## 712 Member Design for Strength

7.12.1 Ultimate Strength Design

The main requirement of structural design is for the structural capacity, SC, to be equal to or greater than the structural demand, SD:

Modification factors are included in each side of the equation. The structural capacity SC is equal to the nominal strength Fn multiplied by a capacity reduction safety factor f:

The nominal strength Fn is the internal ultimate strength at that section of the member. It is usually calculated by the designer according to formulas derived from the theory of mechanics and strength of materials. These strength formulas have been verified and calibrated with experimental testing. They are generally expressed as a function of the cross-section geometry and specified material strengths. There are four types of internal strengths: nominal moment Mn, shear Vn, axial Pn, and torsional moment Tn.

The capacity reduction safety factor f accounts for uncertainties in the theoretical formulas, empirical data, and construction tolerances. The f factor values specified by ACI are listed in Table 7.4.

The structural demand, SD, is the internal force (moment, shear, axial, or torsion) at the section of the member resulting from the loads on the structure. The structural demand is usually obtained by carrying out a structural analysis of the structure using hand, approximate methods, or computer software. Loads to be input are specified by the design codes and the project specifications and normally include dead, live, wind, and earthquake loads. Design codes such and ACI, IBC, and AASHTO also specify the values of safety factors that should be multiplied with the specified loads and how different types of loads should be combined (i.e., SD = 1.2Dead + 1.6Live). ACI load factors and combinations are listed in Table 7.5.

Combining the two equations above, a direct relationship between the nominal strength Fn and the structural demand SD can be obtained

This relationship is convenient because the main design variables, such as reinforcement area, which are usually expressed in terms Fn, can be related directly to the results of the structural analysis.

TABLE 7.4 ACI Strength Reduction Factors f | |

Nominal strength condition |
Strength reduction factor f |

Flexure (tension-controlled) |

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