This report proposes a series of probability-based load factors for use in the design of building structures. This chapter will define some of the terms used and will discuss When a structure or structural element becomes unfit for its intended purpose it is said to have reached a limit state. For most structures the limit states can be divided into two categories: Ultimate Limit States are related to a structural collapse of part or all of the structure. Such a limit state should have a very low probability of occurrence since it may lead to loss of life and major financial losses. The most common ultimate limit states are: a) b) loss of equilibrium of a part or the whole structure considered as a rigid body (e.g. overturning, uplift, sliding); loss of load-bearing capacity of members due to exceeding the material strength, buckling, fracture, fatigue or fire; c) Spread of initial local failure into widespread collapse (progressive collapse or lack of structural integrity); d) very large deformation transformation into a mechanism, overall instability (e.g. wind flutter, ponding instability). Serviceability Limit States are related to disruption of the functional use of the structure and/or damage to or deterioration of the structure. Since there is less danger of loss of life, a higher probability of occurrence may be tolerated than in the case of the ultimate limit states. For buildings the following limit states may be important: a) excessive deflection or rotation affecting the appearance, functional use or drainage of the building or causing damage to non-structural components and their attachment; b) excessive local damage (cracking or splitting, spalling, local yielding or slip) affecting appearance, use or durability of the structure; c) excessive vibration affecting the comfort of the occupants or the operation of equipment. These, in turn, could be divided into groups depending on the load levels to be considered in checking them or the lasting effects of their occurrence. Limit States Design is a process that involves: (1) Identification of all modes of failure or ways in which the structure might fail (2) to fulfill its intended purpose (limit states). Determination of acceptable levels of safety against occurrence of each limit state. (3) Consideration by the designer of the significant limit states. In the design of a normal building, Steps 1 and 2 have already been carried out by the standard committee. The design specification lists the limit states to be considered and presents load and resistance factors for use in checking these limit states. For normal structures, the designer carries out Step 3, generally starting with the most critical limit states for the structure in question. The designer of an unusual structure may have to consider all three steps. The limit states design procedure is, in effect, the traditional engineering design procedure formalized to require specific consideration of the various limit states. Under limit states design, the design of the structure for a bridge or building generally starts with satisfaction of the ultimate limit states followed by checks of the serviceability limit states. The latter checks are either carried out explicitly (by calculating deflections, for example) or by using "deemed to satisfy" clauses such as maximum slenderness ratios, etc. This order of calculation is followed because generally the major functional requirement (major limit state) of the structural components for a building or bridge is to support loads safely. This may not always be true, however. For example, in the design of a water tank or similar sanitary engineering structure, the major functional requirement is that the tank hold water without leaking. Here the order of the design process may well start with consideration of ways to prevent leakage and conclude with checks of whether the resulting strength is adequate. In this context, then, the strength design procedure presented in the ACI Standard 318 [19]*, and the Load and Resistance Factor Design procedure [9] are limit states design procedures. Ideally, however, the complete limit states design concept should be followed because, all too often in the past, designers and specification writers have given their prime attention to the ultimate limit states and not enough to the factors which might render the building unsatisfactory in everyday use. * Numbers in brackets denote references listed in Section 8. Traditionally, structural design has been based on code-specified or service loads and the desired safety has been assumed to exist if the elastically computed stresses did not exceed allowable working stresses which were a preset fraction of the yield strength, crushing strength, modulus of rupture, etc. The loads used in this design process have a high probability of occurrence during the life of the structure. Thus, for example, the dead load is calculated directly from the specified dimensions and assumed densities and is close to the expected dead load. The allowable stresses have been set in an empirical manner to reflect the profession's feeling about the relative variability of various materials. Earlier versions of the ACI Code (for example, the 1951 code) based design on allowable stresses of 0.225 to 0.45 times the concrete strength and 0.5 times the yield strength of the reinforcement; the AISC Specification [26] bases structural steel design on allowable stresses of 0.66 times the yield strength for compact sections in bending; timber specifications base design on 0.2 to 0.25 times the short-term strength of small clear specimens. The advantages of working stress design are: (i) Designers are familiar with it and it is simple to apply. The moments or forces from each load are calculated and added together. The resulting sums are multiplied by load combination or probability factors ranging from 1.0 to 0.66 and are used to proportion sections so that the stresses do not exceed the allowable values. (ii) Structures designed this way are generally believed to behave satisfactorily in service. By keeping stresses low at service loads, deflections, vibrations, crack widths in concrete beams, and the like, were seldom critical. While this was generally true for the types of materials and structures used prior to 1950, the advent of high strength steels and concretes, prestressed concrete and other lightweight structures have made serviceability checks necessary in many more instances. Working stress design also has some disadvantages: (i) A given set of allowable stresses will not guarantee a constant level of safety Consider two roof structures designed for the same snow load using for all structures. the same allowable stresses. One structure, a reinforced concrete beam and slab structure, has considerably higher dead load than the other, a reinforced concrete folded plate. Because the dead load can be estimated with much more precision than the snow load, the roof having the high ratio of dead to live load will have a lower probability of failure than the lighter structure. (ii) DL high -> Safe The working stress format may be unsafe when one load counteracts the effects dead load has been chosen so that the maximum stresses at service loads (1.0 Dead + 1.0 In summary, then, the main advantage of working stress design is its simplicity; however, it can lead to designs with less safety than normally considered adequate, particularly if loads counteract each other. 1.2.2 Strength Design Safety provisions in several design standards are based on the ultimate strength of critical member sections (strength design of reinforced concrete in ACI Standard 318, for example) or the load carrying capacity of members and entire frames (Section 2 of the AISC Specifications). In these and similar standards, design is based on factored loads and factored resistances. The loads are amplified or reduced by load factors depending on the type and sense of the load, while the strengths are reduced by resistance factors less than or equal to unity. For example, ACI Standard 318 bases design in flexure against gravity loads on Note that these are both load and resistance factor design formats. Criteria of this type are an attempt to apply partial factors of safety to those variables in the design equation which are known to be unpredictable. Eq. 2.1 attempts to account for the possibility of understrength and overload, while Eq. 2.2 apparently accounts |