table a.3 Strength-Limited Design at Minimum Mass (Cost,
Energy, Environmental Impact)
Functions and Constraints
Maximize
Tie (tensile strut)
Stiffness, length specified; section area free
σ f /ρ
Shaft (loaded in torsion)
Load, length, shape specified, section area free
σ
ρ
f
2 3
Load, length, outer radius specified; wall thickness free
σ f /ρ
Load, length, wall thickness specified; outer radius free
σ ρ
f
1 2
Beam (loaded in bending)
Load, length, shape specified; section area free
σ
ρ
f
2 3
Load length, height specified; width free
σ f /ρ
Load, length, width specified; height free
σ ρ
f
1 2
Column (compression strut)
Load, length, shape specified; section area free
σ f /ρ
Panel (flat plate, loaded in bending)
Stiffness, length, width specified, thickness free
σ ρ
f
1 2
Plate (flat plate, compressed in-plane, buckling failure)
Collapse load, length and width specified, thickness free
σ ρ
f
1 2
Cylinder with internal pressure
Elastic distortion, pressure and radius specified; wall
thickness free
σ f /ρ
Spherical shell with internal pressure
Elastic distortion, pressure and radius specified, wall
thickness free
σ f /ρ
Flywheels, rotating disks
Maximum energy storage per unit volume; given velocity
ρ
Maximum energy storage per unit mass; no failure
σ f /ρ
table a.4 Strength-Limited Design: Springs, Hinges, Etc. for Maximum Performance
Functions and Constraints
Maximize
Springs
Maximum stored elastic energy per unit volume; no failure
σ f E
2
Maximum stored elastic energy per unit mass; no failure
σ
ρ
f E
2
Elastic hinges
Radius of bend to be minimized (max flexibility without failure)
σ f /E
Knife edges, pivots
Minimum contact area, maximum bearing load
σ f E
3
2 and H
Compression seals and gaskets
Maximum conformability; limit on contact pressure
σ f E
3 2
and 1/E
Diaphragms
Maximum deflection under specified pressure or force
σ f E
3 2
Rotating drums and centrifuges
Maximum angular velocity; radius fixed; wall thickness free
σ f /ρ