Projects Using CES EduPack - MAELabs UCSD

Notes for instructors: Project 9, Bicycle frames
This is a project that can be run at many different levels. The simplest is outlined
on the accompanying project sheet. It can be extended to include aspects of shape
and of trade-off between mass and cost.
Some points to bear in mind.
• The forks and cranks of a bike carry bending moments. The spokes and brake
cables carry tension. The tubular frame of a bike carries bending, torsion, and
axial loads – the bending moments are usually the most severe.
• The design-load must take account of impact – riding the bike off a curb, for
instance – when decelerations of 10G are possible. A lower limit of
15 MPa.m 1/2 on fracture toughness is essential.
• A mountain bike is strength-limited, but stiffness is important too – a bike
that is too stiff gives a harsh ride. In bikes for sprint events, stiffness can be
the most important consideration – excessive flexing of the frame dissipates
energy. Stiffness and strength are constraints, not objectives (they must meet
specified values). Objectives, usually, are mass and cost (for these a
minimum is sought).
• The books by Sharp and by Witt and Wilson are good on bike mechanics.
Oliver is good on materials.
• Typical specification for the forks of a cheap street bike. The fork is modeled
as a tube loaded in bending.
Function • Forks – a hollow tube loaded in compression
Constraints • Strength specified
• Fracture toughness > 15 MPa.m 1/2
Objective • Minimize cost
Free variables • Tube wall thickness
• Choice of material
The selection is made by using the appropriate Material Index. That for a tube of
specified bending strength and minimum cost is
Cm
ρ
M 1 =
σ y
if the outer diameter of the tube is fixed and the wall thickness is the free variable.
A Graph stage of elastic limit σ y against material cost per unit volume C m ρ
(where ρ is the density), with a K1c
> 15 MPa.m 1/2 imposed using a Limit stage
allows materials with low values of M1 to be found. The selection using the
Level 1 database gives steels and cast iron. Cast iron cannot be drawn to thinwalled
tube. It is eliminated if a further constraint on elongation > 40% is added,
but common sense is probably enough to suggest that steel is the best choice.
• Typical specification for the forks of a high-performance mountain bike. The
fork is modeled as a tube loaded in bending.
Function • Forks – a hollow tube loaded in compression
Constraints • Strength specified
• Fracture toughness > 15 MPa.m 1/2
Objective • Minimize mass
Free variables • Tube wall thickness
• Choice of material
The selection is made by using the appropriate Material Index. That for a tube of
specified bending strength and minimum mass is
M 2
ρ
=
σ y
if the tube diameter of the tube is fixed and the wall thickness is free. A Graph
stage of elastic limit σ y against material density ρ , with a K1c > 15 MPa.m 1/2
imposed allows materials with low values of M2 to be found. The selection using
the Level 1 database gives CFRP, Magnesium alloys, and Titanium alloys.
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