Load Factors and Load Combinations

When using ASD, there is no distinction between the loads (i.e., either in magnitude or combination of load types) used to evaluate the ultimate load capacity or the deformation potential of the ground. Thus, the same load magnitudes are used to estimate the ultimate bearing capacity and the

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settlement of a foundation for ASD, despite the inherent uncertainty in loads applied from a structure to its substructure components. LRFD incorporates this uncertainty by application of load factors for various permanent and transient load types using the LRFD equation:

R = R Qi n r i iγ ≤φ η

∑

ηi = Load modifier to account for ductility, redundancy and operational importance (dim)

γi = Load factor for permanent and transient loads (dim) Qi = Load (kN)

φ = Resistance factor (dim)

Rn = Nominal (ultimate) resistance (kN) Rr = Factored resistance (kN)

Selection of the load factor(s) to be used is a function of the type of load and limit state being evaluated. (Recall from Chapter 3 that a limit state is a condition beyond which a foundation or structure component ceases to fulfill its intended function.) This section addresses load factor and load modifier selection. The selection of a resistance factor(s) and estimation of the nominal resistance is presented in Chapters 8 through 10 for design of foundations, Chapters 11 through 14 for design of walls, and in Chapters 15 and 16 for design of culverts.

For the AASHTO LRFD Specification, the limit states, load factors and load combinations which must be investigated are presented in Tables 4-10 and 4-11.

Structure and foundation design by LRFD requires that:

• All applicable limit states be evaluated

• Each load for each limit state be modified by a prescribed load factor, γ • Factored loads for each limit state be combined in a prescribed manner

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Table 4-10 (A3.4.1-1)

Load Combinations and Load Factors

(AASHTO, 1997a)

Use one of these at a time LOAD COMBINATION LIMIT STATE DC DD DW EH EV ES LL IM CE BR PL LS WA WS WL FR (1) TU CR SH EL TG SE EQ IC CT CV STRENGTH-I (unless noted) γp 1.75 1.00 - - 1.00 0.50/ 1.20 γTG γSE - - - - STRENGTH-II γp 1.35 1.00 - - 1.00 0.50/ _1.20 γTG γSE - - - - STRENGTH-III γp - 1.00 1.40 - 1.00 0.50/ _1.20 γTG γSE - - - - STRENGTH-IV

EH, EV, ES, DW DC ONLY γp 1.50 - 1.00 - - 1.00 0.50/ _1.20 - - - - STRENGTH-V γp 1.35 1.00 0.40 0.40 1.00 0.50/ _1.20 γTG γSE - - - - EXTREME EVENT-I γp γEQ 1.00 - - 1.00 - - - 1.00 - - - EXTREME EVENT-II γp 0.50 1.00 - - 1.00 - - - - 1.00 1.00 1.00 SERVICE-I 1.00 1.00 1.00 0.30 0.30 1.00 1.00/ 1.20 γTG γSE - - - - SERVICE-II 1.00 1.30 1.00 - - 1.00 1.00/ _1.20 - - - - SERVICE-III 1.00 0.80 1.00 - - 1.00 1.00/ _1.20 γTG γSE - - - - FATIGUE-LL, IM & CE ONLY - 0.75 - - - - - - - - - CONSTRUCTION 1.25 1.50 1.00 1.25 1.25 1.25 1.00 1.00 1.00 - - - - (1) _{The reduced values of γ are used when calculating force effects other than displacements of joints} and bearings (A14.4.1).

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Table 4-11 (A3.4.1-2)

Load Factors for Permanent Loads, γP

(AASHTO, 1997a)

Load Factor Type of Load

Maximum Minimum

DC: Component and Attachments 1.25 0.90

DD: Downdrag 1.80 0.45

DW: Wearing Surfaces and Utilities 1.50 0.65 EH: Horizontal Earth Pressure

• Active • At-Rest 1.50 1.35 0.90 0.90 EV: Vertical Earth Pressure

• Retaining Structure • Rigid Buried Structure • Rigid Frames

• Flexible Buried Structures • Flexible Metal Box Culverts

1.35 1.30 1.35 1.95 1.50 1.00 0.90 0.90 0.90 0.90

ES: Earth Surcharge 1.50 0.75

From the Table 4-10, the limit states which must be investigated include:

• Strength Limit State • Extreme Event Limit State • Service Limit State

• Fatigue Limit State • Construction Limit State

The limit states are further subdivided based on consideration of applicable load combinations as follows:

• Strength I - Basic load combination related to the normal vehicular use of the bridge without wind.

• Strength II - Load combination relating to the use of the bridge by Owner- specified special design vehicles and/or evaluation permit vehicles, without wind.

• Strength III - Load combination relating to the bridge exposed to wind velocity exceeding 90 km/hr without live loads.

• Strength IV - Load combination relating to very high dead load to live load force effect ratios exceeding about 7.0 (e.g., for spans greater than 75 m).

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• Strength V - Load combination relating to normal vehicular use of the bridge with wind velocity of 90 km/hr.

• Extreme Event I - Load combination including earthquake.

• Extreme Event II - Load combination relating to ice load or collision by vessels and vehicles.

• Service I - Load combination relating to the normal operational use of the bridge with 90 km/hr wind.

• Service II - Load Combination intended to control yielding of steel structures and slip of slip-critical connections due to vehicular live load.

• Service III - Load combination relating only to tension in prestressed concrete structures with the objective of crack control.

• Fatigue - Fatigue and fracture load combination relating to repetitive gravitational vehicular live load and dynamic responses under a single design truck.

• Construction - Load combination relating to construction equipment live load during structure installation/erection.

As will become evident in this and later chapters, most substructure designs will require evaluation of foundation and structure performance at the Strength I and Service I Limit States. These limit states are generally analogous to evaluations of ultimate capacity and deformation behavior in ASD, respectively.

Load factors used in the AASHTO LRFD Specification for permanent loads and labeled as γp in Table 4-10, are presented in Table 4-11 as maximum and minimum values.

In reviewing Tables 4-10 and 4-11, the load factors vary for different load categories and limit states to reflect either the certainty with which the load can be estimated or the importance of each load category for a particular limit state. Some general comments about magnitude and relationship between various load factors are highlighted below:

• A load factor of 1.00 is used for all permanent and most transient loads for Service I.

• The live load factor for Strength I is greater than that for Strength II (i.e., 1.75 versus 1.35) because variability of live load is greater for normal vehicular traffic than for a permit vehicle.

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• The live load factor for Strength I is greater than that for Strength V (i.e., 1.75 versus 1.35) because variability of live load is greater for normal vehicular use without wind than for a bridge subjected to a wind of 90 km/hr, and because less traffic is anticipated during design wind conditions.

• The load factor for wind load on structures for Strength III is greater than for Strength V (i.e., 1.40 versus 0.40) because the wind load represents the primary load for Strength III where structures are subjected to a wind velocity greater than 90 km/hr compared to Strength V where wind velocity of 90 km/hr represents just a component of all loads on the structure.

• The live load factor for Strength III is zero because vehicular traffic is considered unstable and, therefore unlikely, under extreme wind conditions.

• The load factors for wind load for Strength V are less than 1.00 (i.e., 0.40) consistent with the common practice in ASD of allowing somewhat lower factors of safety for structures subjected to both normal vehicle and wind loads.

• The maximum and minimum load factor for downdrag loads represent the extreme values of γpmax and γpmin due to the uncertainty in accurately estimating downdrag loads on piles.

The AASHTO LRFD Specification requires that certain permanent loads, including earth loads, be factored using maximum and minimum load factors as shown in Table 4-11. Criteria for their application require that:

• Load factors be selected to produce the total extreme factored force effect, and for each combination, both maximum and minimum extremes be investigated

• For load combinations where one force effect decreases the effect of another force, the minimum value shall be applied to the load that reduces the force effect;

• For permanent force effects, the load factor which produces the more critical combination shall be selected from Table 4-11; and

• If a permanent load increases the stability or load carrying capacity of a structure component (e.g., load from soil backfill on the heel of a wall), the minimum value for that permanent load also be investigated.

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account for the combined effects of ductility, ηD, redundancy, ηR, and operational importance, ηl. The ηi factors (A1.3.2.1) represent a first attempt at codifying the influence of ductility, redundancy and operational importance on structure performance. For loads for which a maximum value of γi is appropriate:

0.95 = _{D R I} i η η η ≥

η (Eq. 4-34) (A1.3.2.1-2)

For loads for which a minimum value of γi is appropriate:

1.00 1 = I R D i _{η η η} ≤ η (Eq. 4-35) (A1.3.2.1-3)

Due to a lack of precise information, the effect of these modifiers has been judged to range between " 5 percent when accumulated geometrically. With time, it is hoped that improved quantification of ductility, redundancy and operational importance, and their interaction and system synergy, can be attained to better account for these factors in design.

For design at the Strength Limit State, values of ηi range as follows:

• Ductility - ηD

− ηD # 1.05 for non-ductile components and connections − ηD = 1.00 for conventional designs and details

− ηD $ 0.95 for components and connections for which additional

ductility-enhancing measured are specified

• Redundancy - ηR

− ηR # 1.05 for non-redundant components and connections − ηR = 1.00 for conventional levels of redundancy

− ηR $ 0.95 for exceptional levels of redundancy • Operational Importance - ηI

− ηI # 1.05 for important structures − ηI = 1.00 for typical structures

− ηR $ 0.95 for relatively less important structures

Classification of operational Importance should be based on social, survival and/or security or defense requirements. With respect to seismic design, bridges classified as critical or essential as described in Table 4-8, should be considered operationally important structures.

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