Loads, Load Combinations, Resistance Factors

Text: Chapter 2

Code: Sections 9.2 (load combinations), 9.3 (resistance factors)


Typical loads in buildings include:

Dead loads - permanent (non-changing) loads such as self weight of structure, floor and ceiling finishes, utilities, walls, permanent equipment, etc.

Live loads - loads that change frequently in magnitude and position such as building occupants, furniture,etc.

Wind - generates pressures and suctions on building components.

Snow - typically considered acting on roofs only.

Earthquake - inertial forces generated in structure as a result of ground motion.

Others - see textbook or ACI Code.


Load Combinations

Individual loads need to be combined to account for the possibility of several acting at the same instant. In strength design philosophy, the loads are factored for the potential of loads exceeding the assumed values for design.

Load factors are typically 1.0 or greater; a factor of 0.9 (the only factor less than 1.0) is used in Eqs. 9-6 or 9-7 when the dead loads improve the stability of a structure. Load factor magnitudes depend on the variability observed for individual loads. For example, dead loads can be determined fairly accurately and do not vary much; therefore, the load factor for dead loads is relatively small compared with factors for other loads.

The following are the most commonly used load combinations for design of reinforced concrete structures (see ACI 318 section 9.2):

U = 1.4 D (Equation 9-1)

U = 1.2 D + 1.6 L (Equation 9-2)

U = 1.2 D + 1.6 W + 1.0 L (Equation 9-4)

Where U = factored load effect, D = dead load effect, L = live load effect, W = wind effect. A load effect is defined as the axial force, shear force, bending moment, or torsion caused by the application of loads to a structure. Design for all possible effects (P,V, M, or T) needs to be considered. The load factor on the live load, L, in equation 9-4 can be reduced to 0.5 except for garages, areas of public assembly, or all areas where the live load is greater than 100 psf.

Analysis of a structure for different load combinations is typically performed using computer software. A brief description of the procedure required to specify load combinations when using RISA2D is available here (172 KB).

Resistance (strength) Factors

Resistance factors are used to account for the variability in material strength or cross sectional dimensions that may occur during construction. These factors also account for variability in design equations. These factors are generally less or equal to 1.0 and depend on the strength being calculated (e.g. flexural strength, shear strength, etc.). Following is a list of the strength factors most commonly used for this class, as specified in ACI 318 section 9.3:

Flexure and Axial Load

Tension Controlled Sections = 0.9

Compression controlled sections = 0.70 (spirally reinforced members); 0.65 (other reinforced members)

The strength factor (phi) changes with net tensile strain of the cross section as illustrated in the following figure:

Variation of phi factor with net tensile strain (ACI 318 Fig.R9.3.2)

Shear and Torsion = 0.75

Bearing on Concrete = 0.65