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From page 43... ... B-1 Appendix B: Shear Design Provisions This appendix presents the shear design provisions in the most widely used national codes of practice, together with other significant emerging design approaches. The shear design provisions in existing codes of practice are presented in Section B.1. Read the entire page →
From page 44... ... B-2 The steel contribution Vs is calculated based on the 45o truss model as: s dfAV vvs = (B-4) where dbfV wcs '8≤ (in., psi) Read the entire page →
From page 45... ... B-3 prestressing force, cV , sV , and pV , respectively. The cV term is the shear force causing first diagonal cracking while sV is calculated by the 45 o truss analogy of Eq. Read the entire page →
From page 46... ... B-4 The Specifications permit two methods for calculating cwV . The first method is by limiting tf to '4 cf (psi) Read the entire page →
From page 47... ... B-5 2 6.0 ' d V M MVdbfV crdwcci − ++= (in., psi) Read the entire page →
From page 48... ... B-6 ty = distance from centroidal axis of gross section, neglecting reinforcement, to extreme fiber in tension I = moment of inertia about the centroid of the cross section Note that while the vertical component of the prestressing, pV , adds to the shear strength cwV for web-shear cracking, there is no effect of the same vertical component on the shear strength for flexure-shear cracking, ciV . Thus, draping strands increases the web-shear cracking load but can actually decrease the flexure shear cracking load by decreasing the effective depth, d . Read the entire page →
From page 49... ... B-7 all actions on a section, including prestressing, axial loading, and flexure, in the determination of the required amount of shear reinforcement. This approach represents a significant departure from the ACI and AASHTO Standard Specifications in which additional shear design relationships are required for the design of sections subjected to combined actions. Read the entire page →
From page 50... ... B-8 less than the minimum shear reinforcement. The reason for dividing members into two categories is that members having at least the minimum required amount of transverse reinforcement will have well-distributed diagonal cracks. Read the entire page →
From page 51... ... B-9 The crack spacing parameter, zs , needs to be determined to calculate the shear strength for members without shear reinforcement. The crack spacing parameter, zs , is the lesser of vd and the maximum distance between layers of crack control reinforcement but does not need to exceed 2000 mm. Read the entire page →
From page 52... ... B-10 LRFD specifications, the CSA specifications presented below were developed to provide a simpler way to obtain θ and β . In this proposed method, the iteration procedure was removed for design purposes by taking θ = 30 degrees for evaluating the demand of shear on the longitudinal reinforcement. Read the entire page →
From page 53... ... B-11 xεθ 700029 += (B-38) and the coefficient, β , is obtained from Eq. Read the entire page →
From page 54... ... B-12 x d5.2=β , ) 0.50.1( ≤≤ β is an enhancement factor that can be applied if the member is loaded by a concentrated load situated at a distance, dx 5.2≤ , from the face of the support. Read the entire page →
From page 55... ... B-13 resistance is considered using flatter truss angles. The shear resistance of members with shear reinforcement is: θcot) Read the entire page →
From page 56... ... B-14 B.1.7.1 General Remarks The Eurocode EC2, part 1 (1991) has been revised and the final revised draft was published in April 2003 for comments by the different European nations. Read the entire page →
From page 57... ... B-15 slA =the area of the tensile reinforcement, which extends bdl d+ beyond the section considered, where bdl is a bond development length (see Fig. Read the entire page →
From page 58... ... B-16 θ = the angle between inclined concrete struts and the main tension chord wb = the minimum width between tension and compression chords z = the inner lever arm, for a member with constant depth, corresponding to the maximum bending moment in the element under consideration. In the shear analysis of reinforced concrete without axial force, the approximate value 0.9z d≈ may be used. Read the entire page →
From page 59... ... B-17 B.1.8 German Code DIN 1045-1 (2001) B.1.8.1 General Remarks In 2001 the new German code DIN 1045-1 was published and thereby replaced the previous codes DIN 1045 (1988) Read the entire page →
From page 60... ... B-18 EdN = design value of the axial force in the cross-section due to loading or prestressing ( EdN < 0 for compression) cA = area of concrete cross section (mm 2) Read the entire page →
From page 62... ... B-20 ydV = design shear capacity, and wcdV = design ultimate diagonal compressive capacity of web concrete. It is assumed that, after inclined cracking, the shear force is carried by shear reinforcing steel and that the load carrying system is a truss type mechanism. Read the entire page →
From page 63... ... B-21 where edP = effective prestress force in the longitudinal tendon pα = angle between prestressing force and the longitudinal axis of member and bγ = 1.15 For lightweight concrete Eq. Read the entire page →
From page 64... ... B-22 Clause 3.10.3.1 Because inclined cracking can significantly influence the durability of a structure, examination is required for shear cracking at the serviceability limit state. No examination is required if: (1) Read the entire page →
From page 65... ... B-23 (2) The use of a constant value of 45 degrees for the angle of inclination for truss diagonals in beams with shear reinforcement. Read the entire page →
From page 66... ... B-24 to vary linearly from zero, at the point where bonding begins, to a maximum at the end of the transfer length. The transfer length is taken as 50 strand diameters. Read the entire page →
From page 67... ... B-25 The applied shear Vu in regions near supports may be reduced to the value at h/2 from the supports when both the following are satisfied: the support reaction in the direction of the applied shear introduces compression into the support region of the member; and no concentrated load occurs within a distance h from the face of the support. B.2 Other Shear Design Approaches B.2.1 Concrete Shear Strength: Another Perspective - A Read the entire page →
From page 68... ... B-26 For design purposes, Frosch et al. have proposed the following simplified equation for the shear strength of the concrete members: cbfV wcc '5= (psi and in.) Read the entire page →
From page 69... ... B-27 but not more than jdb'180 or (1.241 jdb' ) where 1.241 is in units of MN/m2 . Read the entire page →
From page 70... ... B-28 s dfA s dfA V yvvyvs ≈= nV sb A w v v =ρ sV cV Fig. B-1 Concrete and Steel Contributions to Shear Strength 0 100 200 300 400 500 600 Distance from simple support dbfV wcc '5= dbfV wcc '2= 15 1=l d 20 1=l d 25 1=l d 30 1=l d 8 l 8 3l 2 l ) Read the entire page →
From page 71... ... B-29 Web-Shear Crack Flexure-Shear Crack Fig. B-3 Typical Shear Cracks in Prestressed Concrete Members fv v y v x 1 2 v σ fpc v v v ( fpc, v ) Read the entire page →
From page 72... ... B-30 0 2 4 6 8 10 0 2 4 6 8 10 12 14 16 18 ' cpc ff ' ' 5.3 15.3 c pc c w pcw f f f db VV +=− pcc w pcw ff db VV 3.05.3 ' +=−dbf VV wc pcw ' − Fig. B-5 Approximation of Web-Shear Cracking Force, cwV d/2 V M d/2 mid-span Fig. Read the entire page →
From page 73... ... B-31 Flexural tension side bw Act As sz =dv sz 0.003b szwArea > εx h/2 h/2 Fig. B-7 Terms in Shear Design Equations (Collins, 2002) Read the entire page →
From page 74... ... B-32 1= strut, 2=compression chord, 3=tie; shear reinforcement, 4=tension chord; longitudinal reinforcement Fig. B-10 Truss Model and Notation (Reineck, 2001) Read the entire page →
From page 75... ... B-33 Figure B-13 Free-Body of Cracked Concrete Member Figure B-14 Mohr's Stress Circle Read the entire page →
From page 76... ... B-34 Table B-1 Design Values of β and θ for Members with Transverse Reinforcement Longitudinal Strain, 1000xε × ' * Read the entire page →
From page 77... ... B-35 Table B-3 Design Values of β and θ for Members with Transverse Reinforcement Longitudinal Strain, 1000xε × ' * Read the entire page →
From page 78... ... B-36 Table B-4 Design Values of β and θ for Members without Transverse Reinforcement Longitudinal Strain, 1000xε × xes * Read the entire page →
From page 79... ... B-37 Table B-6 γ Factor Consideration Table B-7 Standard Values for γ Factors Material Factor mγ * Safety factor Limit States for Concrete cγ for Steel sγ Member Factor, bγ Structural Analysis Factor,  aγ Load Factor, fγ Structure Factor, iγ Ultimate Limit State 1.3 1.0 1.15 ~ 1.3* Read the entire page →
From page 80... ... B-38 Table B-8 Application of γ Factors Capacity Member force Characteristic value for material strength kf Characteristic value for load kF mγ fγ Design value for material strength /d k mf f γ= Design load ) d f kF Fγ ψ= ∑ Capacity of member cross section ( ) Read the entire page →

From page 43...

... B-1 Appendix B: Shear Design Provisions This appendix presents the shear design provisions in the most widely used national codes of practice, together with other significant emerging design approaches. The shear design provisions in existing codes of practice are presented in Section B.1.