# Rules of Thumb for Reinforced Concrete

## figure_6.jpg

Figure 6

Although extended calculations and computations are almost always required in reinforced concrete design, they do not play a strong role in the initial part of the design process. For initial design and feasibility checks, Structural Engineers often utilize approximations and rules-of-thumb.
Perhaps the most basic and useful rule-of-thumb is an estimation for designing reinforced concrete beams, such as the ones pictured in Figure 2 on the Designing for Reinforced Concrete page.  This rule of thumb is from the article Simplified Methods in Reinforced Concrete Design by Jerod F. Johnson, Ph.D., S.E. To find the area of steel (As) necessary for a beam, divide the factored moment (Mu), in kip-feet, by four times the distance (d), in inches, from the compression fiber to the centroid of the tension steel  (figure 6).

A_s≈M_u/4d

This rule-of-thumb comes from a set of approximations applied to the equation:
∅M_n=∅A_s f_y (d-a/2)

In most cases, (d-a/2) can be approximated to 0.9 d . Also, f_y=60 ksi in most circumstances. Substituting these:
∅M_n≅∅A_s 60(0.9d)

Substituting M_u for ∅M_n, assigning ∅=0.9, and converting from kip-feet to kip-inches by a multiplication factor of 12 gives:
A_s≅(M_u (12))/0.9(60)(0.9d) =M_u/4.05d

This result is about 1% different from the approximation:
A_s≈M_u/4d

Figure 7

Code Discussion:

Codes and standards serve an essential role in Structural Engineering. Although codes, in the form of general building codes, have been existent since at least 1722 BC with the Code of Hammurabi, modern codes and standards began in 1666 directly after the Great Fire of London. After much of London burned in a fire fueled by close-packed wooden buildings, the Rebuilding of London Act instituted rules or codes concerning fire resistance. This serves as an example of the purpose of engineering codes. They provide the minimum requirements to safeguard against a certain danger or to aid in standardization. In structural engineering, codes specify items such as structural design, structural tests, exterior walls, masonry, steel, and concrete.
Individual state and local governments are allowed to adopt their own codes. However, most adopt codes that are created and maintained by the International Code Council (ICC) or American Concrete Institute (ACI). The ICC publishes the International Building Code (IBC), International Residential Code (IRC), International Energy Conservation Code, and others. The ACI publishes the ACI Building Code, commonly called “Building Code Requirements for Reinforced Concrete,” and “Specifications for Structural Concrete for Buildings” (see Figure 7).