Simple Strain and Deformation — Worked Examples

A $2.00\text{ m}$ gauge length elongates by $2.00\text{ mm}$. Determine the average normal strain.

A steel bar is subjected to $120\text{ MPa}$ tensile stress. Take $E=200\text{ GPa}$ and $L=1.50\text{ m}$. Determine the strain and elongation.

A steel bar carries $80\text{ kN}$ in tension. Its length is $3.00\text{ m}$, area is $500\text{ mm}^2$, and $E=200\text{ GPa}$. Determine the elongation.

A two-segment steel bar carries the same tensile force $P=60\text{ kN}$ through both segments. Segment 1 has $L_1=1.0\text{ m}$ and $A_1=400\text{ mm}^2$; Segment 2 has $L_2=1.5\text{ m}$ and $A_2=600\text{ mm}^2$. Take $E=200\text{ GPa}$. Find the total elongation.

A $50\text{ mm}$ diameter steel bar is in uniaxial tension at $100\text{ MPa}$. Take $E=200\text{ GPa}$ and $\nu=0.30$. Determine the change in diameter.

For an isotropic linear-elastic material, $E=200\text{ GPa}$ and $\nu=0.30$. Determine $G$.

For the same material with $E=200\text{ GPa}$ and $\nu=0.30$, determine $K$.

An aluminum bar with $A=800\text{ mm}^2$, $L=1.20\text{ m}$, and $E=70\text{ GPa}$ carries a $56\text{ kN}$ compressive force. Determine its axial deformation using tension-positive signs.

A prismatic elastic bar carries a fixed axial load with fixed $L$ and $E$. Its cross-sectional area is doubled. Determine the ratio of new deformation to original deformation.

A rigid plate is supported by a steel bar and an aluminum bar of equal length. The steel bar has $A_s=400\text{ mm}^2$, $E_s=200\text{ GPa}$; the aluminum bar has $A_a=600\text{ mm}^2$, $E_a=70\text{ GPa}$. A centered load of $100\text{ kN}$ causes the plate to translate without rotation. Determine the force carried by each bar.