The secant formula provides a method to determined the stress in a column with an eccentric load. The standard form of the formula is
Since the load P is given, 5 kips, the equation is easy to use. The other parameters are,
A = (r_{o}^{2} - r_{i}^{2})π = (3^{2} - 2.75^{2}) π = 4.515 in^{2}
e = 3 in (eccentric distance)
c = 3 in (furthest distance to outside edge)
I = (r_{o}^{4} - r_{i}^{4})π/4 = (3^{2} - 2.75^{2}) π/4 = 18.70 in^{4}
r = (I/A)^{0.5} = (18.70/4.515)^{0.5} = 2.035 in
E = 29,000 ksi
The column height, L, needs to be converted to effective length since this is not a pin-pin column. For a fixed-free column, the effective length is
L_{e} = 2L = 2(30 ft) = 60(12) in = 720 in
Substituting these values into the secant formula gives,
= 1.107 [1 + 2.173 sec(1.0931)]
= 1.107 [1 + 2.173 (2.175)] |