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Re: Mass = Stress resistance?



philidor 11 asked, in relation to this web citation,
http://www.indiana.edu/~rcapub/v18n1/p22.html

 " I think there have to be more factors than just mass in that stress equation.  Could anyone tell me what they are? "   

Stress is the force carried per unit area.  So, the other factor in the stress equation is the bone cross section.   The weight (mass times gravity) that the animal puts on the bone would be divided by the bone cross section to find the stress.  The citation rated bones by the "strength indicator", which is the reciprocal of stress and which is a measure of how little the bone is loaded.  

Variations in ultimate strength (maximum stress at fracture) between kinds of bone can influence  the interpretation as much as does the strength indicator.  Also, most fractures occur under bending forces rather than by direct compression, so more complex analysis involving the shape of the bone cross section and the lever-like loadings on the bone can also come into consideration.  The compressive stress measure used in the citation is nevertheless a useful data point.

Also, here some observations about details in the citation:

"Assuming that the living T. rex would have had a specific gravity (density as compared to water) between 8.5 and 1.00,"

They, of course, must mean 0.85 and 1.00.  The specific gravity of iron is less than 8.

 "(A giganewton is the force needed to move 112,000 tons--roughly the weight of two steam locomotives--one meter.) "

This definition mixes force and energy; it would be correct if it said "lift" about that much in the earth's gravity, rather than move it one meter.  A giganewton is a billion newtons.  For comparisons, a newton is approximately 0.22 pounds force and strong metals break at stresses in a range approximating 1 giganewton per square meter.

 

Al Fraser