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Fig. 4-1 One-way flexure.

Analysis versus Design

Two different types of problems arise in the study of reinforced concrete:

1. Analysis. Given a cross section, concrete strength, reinforcement size and location, and yield strength, compute the resistance or strength. In analysis there should be one unique answer.
2. Design. Given a factored design moment, normally designated as $M_u$, select a suitable cross section, including dimensions, concrete strength, reinforcement, and so on. In design there are many possible solutions.

Although both types of problem are based on the same principles, the procedure is different in each case. Analysis is easier, because all of the decisions concerning reinforcement, beam size, and so on have been made, and it is only necessary to apply the strength-calculation principles to determine the capacity. Design, on the other hand, involves the choice of section dimensions, material strengths, and reinforcement placement to produce a cross section that can resist the moments due to factored loads. Because the analysis problem is easier, this chapter deals with section analysis to develop the fundamental concepts before considering design in the next chapter.

Required Strength and Design Strength

The basic safety equation for flexure is:

$$\begin{array}{cccc}& \text{Reduced nominal strength}\ge \text{factored load effects}& & \text{(4-1a)}\end{array}\backslash text\{Reduced\; nominal\; strength\}\; \backslash ge\; \backslash text\{factored\; load\; effects\}\; \backslash tag\{4-1a\}$$

or for flexure,

$$\begin{array}{cccc}& \varphi M_n\ge M_u& & \text{(4-1b)}\end{array}\backslash phi\; M\_n\; \backslash ge\; M\_u\; \backslash tag\{4-1b\}$$

where $M_u$ is the moment due to the factored loads, which commonly is referred to as the factored design moment. This is a load effect computed by structural analysis from the governing combination of factored loads given in ACI Code Section 9.2. The term $M_n$ refers to the nominal moment strength of a cross section, computed from the nominal dimensions and specified material strengths. The factor $\phi$ in Eq. (4-1b) is a strength-reduction factor (ACI Code Section 9.3) to account for possible variations in dimensions and material strengths and possible inaccuracies in the strength equations. Since the mid 1990s, the ACI Code has referred to the load factors and load combinations developed by ASCE Committee 7, which is responsible for the ASCE Standard for Minimum Design Loads for Buildings and Other Structures [4-1]. The load factors and load combinations given in ACI Code Section 9.2 are essentially the same as those