The ratio of the tensile (or compressive) strength to the density of a material

Question

The ratio of the tensile (or compressive) strength to the density of a material is a measure of how strong the material is "pound for pound." Compare tendon (tensile strength 7.90 MPa, density 1, 100 kg/m^3) to steel (tensile strength 0.51 GPa, density 7, 700 kg/m^3): which is stronger "pound for pound" under tension? Compare bone (compressive strength 160 MPa, density 1, 600 kg/m^3) to concrete (compressive strength 0.39 GPa, density 2, 700 kg/m^3): which is stronger "pound for pound" under compression? Tendon: ratio = _________ times 10 ________ Pa middot m^3/kg Steel: ratio = __________ times 10 __________ Pa middot m^3/kg __________ is stronger than __________ Bone: ratio = ____________ Pa middot m^3/kg Concrete: ratio = ___________ times 10 _________ Pa middot m^3/kg __________ is stronger than ____________.

Explanation / Answer

pound for pound ratio for:

a) Tendon , ratio = tensile strength/density= 79*106/1100 = 7.18*104 Pa-m³/kg

Steel , ratio = tensile strength/density= 0.51*109/7700 = 6.62*104 Pa-m³/kg

Tendon is stronger than steel.

b) Bone, ratio = compressive strength/density= 160*106/1600 = 1.0*105 Pa-m³/kg

concrete, ratio = compressive strength/density= 0.39*109/2700 = 1.4*105 Pa-m³/kg

concrete is stronger than Bone.

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