ABSTRACT

For more than half a century, analysis of reinforced concrete structural members is being done using the so-called parabolic-rectangular stress block method first proposed by ¥/hitney. This paper will present the true parabolic stress method as the analytical alternative analysis for the ultimate strength of reinforced concrete sections. This analytical method uses the parabolic nature of the concrete stress/strain curve and the linear stress strain of steel reinforcement. The interaction these two materials is related by the common deformation as they resist applied loads to their ultimate -.,a'"'""'"'·

2DERIVATION

Figure 1 shows the overlay of the basic parabola to the concrete stress strain curve and the linear strain based on the steel stress/strain curve. From Figure 2, the equation of the basic parabola is given by the relationship

y/x(L - x) = rn/(L/2)2 (1)

The concrete force is defined the maximum useable concrete strain allowed and the maximum area bounded by the curve OMN and the X-axis as shown in Figure 3. From equation (1)

, ? y/x(2 Xm - x) = f c /(xmt or

, 2 y = f c X (2xm - x)/ (xm) (2)

and from the strain diagram,

(3)

Substitute eq. (3) in (2)

The area under this curve calculus is given by

Integrate and evaluate limits from 0 to c to obtain

Differentiate equation ( 6) with respect to em , equate to zero and solve for the value of em to yield the maximum area under the curve.