Deflection of Beams — Worked Examples

A simply supported beam has $L=6.0\text{ m}$, $P=20\text{ kN}$ at midspan, $E=200\text{ GPa}$, and $I=120\times10^6\text{ mm}^4$. Determine the maximum deflection.

A simply supported beam has $L=5.0\text{ m}$, $w=8.0\text{ kN/m}$, $E=200\text{ GPa}$, and $I=100\times10^6\text{ mm}^4$. Determine the maximum deflection.

A cantilever has $L=3.0\text{ m}$, $P=10\text{ kN}$, $E=200\text{ GPa}$, and $I=60\times10^6\text{ mm}^4$. Determine free-end deflection magnitude.

Use the same cantilever stiffness as Example 3, but apply $w=4.0\text{ kN/m}$ over the full $3.0\text{ m}$ span. Determine free-end deflection magnitude.

A $5.0\text{ m}$ simply supported beam has $E=200\text{ GPa}$ and $I=100\times10^6\text{ mm}^4$. It carries a central $10\text{ kN}$ point load and a full-span UDL of $4.0\text{ kN/m}$. Determine midspan deflection.

A cantilever of length $L$ is fixed at $x=0$ and carries a downward point load $P$ at $x=L$. Derive its free-end deflection.

Use the moment-area method for a cantilever with end load $P$ and length $L$. Determine the free-end slope magnitude and tangential deviation.

A beam remains in the same linear-elastic load case, but its moment of inertia is doubled while $E$, load, and span are unchanged. Determine the deflection ratio.

A simply supported beam with a central point load has fixed $P$, $E$, and $I$. The span doubles. How does maximum deflection change?

A simply supported beam carries a central point load and a full-span UDL. Verified standard elastic formulas are available for both, and only the maximum midspan deflection is required. Which method is most efficient?

A simply supported beam and loading are perfectly symmetric about midspan. What is the slope at the center of the span?