Specific modulus

Template:Short description Specific modulus is a materials property consisting of the elastic modulus per mass density of a material. It is also known as the stiffness to weight ratio or specific stiffness. High specific modulus materials find wide application in aerospace applications where minimum structural weight is required. The dimensional analysis yields units of distance squared per time squared. The equation can be written as:

$\text{specific modulus}=E/\rho$

where $E$ is the elastic modulus and $\rho$ is the density.

The utility of specific modulus is to find materials which will produce structures with minimum weight, when the primary design limitation is deflection or physical deformation, rather than load at breaking—this is also known as a "stiffness-driven" structure. Many common structures are stiffness-driven over much of their use, such as airplane wings, bridges, masts, and bicycle frames.

To emphasize the point, consider the issue of choosing a material for building an airplane. Aluminum seems obvious because it is "lighter" than steel, but steel is stronger than aluminum, so one could imagine using thinner steel components to save weight without sacrificing (tensile) strength. The problem with this idea is that there would be a significant sacrifice of stiffness, allowing, e.g., wings to flex unacceptably. Because it is stiffness, not tensile strength, that drives this kind of decision for airplanes, we say that they are stiffness-driven.

The connection details of such structures may be more sensitive to strength (rather than stiffness) issues due to effects of stress risers.

Specific modulus is not to be confused with specific strength, a term that compares strength to density.

Applications

Specific stiffness in tension

The use of specific stiffness in tension applications is straightforward. Both stiffness in tension and total mass for a given length are directly proportional to cross-sectional area. Thus performance of a beam in tension will depend on Young's modulus divided by density.

Specific stiffness in buckling and bending

Specific stiffness can be used in the design of beams subject to bending or Euler buckling, since bending and buckling are stiffness-driven. However, the role that density plays changes depending on the problem's constraints.

Beam with fixed dimensions; goal is weight reduction

Examining the formulas for buckling and deflection, we see that the force required to achieve a given deflection or to achieve buckling depends directly on Young's modulus.

Examining the density formula, we see that the mass of a beam depends directly on the density.

Thus if a beam's cross-sectional dimensions are constrained and weight reduction is the primary goal, performance of the beam will depend on Young's modulus divided by density.

Beam with fixed weight; goal is increased stiffness

By contrast, if a beam's weight is fixed, its cross-sectional dimensions are unconstrained, and increased stiffness is the primary goal, the performance of the beam will depend on Young's modulus divided by either density squared or cubed. This is because a beam's overall stiffness, and thus its resistance to Euler buckling when subjected to an axial load and to deflection when subjected to a bending moment, is directly proportional to both the Young's modulus of the beam's material and the second moment of area (area moment of inertia) of the beam.

Comparing the list of area moments of inertia with formulas for area gives the appropriate relationship for beams of various configurations.

Beam's cross-sectional area increases in two dimensions

Consider a beam whose cross-sectional area increases in two dimensions, e.g. a solid round beam or a solid square beam.

By combining the area and density formulas, we can see that the radius of this beam will vary with approximately the inverse of the square of the density for a given mass.

By examining the formulas for area moment of inertia, we can see that the stiffness of this beam will vary approximately as the fourth power of the radius.

Thus the second moment of area will vary approximately as the inverse of the density squared, and performance of the beam will depend on Young's modulus divided by density squared.

Beam's cross-sectional area increases in one dimension

Consider a beam whose cross-sectional area increases in one dimension, e.g. a thin-walled round beam or a rectangular beam whose height but not width is varied.

By combining the area and density formulas, we can see that the radius or height of this beam will vary with approximately the inverse of the density for a given mass.

By examining the formulas for area moment of inertia, we can see that the stiffness of this beam will vary approximately as the third power of the radius or height.

Thus the second moment of area will vary approximately as the inverse of the cube of the density, and performance of the beam will depend on Young's modulus divided by density cubed.

However, caution must be exercised in using this metric. Thin-walled beams are ultimately limited by local buckling and lateral-torsional buckling. These buckling modes depend on material properties other than stiffness and density, so the stiffness-over-density-cubed metric is at best a starting point for analysis. For example, most wood species score better than most metals on this metric, but many metals can be formed into useful beams with much thinner walls than could be achieved with wood, given wood's greater vulnerability to local buckling. The performance of thin-walled beams can also be greatly modified by relatively minor variations in geometry such as flanges and stiffeners.

Stiffness versus strength in bending

Note that the ultimate strength of a beam in bending depends on the ultimate strength of its material and its section modulus, not its stiffness and second moment of area. Its deflection, however, and thus its resistance to Euler buckling, will depend on these two latter values.

Approximate specific stiffness for various materials

Specific stiffness of the full range of materials

Specific stiffness of materials within the range 0.9–5.0Template:Nbspg/cm³ density and 10–1300Template:NbspGPa stiffness

Approximate specific stiffness for various materials. No attempt is made to correct for materials whose stiffness varies with their density.

Material	Young's modulus (GPa)	Density (g/cm3)	Young's modulus per density; specific stiffness (106 m2s−2)	Young's modulus per density squared (103 m5kg−1s−2)	Young's modulus per density cubed (m8kg−2s−2)	Reference
Latex foam, low density, 10% compression	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Reversible Assembled Cellular Composite Materials	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Self Reprogrammable Mechanical Metamaterials	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Latex foam, low density, 40% compression	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Latex foam, high density, 10% compression	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Latex foam, high density, 40% compression	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Silica aerogel, medium density	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Rubber (small strain)	Template:Nts±0.045	Template:Nts±0.145	Template:Nts±0.051	Template:Nts±0.05655	Template:Nts±0.0621
Expanded polystrene (EPS) foam, low density (1Template:Nbsplb/ft3)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Silica aerogel, high density	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Expanded polystrene (EPS) foam, medium density (3Template:Nbsplb/ft3)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Low-density polyethylene	Template:Nts	Template:Nts±0.015	Template:Nts±0.005	Template:Nts±0.005	Template:Nts±0.015
PTFE (Teflon)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Duocel aluminum foam, 8% density	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Extruded polystrene (XPS) foam, medium density (Foamular 400)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Extruded polystrene (XPS) foam, high density (Foamular 1000)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
HDPE	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Duocel copper foam, 8% density	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Polypropylene	Template:Nts±0.3	Template:Nts	Template:Nts±0.33	Template:Nts±0.37	Template:Nts±0.41
Polyethylene terephthalate	Template:Nts±0.35	Template:Nts±0.0425	Template:Nts±0.3	Template:Nts±0.23	Template:Nts±0.225
Nylon	Template:Nts±1.0	Template:Nts	Template:Nts±0.9	Template:Nts±0.75	Template:Nts±0.65
Polystyrene	Template:Nts±0.25	Template:Nts	Template:Nts±0.2	Template:Nts±0.25	Template:Nts±0.2
Biaxially-oriented Polypropylene	Template:Nts±1.0	Template:Nts	Template:Nts±1.11	Template:Nts±1.23	Template:Nts±1.37
Medium-density fibreboard	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Titanium foam, low density	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Titanium foam, high density	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Foam glass	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Copper (Cu)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Brass and bronze	Template:Nts±12.5	Template:Nts±0.165	Template:Nts±2.0	Template:Nts±0.25	Template:Nts±0.03
Zinc (Zn)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Oak wood (along grain)	Template:Nts	Template:Nts±0.17	Template:Nts±3.5	Template:Nts±9.5	Template:Nts±20.0
Concrete (under compression)	Template:Nts±10	Template:Nts	Template:Nts±4	Template:Nts±1.75	Template:Nts±0.7
Glass-reinforced plastic	Template:Nts±14.45	Template:Nts	Template:Nts±8	Template:Nts±4.35	Template:Nts±2.5
Pine wood	Template:Nts	Template:Nts±0.155	Template:Nts±6	Template:Nts±26	Template:Nts±89
Balsa, low density (4.4 lb/ft3)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Tungsten (W)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Sitka spruce green	Template:Nts±0.7	Template:Nts	Template:Nts±2	Template:Nts±5	Template:Nts±13
Osmium (Os)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Balsa, medium density (10 lb/ft3)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Steel	Template:Nts	Template:Nts±0.15	Template:Nts±0.5	Template:Nts±0.1	Template:Nts±0.02
Titanium alloys	Template:Nts±7.5	Template:Nts	Template:Nts±2	Template:Nts±0.35	Template:Nts±0.08
Balsa, high density (16 lb/ft3)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Wrought iron	Template:Nts±10	Template:Nts±0.2	Template:Nts±2	Template:Nts±0.35	Template:Nts±0.055
Magnesium metal (Mg)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Sitka spruce dry	Template:Nts±0.8	Template:Nts	Template:Nts±2	Template:Nts±5	Template:Nts±12
Macor machineable glass-ceramic	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Cordierite	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Glass	Template:Nts±20	Template:Nts±0.2	Template:Nts±10	Template:Nts±4.8	Template:Nts±2.1
Tooth enamel (largely calcium phosphate)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
E-Glass fiber	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Molybdenum (Mo)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Basalt fiber	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Zirconia	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Tungsten carbide (WC)	Template:Nts±100	Template:Nts	Template:Nts±6.5	Template:Nts±0.4	Template:Nts±0.025
S-Glass fiber	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Flax fiber	Template:Nts±34	Template:Nts±0.15	Template:Nts±29.35	Template:Nts±25	Template:Nts±21
single-crystal Yttrium iron garnet (YIG)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Kevlar 29 (tensile only)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Steatite L-5	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Mullite	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Dyneema SK25 Ultra-high-molecular-weight polyethylene (tensile only)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Beryllium, 30% porosity	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Kevlar 49 (tensile only)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Silicon	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Alumina fiber (Al2O3)	Template:Nts	Template:Nts±0.315	Template:Nts±7	Template:Nts±4	Template:Nts±1.74
Syalon 501 Silicon nitride	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Sapphire	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Alumina	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Carbon fiber reinforced plastic (70:30 fibre:matrix, unidirectional, along grain)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Dyneema SK78/Honeywell Spectra 2000 UHMWPE (tensile only)	Template:Nts±11	Template:Nts	Template:Nts±11	Template:Nts±12	Template:Nts±12
Silicon carbide (SiC)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Beryllium (Be)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Boron fiber	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Boron nitride	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Diamond (C)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Dupont E130 carbon fiber	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts

Approximate specific stiffness for various species of wood

Material	Young's modulus (GPa)	Density (g/cm3)	Young's modulus per density; specific stiffness (106 m2s−2)	Young's modulus per density squared (103 m5kg−1s−2)	Young's modulus per density cubed (m8kg−2s−2)
Applewood or wild apple (Pyrus malus)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Ash, black (Fraxinus nigra)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Ash, blue (quadrangulata)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Ash, green (Fraxinus pennsylvanica lanceolata)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Ash, white (Fraxinus americana)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Aspen (Populus tremuloides)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Aspen, large tooth (Populus grandidentata)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Basswood (Tilia glabra or Tilia americanus)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Beech (Fagus grandifolia or Fagus americana)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Beech, blue (Carpinus caroliniana)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Birch, gray (Betula populifolia)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Birch, paper (Betula papyrifera)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Birch, sweet (Betula lenta)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Buckeye, yellow (Aesculus octandra)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Butternut (Juglans cinerea)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Cedar, eastern red (Juniperus virginiana)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Cedar, northern white (Thuja occidentalis)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Cedar, southern white (Chamaecyparis thvoides)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Cedar, western red (Thuja plicata)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Cherry, black (Prunus serotina)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Cherry, wild red (Prunus pennsylvanica)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Chestnut (Castanea dentata)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Cottonwood, eastern (Populus deltoides)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Cypress, southern (Taxodium distichum)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Dogwood (flowering) (Cornus Florida)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Douglas fir (coast type) (Pseudotsuga taxifolia)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Douglas fir (mountain type) (Pseudotsuga taxifolia)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Ebony, Andaman marble-wood (India) (Diospyros kursii)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Ebony, Ebè marbre (Mauritius, E. Africa) (Diospyros melanida)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Elm, American (Ulmus americana)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Elm, rock (Ulmus racemosa or Ulmus thomasi)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Elm, slippery (Ulmus fulva or pubescens)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Eucalyptus, Karri (W. Australia) (Eucalyptus diversicolor)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Eucalyptus, Mahogany (New South Wales) (Eucalyptus hemilampra)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Eucalyptus, West Australian mahogany (Eucalyptus marginata)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Fir, balsam (Abies balsamea)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Fir, silver (Abies amabilis)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Gum, black (Nyssa sylvatica)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Gum, blue (Eucalyptus globulus)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Gum, red (Liquidambar styraciflua)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Gum, tupelo (Nyssa aquatica)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Hemlock eastern (Tsuga canadensis)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Hemlock, mountain (Tsuga martensiana)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Hemlock, western (Tsuga heterophylla)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Hickory, bigleaf shagbark (Hicoria laciniosa)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Hickory, mockernut (Hicoria alba)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Hickory, pignut (Hicoria glabra)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Hickory, shagbark (Hicoria ovata)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Hornbeam (Ostrya virginiana)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Ironwood, black (Rhamnidium ferreum)	Template:Nts	Template:Nts	Template:Nts±1.64	Template:Nts±2.78	Template:Nts±3.56
Larch, western (Larix occidentalis)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Locust, black or yellow (Robinia pseudacacia)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Locust honey (Gleditsia triacanthos)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Magnolia, cucumber (Magnolia acuminata)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Mahogany (W. Africa) (Khaya ivorensis)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Mahogany (E. India) (Swietenia macrophylla)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Mahogany (E. India) (Swietenia mahogani)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Maple, black (Acer nigrum)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Maple, red (Acer rubrum)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Maple, silver (Acer saccharinum)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Maple, sugar (Acer saccharum)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Oak, black (Quercus velutina)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Oak, bur (Quercus macrocarpa)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Oak, canyon live (Quercus chrysolepis)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Oak, laurel (Quercus Montana)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Oak, live (Quercus virginiana)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Oak, post (Quercus stellata or Quercus minor)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Oak, red (Quercus borealis)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Oak, swamp chestnut (Quercus Montana (Quercus prinus))	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Oak swamp white (Quercus bicolor or Quercus platanoides)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Oak, white (Quercus alba)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Paulownia (P. tomentosa)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Persimmon (Diospyros virginiana)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Pine, eastern white (Pinus strobus)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Pine, jack (Pinus banksiana or Pinus divericata)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Pine, loblolly (Pinus taeda)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Pine, longleaf (Pinus palustris)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Pine, pitch (Pinus rigida)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Pine, red (Pinus resinosa)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Pine, shortleaf (Pinus echinata)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Poplar, balsam (Populus balsamifera or Populus candicans)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Poplar, yellow (Liriodendron tulipifera)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Redwood (Sequoia sempervirens)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Sassafras (Sassafras uariafolium)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Satinwood (Ceylon) (Chloroxylon swietenia)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Sourwood (Oxydendrum arboreum)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Spruce, black (Picea mariana)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Spruce, red (Picea rubra or Picea rubens)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Spruce, white (Picea glauca)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Sycamore (Platanus occidentalis)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Tamarack (Larix laricina or Larix americana)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Teak (India) (Tectona grandis)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Walnut, black (Juglans nigra)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Willow, black (Salix nigra)	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts

Specific stiffness of the elements

Material	Young's modulus (GPa)	Density (g/cm3)	Young's modulus per density; specific stiffness (106 m2s−2)	Young's modulus per density squared (103 m5kg−1s−2)	Young's modulus per density cubed (m8kg−2s−2)
Thallium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Cesium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Arsenic	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Lead	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Indium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Rubidium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Selenium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Bismuth	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Europium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Ytterbium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Barium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Gold	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Plutonium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Cerium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Praseodymium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Cadmium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Neodymium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Hafnium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Lanthanum	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Promethium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Thorium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Samarium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Lutetium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Terbium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Tin	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Tellurium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Gadolinium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Dysprosium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Holmium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Erbium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Platinum	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Thulium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Silver	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Antimony	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Lithium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Palladium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Zirconium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Sodium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Uranium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Tantalum	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Niobium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Calcium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Yttrium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Copper	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Zinc	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Silicon	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Vanadium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Tungsten	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Rhenium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Rhodium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Nickel	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Iridium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Cobalt	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Scandium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Titanium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Magnesium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Aluminum	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Manganese	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Iron	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Molybdenum	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Ruthenium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Chromium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts
Beryllium	Template:Nts	Template:Nts	Template:Nts	Template:Nts	Template:Nts

See also

• Specific strength