Deflection of Structures - Examples

A beam is fixed at $x=0$. State the geometric boundary conditions used in an elastic-curve solution.

A cantilever of length $L=3.0\text{ m}$ has $E=200\text{ GPa}$ and $I=60\times10^6\text{ mm}^4$. A downward tip load $P=20\text{ kN}$ acts at the free end. Find the tip deflection magnitude.

Using the data from Example 2, determine the tip rotation magnitude.

A simply supported beam has $L=6.0\text{ m}$, $E=200\text{ GPa}$, $I=120\times10^6\text{ mm}^4$, and a centered load $P=40\text{ kN}$. Determine the maximum deflection magnitude.

Between points $A$ and $B$, the $M/EI$ diagram is a rectangle of constant ordinate $0.002\text{ rad/m}$ over $4.0\text{ m}$. Find $\theta_B-\theta_A$.

A triangular $M/EI$ diagram from $A$ to $B$ has base $6.0\text{ m}$ and peak ordinate $0.003\text{ rad/m}$ at $B$. Find the tangential deviation of $B$ from the tangent at $A$.

State the conjugate support corresponding to a real cantilever's fixed end and free end.

For a target joint displacement, two truss members have $(N,n,L,AE)$ values: member 1 $(40\text{ kN},0.60,2.0\text{ m},200000\text{ kN})$ and member 2 $(-30\text{ kN},-0.40,3.0\text{ m},150000\text{ kN})$. Find the displacement contribution sum.

Over a $2.0\text{ m}$ segment, let $M=30\text{ kN}\cdot\text{m}$, $m=0.50\text{ m}$ for a unit-load system, and $EI=40000\text{ kN}\cdot\text{m}^2$. Find the displacement contribution.

The elastic strain energy of a one-degree system is $U=P^2/(2k)$. Use Castigliano's theorem to determine displacement in the direction of $P$.

A verified linear-elastic model gives displacement at coordinate $A$ from a unit load at $B$ as $2.4\text{ mm}$. What displacement should a unit load at $A$ produce at coordinate $B$?