Drawing

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E6
Analyzing the Stress on the Trebuchet Axle continued
For an axle with a given radius, and material: The greater the force P, and the span L, the more
likely it is that the axle will fail. Conversely, if the span L is decreased, the axle will support
greater loads.
In order to ensure that the axle will not deform (bend) beyond its yield point, it must be
designed with an adequate cross section and material strength. The maximum load or stress that
a beam or axle can support without suffering permanent deformation is called the maximum
allowed stress. A reasonable value for the maximum allowed stress can be calculated using the
simplified flexural formula show below.
The “Flexural formula” can be employed to calculate the:
)1. Required material strength. ( S
max
2. Required axle radius. ( r )
3. Required axle span. ( L )
Flexural Formula
For an axle with a given circular cross-section, the yield strength or maximum allowed stress S is:
max
3
max
r
L
P)
1
(S 
S
Where:
P = Load (Force) on the center of the axle
L = Span (Distance between the supports)
r = Radius of the axle
Using the Flexural Formula
Assume you are designing a model trebuchet with the following parameters:
SI Units Imperial Units
m
Counterweight Mass 1000g 2.2lbs
1
m Projectile Mass 20g 0.022lbs
2
mb Beam Mass 100g 0.22lbs
L Counterweight Arm Length 10cm 0.33ft
1
L Throwing Arm Length 45.5cm 1.50ft
2
L Sling Length 37.5cm 1.23ft
3
L Counterweight Pivot Arm 10cm 0.328ft
4
L Axle Height 25cm 0.82ft
5
Axle Radius ( r ) 0.3cm 0.0098ft (0.118in)
Axle Span ( L ) 10cm 0.328ft (3.94in)
Axle Material 304 Steel Yield Strength 205 MPa 30,000psi
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