|
The cross sections of reinforced concrete column with axial load
and biaxial bending often have three unknowns : (1) maximum
concrete compressive stress ,(2) the inclination and (3) depth
of neutral axis. Theoretically,they can be obtained with three
simultaneous nonlinear equations of (F＝0 ,(Mx＝0, and (My=88饗
ecause it is difficult and complex to derive these three
equations and the poor of numerical methods and computing tools,
many reseachers usually made some simplifying assumptions in
attempt to overme these difficulties, but the results can not
reflect the actual behavior of biaxially loaded column. For
example, the inclination of neutral axis was proposed, material
stress-strain relationship was assumed to be linear, equivalent
compressive stress block of concrete was estimated as ACI Code,
or adopting equivalent springs to represent cross section of
columns.Therefore, the aim of this paper is to directly, really,
and completely derive three simultaneous nonlinear equations,
and use computer program carry out fastly and exactly. At the
same time, this method can be adopted to study about the
behavior of biaxially loaded column later.
This analysis is based on the assumption that plane section
remains plan before and after bending, and utilizes the modified
Kent and Park stress-strain curve for concrete and a complete
idealized stress-strain curve for steel to integrate directly
resultant force and moment of biaxially loaded reinforced
concrete column section. Based on those, three simultaneous
nonlinear equations is derived and solved by modified the
Newton-Raphson method to obtain maximum concrete compressive
stress in the cross sectio the inclination and depth of neutral
axis. Besides, this paper modifies the equation of effective
flexural rigidity presented by ACI Code, and use it to find the
load-deformation curves of biaxially or uniaxially loaded
columns, including the failure and unloading step of member.
In order to verify the directly analytical method and stiffness
equation of column presented by this paper, this research
analyzes 40 experimental specimens of ultimate loads and 11
experimental specimens of P-△ curve for columns. By comparing
test and theoretical values, it is evident that results show an
excellent agreement. Besides, this paper investigates load-
contour diagrams and neutral axis angle of biaxially loaded RC
columns, and presents an equation to determine neutral axis
angle at compressive ilure.
Keyword : RC column , biaxially bending, column stiffness,
failure surface, load-contour curve, the neutral axis angle.
|