Do I have to use fork terminals on stranded wire under a screw?
There is no code section that says use a fork terminal. What the code says is that the termination has to be made in a way the device is listed for, and that is where stranded conductor gets complicated.
The controlling sections
Section 110.14(A) of the 2023 NEC covers terminals. Connection of conductors to terminal parts shall ensure a thoroughly good connection without damaging the conductors and shall be made by means of pressure connectors including set screw type, solder lugs, or splices to flexible leads. It also states that connection by means of wire binding screws or studs and nuts that have upturned lugs or the equivalent shall be permitted for 10 AWG or smaller conductors. Terminals for more than one conductor and terminals used to connect aluminum shall be so identified.
Section 110.3(B) then requires listed equipment to be installed and used in accordance with the instructions included in the listing or labeling. If a receptacle is marked for solid conductor only, landing stranded under the screw violates 110.3(B) even though 110.14(A) permits binding screws in general.
Reading the device
Most standard residential devices are listed for 14 through 10 AWG copper, solid or stranded, under the binding head screw. The restriction that trips people up is the push in hole, not the screw. Some specification grade and industrial devices, and many equipment terminal blocks, carry a marking such as solid only or stranded only. Look at the yoke and the back of the device before you decide.
Where a device screw is listed for stranded, wrapping the strands clockwise around the screw and tightening to the marked torque is compliant. Section 110.14(D) requires terminations to be torqued to the value provided by the manufacturer using a calibrated tool where a torque value is indicated. That section became mandatory in the 2017 cycle and inspectors do check for a torque tool on the job.
When to use a fork or ring terminal
Use one when the device is not listed for stranded, when the equipment terminal is a stud rather than a binding screw, when strand escape is likely on a control panel with vibration, or when the manufacturer instructions call for it. The terminal itself must be a listed pressure connector applied with the matching crimp tool. A ferrule serves a similar purpose on terminal blocks and is listed for that use. What is never acceptable is tinning the conductor with solder to hold the strands together. Section 110.14(A) does not recognize solder as the mechanical means of a terminal connection, and solder creep under a screw causes long term loosening.
Field takeaway
No fork terminal is required by code. Check the device marking, use a listed fork or ferrule where the device is not listed for stranded or where the instructions call for it, torque to the marked value, and never solder the strands.