In an earlier thread on stainless vs carbon steels there was some confusion on which mechanical/material properties were responsible for oberved performance. Some people didn't understand and refused to believe that hardening a steel didn't change it's elastic eflection, or that that the modulus of elasticity changes so little that it's not uncommon for it to be stated as only one value, 30*10^6 psi. As shown below it contributes little to deflection, and considering that one has exhausted the ability to change deflection with changes in E it's easy to see why it's not uncommon for it to be stated that it doesn't change.
Deflection of a rectangular beam, one end fixed with load on the other end. Stress vs available tensile/yield strength may in fact result in plastic deformation, something that I didn't check for. Better assumptions, values, formulas, etc. welcomed.
ymax = maximum deflection = (PL^3)/(3EI)
P = load.
L = length of beam.
E = modulus of elasticity, which ranges from 27*10^6 psi for some stainless steels to 30*10^6 psi for carbon steels, whether soft or hard.
I = moment of intertia = (bd^3)/12 where b is width and d is thickness (height).
Changes in maximum deflection as a steel beam 1.5in wide, 0.125in thick, 3in long, and with a 100lb load is changed:
0.137in to 0.123in (a difference of 0.014in) as the modulus of elasticity is changed from 27*10^6 psi to 30*10^6 psi.
0.291in to 0.036in (a difference of 0.255in) as the thickness is changed from 3/32in to 3/16in.
0.123in to 0.074in (a difference of 0.049in) as the width is changed from 1.5in to 2.5in.
0.061in to 0.184in (a difference of 0.123in) as the load is changed from 50 lbs to 150 lbs.
0.055in to 0.437in (a difference of 0.382in) as the length is changed from 2in to 4in.
Deflection of a rectangular beam, one end fixed with load on the other end. Stress vs available tensile/yield strength may in fact result in plastic deformation, something that I didn't check for. Better assumptions, values, formulas, etc. welcomed.
ymax = maximum deflection = (PL^3)/(3EI)
P = load.
L = length of beam.
E = modulus of elasticity, which ranges from 27*10^6 psi for some stainless steels to 30*10^6 psi for carbon steels, whether soft or hard.
I = moment of intertia = (bd^3)/12 where b is width and d is thickness (height).
Changes in maximum deflection as a steel beam 1.5in wide, 0.125in thick, 3in long, and with a 100lb load is changed:
0.137in to 0.123in (a difference of 0.014in) as the modulus of elasticity is changed from 27*10^6 psi to 30*10^6 psi.
0.291in to 0.036in (a difference of 0.255in) as the thickness is changed from 3/32in to 3/16in.
0.123in to 0.074in (a difference of 0.049in) as the width is changed from 1.5in to 2.5in.
0.061in to 0.184in (a difference of 0.123in) as the load is changed from 50 lbs to 150 lbs.
0.055in to 0.437in (a difference of 0.382in) as the length is changed from 2in to 4in.
