Moments and Couples Examples

A $12.0\ \text{kN}$ downward force acts $2.50\ \text{m}$ to the right of point $O$. Find its moment about $O$ using counterclockwise positive.

A force is applied at $(x,y)=(3.00,1.50)\ \text{m}$ with components $F_x=8.00\ \text{kN}$ and $F_y=10.0\ \text{kN}$. Find the moment about the origin.

A $40.0\ \text{kN}$ brace force has a line of action passing exactly through joint $A$. Determine its moment about $A$.

Two opposite $5.00\ \text{kN}$ horizontal forces are separated vertically by $0.800\ \text{m}$. Determine the couple magnitude.

About point $O$, one force produces $+24.0\ \text{kN}\cdot\text{m}$ and another produces $-15.0\ \text{kN}\cdot\text{m}$. A $+6.00\ \text{kN}\cdot\text{m}$ applied couple also acts. Determine the resultant moment.

A $20.0\ \text{kN}$ downward force is applied $1.20\ \text{m}$ to the right of point $O$. Move the force to $O$ and determine the required couple.

A $10.0\ \text{kN}$ force at a balcony edge has components $F_x=6.00\ \text{kN}$ to the right and $F_y=8.00\ \text{kN}$ downward. The application point is $2.00\ \text{m}$ right and $0.500\ \text{m}$ above support $A$. Find $M_A$.

A beam has a $15.0\ \text{kN}$ downward force $4.00\ \text{m}$ from support $A$ and an applied $+20.0\ \text{kN}\cdot\text{m}$ counterclockwise couple. Determine the net moment about $A$.

A $32.0\ \text{kN}$ force has a line of action whose shortest distance from point $O$ is $1.40\ \text{m}$. Determine the moment magnitude about $O$.

A force is applied at $\vec{r}=(-2.00\,\hat{i}+1.50\,\hat{j})\ \text{m}$ and has components $\vec{F}=(6.00\,\hat{i}-10.0\,\hat{j})\ \text{kN}$. Determine the scalar moment about the origin.

A force $\vec{F}=(8.00\,\hat{i}+12.0\,\hat{j})\ \text{kN}$ acts at point $A=(1.20,-0.500)\ \text{m}$ relative to point $O$. Replace it by an equivalent force-couple system at $O$.