# Strength Design with Factored Loads

Safe, economical strength design of reinforced concrete structures requires that their ultimate-load-carrying capacity be predictable or known. The safe, or service-loadcarrying capacity can then be determined by dividing the ultimate-load-carrying capacity by a factor of safety.

The ACI 318 Building Code provides for strength design of reinforced concrete members by use of factored loads (actual and specified loads multiplied by load factors). Factored axial forces, shears, and moments in members are determined as if the structure were elastic. Strength-design theory is then used to design critical sections for these axial forces, shears, and moments.

Strength design of reinforced concrete flexural members (Art. 9.46) may be based on the following assumptions and applicable conditions of equilibrium and compatibility of strains:

1. Strains in the reinforcing steel and the concrete is directly proportional to the distance from the neutral axis (Fig. 9.12) except for deep flexural members with a span-depth ratio less than 1.25 of the clear span for simple spans and 2.5 for continuous spans. See also Art. 9.88.

2. The maximum usable strain at the extreme concrete compression surface equals 0.003 in / in

3. When the strain, in. / in. in reinforcing steel is less than ƒy /Es, where ƒy

yield strength of the steel and Es its modulus of elasticity (29,000,000 psi), the steel stress, psi, equals 29,000,000 times the steel strain. After the steel yield strength has been reached, the stress remains constant at ƒy, though the strain increases.

4. Except for prestressed concrete (Art. 9.104) or plain concrete, the tensile strength of the concrete is negligible in flexure.

5. The shape of the concrete compressive distribution may be assumed to be a rectangle, trapezoid, parabola, or any other shape in substantial agreement with comprehensive strength tests.

6. For a rectangular stress block, the compressive stress in the concrete should be taken as . This stress may be assumed constant from the surface of max- 0.85ƒc imum compressive strain to a depth of a 1c, where c is the distance to the neutral axis (Fig. 9.12). For 4000 psi, 1 0.85. For greater concrete ƒc strengths, 1 should be reduced 0.05 for each 1000 psi in excess of 4000, but 1 should not be taken less than 0.65.

(See also Art. 9.8.2 for columns).

## Strength-Reduction Factors

The ACI Code requires that the strength of a member based on strength design theory include strength-reduction factors to provide for small adverse variations in materials, workmanship, and dimensions individually within acceptable tolerances.

The degree of ductility, importance of the member, and the accuracy with which the member’s strength can be predicted were considered in considered in assigning values to :

should be taken as 0.90 for flexure and axial tension; 0.85 for shear and torsion; 0.70 for bearing on concrete; for axial compression combined with bending, 0.75 for members with spiral reinforcement, and 0.70 for other members; and 0.65 for flexure, compression, shear, and bearing in structural plain concrete.

## Load Factors

For combinations of loads, a structure and its members should have the following strength U, computed by adding factored loads and multiplying by a factor based on probability of occurrence of the load combination:

Dead load D and live load L, plus their internal moments and forces: