ACI 350.3-06 - flexural stiffness k in SI units

[azwanzig]

In ACI 350.3-06, Seismic Design of Liquid-Containing Structures, on page 36 in the commentary formulas are provided for deriving the flexural stiffness, k, for a fixed-base, free-top cantilever wall in both imperial and SI units. It appears that k is derived from the deflection formula for a cantilever beam with a point load at its tip, k = 3 E I / L^3. In SI units, the formula given is inconsistent with the defined variables. The SI formula in the standard (accounting for errata) is k = Ec*(tw/h)^3/(4*10^3) and should result in units of kN/m. The units for the variables, as defined, are: Ec in MPa, tw in mm, h in m. As given, the resultant k is in units of 10^9 kN/m, or kN-mm^4/m^5. For the formula to result in units of kN/m, the units for tw need to be in m, not mm. It seems that the formula given in the standard should be k = Ec*(tw/1000/h)^3/(4*10^3)

Does this make sense, or am I off base?
Thanks!

 

[azwanzig]

Ok, I got it. Please disregard the above post. Using E in MPa, tw in mm and h in m, the formula as given in the errata for the standard results in units of N/m assuming that you use a 1000mm wall strip.

Thanks!