A uniform $6.00\text{ m}$ beam weighs $500\text{ N}$. It is supported at $x=0$ and $x=5.00\text{ m}$. A $200\text{ N}$ person stands at $x=2.00\text{ m}$. Determine the two vertical support reactions.

Enlarge

A uniform $10.0\text{ kg}$ ladder rests at $60.0^\circ$ above a rough floor against a smooth vertical wall. Determine the minimum coefficient of static friction required for equilibrium using $g=9.80\text{ m/s}^2$.

Enlarge

Masses of $2.00\text{ kg}$, $3.00\text{ kg}$, and $5.00\text{ kg}$ are located on the $x$-axis at $0$, $2.00\text{ m}$, and $6.00\text{ m}$, respectively. Determine $x_{cm}$.

A member carries an axial tensile force of $80.0\text{ kN}$ over a cross-sectional area of $400\text{ mm}^2$. Determine the average normal stress.

A $2.00\text{ m}$ long bar experiences tensile stress $150\text{ MPa}$ while remaining linear elastic. Its Young's modulus is $200\text{ GPa}$. Determine strain and elongation.

A tensile member must carry $120\text{ kN}$ while keeping normal stress at or below $160\text{ MPa}$. Determine the minimum required area.

A material is subjected to shear stress $60.0\text{ MPa}$ and has shear modulus $G=75.0\text{ GPa}$. Determine the shear strain.

A liquid-like compressible specimen with bulk modulus $B=2.20\text{ GPa}$ experiences a hydrostatic pressure increase of $5.00\text{ MPa}$. Determine the fractional volume change.

A $6.00\text{ m}$ bar has coefficient of linear expansion $\alpha=12.0\times10^{-6}/^\circ\text{C}$ and is heated by $40.0^\circ\text{C}$ while free to expand. Determine the thermal elongation.

The same material has $E=200\text{ GPa}$, $\alpha=12.0\times10^{-6}/^\circ\text{C}$, and temperature increase $40.0^\circ\text{C}$. If axial expansion is fully restrained, determine the stress magnitude.

An idealized bilinear material has $E=200\text{ GPa}$, modeled yield stress $\sigma_y=250\text{ MPa}$, and post-yield tangent modulus $E_t=4.00\text{ GPa}$. Determine the strain at an applied stress of $330\text{ MPa}$.