Question

AW12x14 A36 steel section is used as a column. If the column is 15 ft long with pin supports at each end, then the largest permissible compressive axial load is most nearly... O 783 kips O 21 kips 0 241 kips O 150 kips

Answer 1

Given section is W12*14 A36 steel section.

This section denotes i section.

From cross sectional engineering data of structural steel I wide section

we get

Area of i section is 4.16 in²

Area Moment of intertia about one axis(I_xx) = 88.6 in⁴

Area Moment of inertia about second perpendicular axis (I_yy) = 2.36 in⁴

Length of the column (L) = 15 ft = 15*12 = 180 in

Since both ends are hinged or pinned effective length = L = 180 in

Youngs modulus of A36 steel (E) = 29 * 10⁶ psi = 29000 kpsi

$Critical load = \frac{\prod ^{2}EI}{L^{2}}$

where I = minimum area moment of inertia = min{88.6,2.36} = 2.36 in⁴

substituting values in above equation

critical compressive load = $\frac{\prod ^{2}*29*10^{3}*2.36}{180^{2}}$

= 20.84 kips

Largest permissible axial load = 21 kips (approximately)

Since other options are not nearer to 20.84 kips , 21 kips is correct option.