Internal Forces in Beams Examples

A cantilever extends $3.00\ \text{m}$ from a fixed wall and carries a $12.0\ \text{kN}$ downward force at the free end. Determine the internal shear and moment magnitudes at the wall section.

A $6.00\ \text{m}$ simply supported beam carries a $30.0\ \text{kN}$ downward load at midspan. Determine the support reactions, maximum shear magnitude, and maximum moment.

A $10.0\ \text{m}$ simply supported beam carries $w=5.00\ \text{kN/m}$ over the full span. Determine the maximum positive moment.

Over a $4.00\ \text{m}$ interval, a downward uniform load of $3.00\ \text{kN/m}$ acts. If the shear at the left end is $+8.00\ \text{kN}$, determine the shear at the right end.

The shear is a constant $+6.00\ \text{kN}$ over a $2.50\ \text{m}$ segment. If the moment at the segment start is $4.00\ \text{kN}\cdot\text{m}$, determine the moment at the end.

Immediately to the left of a $20.0\ \text{kN}$ downward point load, the shear is $+7.00\ \text{kN}$. Determine the shear immediately to the right.

A beam interval has $M(x)=20x-2x^2$ in $\text{kN}\cdot\text{m}$ for $0\le x\le8\ \text{m}$. Find the interior stationary point and compare it with the interval boundaries.

A beam has no concentrated transverse force at $x=2.00\ \text{m}$ but carries a concentrated applied couple of magnitude $10.0\ \text{kN}\cdot\text{m}$ there. What qualitative changes occur in the diagrams?

An $8.00\ \text{m}$ simply supported beam carries $w=6.00\ \text{kN/m}$ only from $x=2.00\ \text{m}$ to $x=6.00\ \text{m}$. Determine the reactions and the maximum positive bending moment.

Over $0\le x\le3.00\ \text{m}$, the downward load is $w(x)=kx$ with load gradient $k=2.00\ \text{kN/m}^2$. At $x=0$, $V(0)=9.00\ \text{kN}$ and $M(0)=0$. Determine $V(x)$ and $M(x)$.

A beam is supported at $A$ at $x=0$ and $B$ at $x=6.00\ \text{m}$, with an overhang to $x=8.00\ \text{m}$. A $10.0\ \text{kN}$ downward point load acts at the free end. Determine the reactions and the governing absolute bending moment.

Immediately to the left of a concentrated applied couple, the bending moment is $M^-=+12.0\ \text{kN}\cdot\text{m}$. Under the adopted diagram sign convention, the applied couple has signed magnitude $C=-7.00\ \text{kN}\cdot\text{m}$. Determine the moment immediately to the right.