developed by ASCE Committee 7. The strength-reduction factors given in ACI Code Section 9.3 are based on statistical studies of material properties [4-2] and were selected to give approximately the same level of safety as obtained with the load and strength-reduction factors used in earlier editions of the code. Those former load and strength-reduction factors are still presented as an alternative design procedure in Appendix C of the latest edition of the ACI Code, ACI 318-08 [4-3]. However, they will not be discussed in this book.
For flexure without axial load, ACI Code Section 9.3.2.1 gives $\phi = 0.90$ for what are called tension-controlled sections. Most practical beams will be tension-controlled sections, and $\phi$ will be equal to $0.90$. The concept of tension-controlled sections will be discussed later in this chapter. The product, $\phi M_n$, commonly is referred to as the reduced nominal moment strength.
Positive and Negative Moments
A moment that causes compression on the top surface of a beam and tension on the bottom surface will be called a positive moment. The compression zones for positive and negative moments are shown shaded in Fig. 4-2. In this textbook, bending-moment diagrams will be plotted on the compression side of the member.
Symbols and Notation
Although symbols are defined as they are first used and are summarized in Appendix B, several symbols should essentially be memorized because they are commonly used in discussions of reinforced concrete members. These include the terms $M_u$ and $M_n$ (defined earlier) and the cross-sectional dimensions illustrated in Fig. 4-2. The following is a list of common symbols used in this book:
- $A_s$ is the area of reinforcement near the tension face of the beam, tension reinforcement, $\text{in.}^2$.
- $A_s'$ is the area of reinforcement on the compression side of the beam, compression reinforcement, $\text{in.}^2$.
- $b$ is a general symbol for the width of the compression zone in a beam, in. This is illustrated in Fig. 4-2 for positive and negative moment regions. For flanged sections this symbol will normally be replaced with $b_e$ or $b_w$.
(a) Positive moment (compression on top). (b) Negative moment (compression on bottom).
Fig. 4-2 Cross-sectional dimensions.