE}$\$, what is the strain energy \$U\$ stored in the bar?

Question 2

A cantilever beam with length \$L=2\,$\mathrm{m}$\$, moment of inertia \$I=$1\times10^{-6}$\,$\mathrm{m^4}$\$, and Young’s modulus \$E=210\,$\mathrm{GPa}$\$ carries a concentrated load \$P=1000\,$\mathrm{N}$\$ at its free end. Using Castigliano’s theorem, the deflection at the free end is \$$\delta$=$\frac{PL^3}{3EI}$\$. What is \$$\delta$\$?

Question 3

A column of length \$L=3\,$\mathrm{m}$\$ with flexural rigidity \$EI=9000\,$\mathrm{N\cdot m^2}$\$ is fixed at one end and free at the other. Taking the effective length factor as \$K=2\$, what is the Euler critical buckling load \$P_{cr} = $\pi^2$EI/(K L)^2\$?

Question 4

A prismatic beam of length \$L=2\,$\mathrm{m}$\$, modulus \$E=200\,$\mathrm{GPa}$\$, and moment of inertia \$I=$4\times10^{-6}$\,$\mathrm{m^4}$\$ is subjected to a constant bending moment \$M=500\,$\mathrm{N\cdot m}$\$. Using the strain energy formula \$U=$\dfrac{M^2L}{2EI}$\$, what is \$U\$?

Question 5

For a column with effective length \$L_e=3\,$\mathrm{m}$\$, second moment of area \$I=$8\times10^{-6}$\,$\mathrm{m^4}$\$, and cross-sectional area \$A=$4\times10^{-4}$\,$\mathrm{m^2}$\$, the slenderness ratio is defined as \$$\lambda$=$\dfrac{L_e}{r}$\$ where \$r=$\sqrt{I/A}$\$. What is \$$\lambda$\$?