Force Systems Examples

Three roof cables meet at one pin connection and pull in different directions. Classify the planar force system.

A $60.0\ \text{kN}$ force acts $40.0^\circ$ above the positive $x$-axis. Determine its components.

A $25.0\ \text{kN}$ force acts $30.0^\circ$ above the negative $x$-axis. Determine its signed components.

Forces at a joint have components $(30,0)$, $(-10,20)$, and $(0,-5)$ kN. Determine the resultant.

A concurrent force system has resultant $R=42.0\ \text{kN}$ acting at $25.0^\circ$ above the positive $x$-axis. Determine the equilibrant.

A beam carries a uniform load of $8.00\ \text{kN/m}$ over $6.00\ \text{m}$. Replace it with an equivalent concentrated load.

A load varies linearly from zero to $12.0\ \text{kN/m}$ over $4.00\ \text{m}$. Determine its equivalent force and location measured from the zero-intensity end.

A designer replaces a $10.0\ \text{kN/m}$ uniform load over $5.00\ \text{m}$ by a $50.0\ \text{kN}$ point load placed $1.00\ \text{m}$ from the left end. Is the replacement statically equivalent?

At a roof connection, one force is $40.0\ \text{kN}$ at $30.0^\circ$ and another is $25.0\ \text{kN}$ at $140^\circ$, with both angles measured counterclockwise from the positive $x$-axis. Determine the resultant magnitude and direction.

A distributed load varies linearly from $6.00\ \text{kN/m}$ at the left end to $14.0\ \text{kN/m}$ at the right end over $4.00\ \text{m}$. Determine the equivalent force and its location from the left end.

A concurrent system has resultant components $R_x=-18.0\ \text{kN}$ and $R_y=+24.0\ \text{kN}$. Determine the equilibrant in component and polar form.