Page 156 - Civil Engineering Formulas

94 CHAPTER THREE

The portion of the required strength of axially loaded encased composite
columns resisted by concrete should be developed by direct bearing at connec-
tions or shear connectors can be used to transfer into the concrete the load
applied directly to the steel column. For direct bearing, the design strength of the
2
2
concrete is 1.7 c f c A b , where c 0.65 and A b loaded area, in (mm ). Cer-
tain restrictions apply.
ELASTIC FLEXURAL BUCKLING OF COLUMNS

Elastic buckling is a state of lateral instability that occurs while the material is
stressed below the yield point. It is of special importance in structures with slen-
der members. Euler’s formula for pin-ended columns (Fig. 3.7) gives valid
results for the critical buckling load, kip (N). This formula is, with L/r as the
slenderness ratio of the column,
2

EA
P (3.25)
(L/r) 2

P P
y

y(x)
P
M(X)
L
x

P M(X)

P
P
(a) (b)
FIGURE 3.7 (a) Buckling of a pin-ended column under axial load.
(b) Internal forces hold the column in equilibrium.