Getting the loads right

This is a static copy of the chapter for search engines. The interactive version has animated figures, check questions, and buttons that load the example into the calculator.

Nothing else in the calculation matters if the loads are wrong. For a shaft, the loads come from whatever is mounted on it, and each component has its own rules.

Start from power and speed

T = Pω = 9550 · P [kW]n [rpm] [N·m]

That is the torque the shaft has to carry between the input and the output. ShaftLab shows it in panel 01 as a reminder, but it never assumes it — you tell each element how much torque it puts in or takes out, and the tool checks that the total balances to zero.

Gears

A spur gear puts two forces into a shaft, not one. The tangential force carries the torque; the radial force does nothing useful and bends the shaft anyway. A helical gear adds a third.

F_t = 2Td F_r = F_t·tan αcos β F_a = F_t·tan β

d is the pitch diameter, α the pressure angle (20° unless you know otherwise) and β the helix angle (0 for a spur gear). Two things people forget:

The radial force is not small. At α = 20° it is 36 % of the tangential force, it does no useful work, and it bends the shaft just as hard.
A helical gear’s axial force also bends the shaft. It acts at radius d/2, so it applies a concentrated couple F_a·d/2 at the gear station. On a big-diameter gear that couple can dominate.

Belts and chains

A belt drive loads the shaft with the sum of the two strand tensions, not the difference. The difference is what transmits the torque; the sum is what the bearings feel:

F_t = 2Td F_shaft = c · F_t

Drive	typical c	why
chain / toothed belt	1.1 – 1.3	almost no pretension needed
V-belt	1.8 – 2.5	needs pretension to grip
flat belt	2.5 – 3.5	needs a lot of pretension

This is why swapping a chain drive for a V-belt on an existing shaft is not a neutral change.

Direction matters — use two planes

A gear at the top of the shaft and a gear at the side load it in different directions. You cannot add their bending moments arithmetically. Resolve everything into two perpendicular planes, solve each as an ordinary beam, and combine at the end:

M(x) = √( M_y(x)² + M_z(x)² )

In ShaftLab the angle φ does this for you: 0° points up (+y), 90° points towards the viewer (+z).

💡 If two elements are 90° apart, the resultant moment is much smaller than the sum — sometimes you can halve the bending on a shaft simply by choosing where the driven machine sits.

Example

A motor shaft with an overhung V-belt pulley. Notice how the overhang, not the span, decides the bending moment — and what the belt pull factor does to it.