Currently, the formula I am using to calculate the rotational torque applied onto an axis is $T = Fr\sin \theta$, where $T$ is the torque (in $\mathrm{N\ m}$), $F$ is the force acting, $r$ is the distance between the point on the object at which the force is acting and the centre of rotation (the pivot point), and $\theta$ is angle between $F$ and $r$. However, this assumes the force is being applied on a single point.

Is there a formula or method to calculate the torque applied when the force is applied uniformly across the entire object? For example, if a gate of length $200\ \mathrm{cm}$ has a force of $200\ \mathrm{N}$ applied uniformly across it, what would be the torque experienced?