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Review of RC I

설계 안전성 (Safety)에 대한 기본 요구 조건

강도(Strength),

강성(Stiffness),

안정성(Stability)

설계법

required strength ≤ available strength

(1) 허용응력설계(Working Stress Design, or Allowable Stress Design (ASD))

사용재료가 이상적인 탄성, 소성재료라고 가정한다. 사용하중 하에서는 사용재료가 탄성영역에 있다고 가정한다. (σ

a<σy)

≧

예)철근: 철근의 허용인장강도 콘크리트:허용응력은 콘크리트 허용압축강도 ′문제점 : ① 설계상의 제한과 판단을 총사용 하중의 응력에 근거하기 때문에 여러 하중의 서로 다른 불확실성 정도

가 고려되지 않음. 예 : 일반적으로 적재하중은 고정하중에 비하여 훨씬 불확실하고 다양하게 분포된다.

② 탄성적으로 계산된 응력은 크리프나 건조수축과 같은 하중 재하시간 효과를 쉽게 고려할 수 없음.

[예제] 정사각형 보에서의 P=120 kN 의 축하중이 작용하고, σy = 30 kN/㎠, F.S(안전율) ≥ 1.5일 때 보의 단면을 허

용응력 설계하여라.

(2) 극한강도설계법(Ultimate Strength Design, Limit State Design, Load resistance factor design)

Load factors are applied to the service loads, and a member is selected that will have enough strength to resist the factored loads. In addition, the theoretical strength of the member is reduced by the application of a resistance factor.Load Resistance Factor Design (LRFD)-하중저항계수설계법

① 각 하중의 불확실성을 각 하중계수로 적절하게 고려할 수 있음

② 강도저감계수도 파괴모드에 따라 불확실성이 다른 것을 고려하고 있음.

[예제] 정사각형 보에서의 P=120 kN 의 축하중이 작용하고,

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1. 설계식 (극한강도설계법)

Pu, Vu, Mu는 하중계수 포함되어 있음

Pn, Vn, Mn은 공칭강도임

2. 보부재 + 일방향슬래브부재 1) 휨 2) 전단

3. 기둥부재 1) 압축 2)압축+휨

4. 기초 1) 전단 (일방향, 이방향) 2)휨

1. 설계식 (극한강도설계법)-하중계수

2003기준 2007기준

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강도감소계수

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1.5 30.077 ( ) (3.4.1)c c cuE m f MPa=

38500 ( ) (3.4.1)c cuE f MPa=

� KCI 2007 :

o 콘크리트의 할선탄성계수는 콘크리트의 단위질량 mc 의 값이 1,450~2,500 kg/m3 인 콘크리트의 경우

o 다만 보통골재를 사용한 콘크리트(mc=2,300 kg/m3)의 경우

여기서, fcu = fck + 8 (MPa)

o 크리프 계산에 사용되는 콘크리트의 초기 접선탄성계수와 할선탄성계수와의 관계

Ec = 0.85 Eci (3.4.3)

용어

fck: 콘크리트 설계기준 압축강도 fcu: 재령 28일 콘크리트 평균 압축강도 fcr: 콘크리트 배합강도

2-7 REVISIONS TO LOAD FACTORS AND LOAD COMBINATIONS IN THE 2002 ACI CODEThe 2002 ACI Code presents two separate but intertwined revisions to the load factors, load combinations, and resistance

factors. The new load factors and load combinations in ACI 318-02 Sections 9.2.1 through 9.2.5 are from ASCE 7-98, Minimum Design Loads for Buildings and Other Structures[2-2],with slight modifications. The load factors from ACI 318-02 Section 9.2 must be used with the strength reduction factors in ACI 318-02 Sections 9.3.1 through 9.3.5. The previous ACI load combinations and resistance factors have been moved to code Appendix C of the 2002 Code. Sections C.2.1 through C.2.7 and Sections C.3.2.1 through C.3.5. The new load factors and strength reduction factors were derived in [2-7] for use in the design of steel, timber, masonry, and concrete structures and are used in the AISC LRFD Specification for steel structures. For concrete structures, new resistance factors compatible with the new load factors were derived by ACI Committee 318 and Nowak and Szerszen [2-10].

The primary changes are as follows:1. The load factors and load combinations in Appendix C of the 1999 Code were interchanged with those in Sections

9.2 and 9.3 of the 1999 Code.It was the intent of ACI Committee that the traditional ACI load factors and load combinations, currently in Appendix C of the 2002 code, would be deleted in the 2008 Code leaving Sections 9.2.1 and 9.3.2 as the only source of load factors, load combinations and strength reduction factors in future editions of ACI 3182. The second revision changed the way that the ACI code distinguishes between ductile and brittle members when

selecting strength reduction factors, Φ. Traditionally, the 1999 and earlier codes assigned a Φ factor of 0.9 for ductile flexural failures of beams and slabs, and Φ factors of 0.7 to 0.75 for brittle failures of tied and spiral columns, respectively. These factors were based on arbitrary conceptions of what constituted ductile and brittle failures. The definitions of ductility used to define the strength reduction factors for beam, slabs, and columns in the 2002 code are based on the curvatures computed from the strains in the tension steel at the ultimate limit state. In this sense the curvature is used as a measure of the ductility of beams, slabs, or columns. Load factors and load combinations are discussed in this chapter. The new strength reduction factors, Φ, will not be discussed until the necessary flexural theory has been developed in Chapters 4, 5, and 11.

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Terminology and Notation

The ACI Code uses the subscript u to designate the required strength, which is a load effect computed from combinations of factored loads. The sum of the combination of factored load is U as, for example, in

. .U 1 2D 1 6L= + (2-4)Where the symbol U and subscript u are used to refer to the sum of the factored loads in terms of loads, or

in terms of the effects of the factored loads, uM , uV , uP .The member Strengths computed using the specified material strengths, f'c (fck) and fy, and the nominal dimensions, b and

d shown on the drawings, are referred to as the nominal moment capacity, nM , or nominal shear capacity, nV , and so on. The usable strength or design strength is the nominal strength multiplied by a strength-reduction factor, Φ. The design equation is thus:

n uM Mf ³ (2-2b) n uV Vf ³ (2-2c)

Load Factors and Load Combinations from ACI 318-02 Sections 9.2.1 through 9.2.5. (The New Provisions) Load CombinationsThe safety provisions from ACI Chapter 9 will be presented first, followed by provisions in ACI Appendix C. Structural failures usually occur under combinations of several loads. In recent years these combinations have been presented in what is referred to as the companion action format. This is an attempt to model the expected load combinations. The load combinations in ACI 318-02 Section 9.2.1 are examples of companion action load combinations chosen to represent realistic load combinations that might occur. In principle, each of these combinations includes one or more (1) permanent loads (D,F and T) with load factors of 1.2, plus (2) the dominant or principal variable load (L, S, W, or others) with a load factor of 1.6, plus one or more (3) companion-action variable loads. The companion action loads are computed by multiplying the specified loads (L, S, W, or others) by companion action load factors between 0.2 and 1.0. The companion-action load factors were chosen to provide results for the companion actions loads that would be likely during an instance in which the principal variable load is maximized. In the design of structural members in buildings that are not subjected to significant wind or earthquake forces, and members unaffected by wind or earthquakes, the factored loads are computed from :

. ( )U 1 4 D F= + (2-5)

where D is the specified dead load and F is the load due to the weight and pressures of fluids with well-defined densities and in tanks in which the maximum height of the fluid is controlled. Because these equations are used in many chapters we will refer to them by their ACI members. For combinations including dead load; live load, L; and roof loads:

. ( ) . ( ) . ( , or , or )rU 1 2 D F T 1 6 L H 0 5 L S R= + + + + +

The terms in (2-5) through (2-12) may be expressed as direct loads (such as distributed loads from dead and live weight) or load effects (such as moments and shears caused by the given loads). The design of a roof structure, or the columns and footings supporting a roof and one or more floors, would take the roof live load equal to the largest of the three

loads ( , or , or )rL S R , with the other two roof loads in the brackets taken as zero. If any of T, F, of H is zero, the

corresponding term drops out of ACI Eq. (9-2). Thus, for the common case of a member supporting dead and live load

only, ACI Eq. (9-2) is written as : . .U 1 2D 1 6L= + (2-4)

If the roof load exceeds the floor live loads, or if a column supports a total roof load that exceeds the total floor live

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load supported by the column :

. . ( ,or ,or ) ( . or . )rU 1 2D 1 6 L S R 1 0L 0 8W= + + (2-7) (ACI Eq. 9-3)

The roof loads are principal variable actions in ACI Eq. (9-3), and they are companion variable actions in ACI Eq. (9-4) and (9-2).

. . . + . ( ,or ,or )rU 1 2D 1 6W 1 0L 0 5 L S R= + + (2-8) (ACI Eq. 9-4)

Wind load is the principal variable action in ACI Eq. (9-4) and is a companion variable action in ACI Eq. (9-3) Earthquake LoadsIf earthquake loads are significant :

. . . .U 1 2D 1 0E 1 0L 0 2S= + + + (2-9) (ACI Eq. 9-5)

where the load factor of 1.0 for the earthquake loads corresponds to a strength level earthquake which has a much longer return period, and hence is larger than a serviceloadearthquake.Iftheloadingcodeusedinajurisdictionisbasedonthesmallerserviceloadearthquake,theloadfactoronEis1.4 instead of 1.0 (ACI Section 8.2.1(c)).If the effects of dead loads stabilize the structure against wind or earthquake loads, as shown in Fig 2-7 :

. . .U 0 9D 1 6W 1 6H= + + (2-10) (ACI Eq. 9-6)

Or . . .U 0 9D 1 0E 1 6H= + + (2-11) (ACI Eq. 9-7)

Comparison of New and Old Load and Resistance Factors The new set of load and resistance factors in ACI 318-02 Sections 9.2 and 9.3 were chosen to give similar amounts of reinforcement in designs carried out by the two alternative sets of load and resistance factors [2-10]. There in one very significant departure from this goal, however. The resistance factor for flexure in the 2002 code was set at Φ = 0.9 [2-10] which is higher than the Φ = 0.80 or 0.85 needed to give the same designs as obtained previously. The new strength-reduction factor for flexure was established by a calibration of the ACI Code, which suggested that Φ = 0.90 gave safety levels for tension-controlled beams that were comparable to those for other structural actions [2-10].For a hypothetical case of a beam loaded in flexure by nominal dead and live loads D and L, with L half as big as D, the load and resistance factors in ACI Sections 9.2.1 through 9.2.5 and 9.3.1 through 9.3.5 give

( 2002f times the 2002 nominal resistance)≥(product of 2002 load factors and loads)

,( ) [ . ( . )] . . .2002 n 2002R 1 2 D 1 6 L 1 2D 1 6 0 5Df ³ ´ + ´ = + ´

, . /( )n 2002 2002R 2 0D f=

where for tension-controlled flexural failures, 2002f is taken equal to 0.90, giving

.nR 2 22D³This compares with the factored strength ratio from Chapter 9 of ACI 318-99

,( ) ( . . . )1999 n 1999R 1 4 D 1 7 0 5Df ³ ´ + ´

Or , . / . .n 1999R 2 25D 0 9 2 5D³ =

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Thus, the 2002 load and resistance factors give structures with about 2.22/2.50=0.89 times as much flexural reinforcement as required by the ACI Codes from 1971 through 1999. A smaller amount of reinforcement resisting the same load means the service load stress in the steel will be higher in the 2002 design than in the 1999 design. This will result in larger crack widths and larger deflections than those expected for the 1999 code. Although fatigue is seldom a problem in reinforced concrete buildings, higher service load steel stresses may require that fatigue strength be considered if over 20,000 cycles of load are expected. A design must use one set of load and resistance factors either all from ACI Code Chapter 9 or all from Appendix C. For other limit states the difference between the traditional ACI load factors (in ACI 318-02 Sections C.9.2.1 through C.9.2.5) and the factors based on ASCE 7 (in ACI 318-02 Sections 9.2.1 through 9.2.5) is much less than the 9 percent provided for flexure. In examples in this book, the load and resistance factors in ACI 318-02 Sections 9.2 and 9.3 will generally be used.

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This computation is repeated for a sufficient number of sections to make it possible to draw shearing-force and bending-moment envelops for the beam. (Bending-moment envelops are discussed in Section 10-3.) The solution of the four equations given above can easily be programmed for a programmable calculator with D, L, and W as input values and the

seven values of U and/or the maximum positive and negative values of the factored load effect as output.