Rock-Bolt Torque-Tension Curve Explorer (2D)

Bolt & Anchor

Bolt diameter 20 mm

Anchor / rock quality

Turning speed 1.0×

Target torque 420 Nm

Install

Live readout

Turn angle

0.0 turns

Torque

0 Nm

Clamping force

0 kN

Status

Idle

Bolts installed

Bolts stripped

Elastic tensioning — safe window Yielding — thread starting to slip Stripped / over-torqued — bolt failed

How the curve is built

The 3D Robotic Bolter animates a twin-boom rig drilling and driving rock bolts against a target torque, but never shows what is happening inside the joint while the wrench turns. This 2D companion strips the rig away and plots the actual torque-vs-turning-angle curve for a single resin-anchored bolt, the same curve a real torque wrench trace would show.

Thread engagement (θ < θ0):  T ≈ 0.15·θ  (free spin, no clamp yet)
Elastic tensioning:           T = k·(θ − θ0)   [k set by rock/resin stiffness]
Yield onset at F ≥ Fy:        slope drops to 0.12·k (plastic stretch)
Over-torque at F ≥ Fu:        thread strips → T collapses to ~0

Clamping force:  F = T / (K · d)   [K = 0.2 nut-factor, d = bolt diameter]

Bolt diameter — a fatter shank carries more force per Newton-metre of torque (F = T / (K·d)), and its thread also yields at a higher torque.
Anchor / rock quality — a fully cured resin anchor in hard rock is stiff: torque rises fast with a small turn. Weak, uncured resin in soft rock is compliant: the same torque needs many more turns, and the safe window is wider but the bolt is more likely to spin without ever clamping.
Turning speed — only changes how fast the animation plays; the torque-angle curve itself is rate-independent.
Target torque — the value the rig's controller is told to stop at. Land inside the green band for a good install; overshoot past the yield knee and the thread strips.

This is the real bolted-joint torque-tension relationship used to spec every rock bolt, structural fastener and lug nut: torque only ever tells you the clamping force indirectly, through a stiffness that depends on the anchor you turned it into.

Rock / resin anchor Bolt shank Wrench head

Bolt cross-section

Idle

Torque vs. turn angle