The reinforced concrete column shown in the figure has a
rectangular cross section. The column
is subjected to a 100 kips axial compressive force at its top in addition to uniform lateral load, w
along the top 8 ft of the column height. Unit weight of concrete is 150 pcf and the specified
concrete compressive strength, fc' is 4,000 psi.
Assume the column is subjected to the uniformly
load, w, in the top 8 ft of column length in both directions simultaneously (i.e. column is subjected
to bi-axial bending). The lateral uniform loads are increased until cracking occurs in the column. What is the value
of the uniform lateral load at which the column cracks? (Hint: Axial compressive forces
increase the concrete stress at which cracking occurs. The cracking stress is equal to
modulus of rupture in addition to concrete compressive stresses resulting from axial loads).