In the strength design method, the safety of concrete structures is ensured by using load factors and strength reduction factors. The load factors are used to increase the amount of applied load on a structure to account for possible load increase during the building's life span. Whereas strength reduction factors (usually having a value <1) are used to decrease the estimated strength of concrete members to consider uncertainties in materials and errors in workmanship.
Strength reduction factors and load factors are estimated based on probabilistic methods that account for variability in all aspects of engineering. There are a number of load factors that differ based on the load type and load combinations.
The ACI 318-19 provides load factors and various load combinations for the possible applied loads and the strength reduction factors for various concrete elements like beams, columns, and slabs.
1. Load Factors
The load factor for each type of load is different based on the degree of accuracy of the load estimation and possible variations during the service life of the structure. Load factors for dead loads are less than that of live loads because the former can be estimated accurately, and hence the degree of uncertainty is low.
However, the latter can vary over the service life of the element, and that is why the degree of uncertainty is high. Table-1 established by ACI code provides different load factors for various load combinations:
Table-1: Different Load Factors and Load Combinations Provided by ACI 318-19 Section 5.3
|Primary Load types||Load combinations||ACI 318-19 Equations|
|Dead load||U = 1.4D||5.3.1a|
|Live load||U = 1.2D + 1.6L + 0.5(Lr or S or R)||5.3.1b|
|Roof live load or snow load or rain load||U = 1.2D + 1.6(Lr or S or R) + (1.0L or 0.5W)||5.3.1c|
|Wind load||U = 1.2D + 1.0W + 1.0L + 0.5(Lr or S or R)||5.3.1d|
|Earthquake or seismic load||U = 1.2D + 1.0E + 1.0L + 0.2S||5.3.1e|
|Wind load||U = 0.9D + 1.0W||5.3.1f|
|Earthquake seismic load||U = 0.9D + 1.0E||5.3.1g|
- Consider the effect of one or more loads, not acting at the same time to find out whether they yield the most critical load combination or not.
- The live load factor in equations (5.3.1c to 5.4.1d) can be reduced to 0.5 except for garages, areas designated as a place of public assembly, and areas where the live load is greater than 4.8 KN/m2.
- According to ACI 318-19 Section 5.3.4, if applicable, live loads such as concentrated live loads, vehicular loads, crane loads, loads on handrails, guardrails, vehicular barrier systems, impact effects, and vibration effects should be included in equations (5.3.1a to 5.4.1f).
- If wind loads are provided at service-level loads, the wind load factor 1 in equation (5.3.1d) and (5.3.1e) should be increased to 1.6, as per ACI 318-19 section 5.3.5. The same section also states that the wind load factor of 0.8 replaces 0.5 in the equation (5.3.1c).
- Make rooms for differential settlement and volume changes through the provision of expansion joints, shrinkage, temperature reinforcement, and ductile joints.
- If fluid load is present, then include it as follows:
- Include fluid load with a load factor of 1.4 in equation 5.3.1a if it acts alone or adds to the effects of dead load.
- If fluid load adds to the primary load, it shall be included with a load factor of 1.2 in equation 5.3.1b through 5.3.1e.
- If the effect of the fluid load is permanent and counteracts the primary load, it shall be included with a load factor of 0.9 in equation 5.3.1g.
- Ignore the fluid load if its presence is temporary and counteracts the primary load.
- If present, consider lateral earth pressure in the load combination equations as follows:
- Compute lateral earth pressure with a load factor of 1.6 if it acts alone or adds to the primary load effect.
- If lateral earth pressure exists permanently and counteracts the primary load effect, then include it with a load factor of 0.9.
- Neglect the lateral earth pressure if its presence is temporary and counteracts the primary load effect.
2. Strength Reduction Factors
The strength reduction factor is used to decrease the estimated strength of structural members, i.e., to compute the design strength of concrete elements. It is used to account for uncertainties in materials, possible design, and construction errors.
The ACI 318-19 specifies the strength reduction factors for different concrete elements like beams, columns, slabs, and for various forces that influence the members such as moments, shears, and torsion. Table-2 presents various reduction factors based on actions and concrete elements.
Table-2: Strength Reduction Factors for Various Actions and Concrete Elements Based on ACI 318-19
|Actions or structural member||Strength reduction factor|
|Tension controlled beams and slab||0.90|
|Shears and torsions in beams||0.75|
|Columns||0.65 for tie and 0.75 for spirally reinforced concrete column|
|Bearing on concrete||0.65|
|Plain concrete elements||0.60|
|Brackets and corbels||0.75|
|Struts, ties, nodal zones, and bearing areas designed in accordance with the strut-and-tie method||0.75|
|Anchors in concrete elements||0.45 to 0.75|
|Components of connections of precast members controlled by yielding of steel elements in tension||0.9|
|Post-tensioned anchorage zones||0.75|
Purpose of Strength Reduction Factors
- To account for inaccuracies in the equations of design.
- To reflect the significance of structural members.
- To account for probable under-strength of structural elements because of change in material strength and dimensions of the concrete member.
- To reflect the available ductility and needed reliability of the structural member under load effects.
- The strength reduction factor for the compression-controlled member is 0.65. The compression-controlled member is brittle and fails suddenly without showing any sign of failure, such as large deflection. Additionally, the compression-controlled elements are sensitive to variations in concrete properties.
- Tension-controlled member is ductile and shows signs of failures through cracks and significant deflection.
- For tension-controlled section εt≥0.005, for compression-controlled section εt≤0.002. The transition zone is located between the compression and tension-controlled sections.
- The strength factors for members in the transition zone is computed using equations provided in Figure-1.
- Alternatively, you can use (c/dt) to determine the type of section. Sections where (c/dt) ≥0.600 are categorized as brittle and sections where (c/dt) ≤0.375 section are ductile.
The strength reduction factor is used to decrease the estimated strength of structural members, i.e., to compute the design strength of concrete elements.
1. To account for inaccuracies in the equations of design.
2. To reflect the significance of structural members.
3. To account for probable under-strength of structural elements because of change in material strength and dimensions of the concrete member.
4. To reflect the available ductility and needed reliability of the structural member under load effects.
The load factors are used to increase the amount of applied load on a structure to account for possible load increase during the building's life span.
Load factors are commonly more than one and differ based on load type and load combinations. The ACI 318-19 provides load factors and various load combinations for the possible applied loads.
As the failure of columns is brittle, they are more critical than the failure of the beam, which is ductile. Columns are usually compression-controlled, whereas beams are tension-controlled.
Strength reduction factors and load factors are estimated based on probabilistic methods that account for variability in all aspects of engineering.
LOAD & RESISTANCE FACTOR DESIGN (LRFD)