Simplified Shear Design of Structural Concrete Members: Appendixes (2005) / Chapter Skim
Currently Skimming:
Pages 150-188
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 150... ...
F-1 APPENDIX F: Recommended Revisions to Shear Provisions of AASHTO LRFD Concrete Provisions F.1 Scope This Appendix details the revisions to the shear provisions of Section. 5.8.3 of the LRFD Provisions recommended as a result of this study.
|
From page 151... ...
F-2 effective as that at a distance greater than "dv" from the support. The MCFT, the basis for the existing AASHTO LRFD shear provisions, was derived from tests on plate elements uniformly loaded along their edges.
|
From page 152... ...
F-3 The limitation on shear strength is principally imposed to guard against diagonal compression failure. The diagonal compressive stress, fd is determined as, = ( sin cos )
|
From page 153... ...
F-4 LRFD method while largely eliminating the need for the iterative procedures of the current LRFD method. Therefore, modification of the current general procedures of Section 5.8.3.4.2 of the current LRFD method by adoption of the CSA 2004 method is proposed.
|
From page 155... ...
F-6 7) Truss Model with Crack Friction; 8)
|
From page 156... ...
F-7 is 2500 psi plus the stress that is taken by the vertical component of the prestressing. By contrast, the AASHTO STD and ACI 318-02 limit is just 1000-1400 psi.
|
From page 157... ...
F-8 Thus, the web-shear cracking force, cwV , can be expressed as: cw cw v vV v b d= (F-13) Consistent with the current specifications it is suggested that vd need not be taken less than the greater of 0.9 ed or 0.72h , where ed is effective depth and h is overall depth.
|
From page 158... ...
F-9 Fig. F-4 illustrates the web-shear cracking strengths calculated by AASHTO STD (& ACI 318)
|
From page 159... ...
F-10 '0.63 cr ci c v v d V MV f b d V M = + + (in. and psi units)
|
From page 160... ...
F-11 Thus, cot 1 pc t f fθ = + , and this equation can also be linearized using the first two terms of a Taylor Series expansion as: cot 1 0.36 pc t f fθ = + (F-29) Figure F-7 compares the angles of inclination of the strut from Eqs.
|
From page 161... ...
F-12 recommended minimum amount of shear reinforcement is the same as the current LRFD requirement: 0.0316 ' vv c y b sA f f≥ (in. and ksi units)
|
From page 163... ...
F-14 5.8.3.1 General The sectional design model may be used for shear design where permitted in accordance with the provisions of Article 5.8.1 C5.8.3.1 In the sectional design approach, the component is investigated by comparing the factored shear force and the factored shear resistance at a number of sections along its length. Usually this check is made at the tenth points of the span and at locations near the supports.
|
From page 164... ...
F-15 Figure 5.8.3.2-1 Critical Section for Shear. Otherwise, the design section shall be taken at the internal face of the support.
|
From page 165... ...
F-16 Figure C5.8.3.2-3 Simplified Design Section For Loads Applied at or Above the Middepth of the Member. If the significant portion of the loads being resisted by the member are applied at a bearing resting on top of the member, the shear failure zone extends for a distance of approximately dv cot θ beyond the point of load application as shown in Figure C4.
|
From page 166... ...
F-17 If the shear stress at the design section calculated in accordance with 5.8.2.9 exceeds 0.18f'c and the beamtype element is not built integrally with the support, its end region shall be designed using the strut-and-tie model specified in Article 5.6.3. Figure C5.8.3.2-4 Effective Transverse Reinforcement to Members Subjected Primarily to Concentrated Loads.
|
From page 167... ...
F-18 down into the end bearing. Where the beam has a thin web so that the shear stress in the beam exceeds 0.18f'c, there is the possibility of a horizontal shear failure along the interface between the web and the lower flange of the beam.
|
From page 168... ...
F-19 Av = area of shear reinforcement within a distance s (in.2) Vp = component in the direction of the applied shear of the effective prestressing force; positive if resisting the applied shear (kip)
|
From page 169... ...
F-20 Vi = factored shear force at section due to externally applied loads occurring simultaneously with Mmax (kip) Mcr = moment causing flexural cracking at section due to externally applied loads (kip-in)
|
From page 170... ...
F-21 • Vcw shall be determined by pvvpcccw VdbffV ++= )
|
From page 172... ...
F-23 with the denominator of the equation replaced by 2(EsAs+EpsAps+EcAct) , except that εx shall not be taken less than –0.20 x 10-3.
|
From page 173... ...
F-24 which are terminated at a distance less than their development length from the section under consideration shall be ignored fpo = a parameter taken as modulus of elasticity of prestressing tendons multiplied by the lockedin difference in strain between the prestressing tendons and the surrounding concrete (ksi)
|
From page 174... ...
F-25 Figure 5.8.3.4.3.2-1 Illustration of Shear Parameters for Section Containing at Least the Minimum Amount of Transverse Reinforcement, Vp=0.
|
From page 175... ...
F-26 Figure 5.8.3.4.2-2 Longitudinal Strain, εx for Sections Containing Less than the Minimum Amount of Transverse Reinforcement. Figure 5.8.3.4.32-23 Definition of Crack Spacing Parameter, sx.
|
From page 176... ...
F-27 Figure C5.8.3.4.3.2-1 Detailed Sectional Analysis to Determine Shear Resistance in Accordance with Article 5.8.3.1. Figure C5.8.3.4.3.-2 More Direct Procedure to Determine Shear Resistance in Accordance with Article 5.8.3.4.3.2.
|
From page 177... ...
F-28 Figure C5.8.3.4.3.2-4 Assumed Relations Between Axial Force in Flange and Axial Strain of Flange.
|
From page 178... ...
F-29 Figure C5.8.3.4.3.2-5 Flow Chart for Shear Design of Section Containing at Least Minimum Transverse Reinforcement. Start Determine bv and dv, Calculate Vp.
|
From page 179... ...
F-30 Figure C5.8.3.4.2-6 Typical Shear-Moment Interaction Diagram. More details on the procedures used in deriving the tabulated values of θ and β are given in Collins and Mitchell (1991)
|
From page 180... ...
F-31 Table 5.8.3.4.2-2 Values of θ and β for Sections with Less than Minimum Transverse Reinforcement.
|
From page 181... ...
F-32 area required to resist the maximum moment acting alone. This provision applies where the reaction force or the load introduces direct compression into the flexural compression face of the member.
|
From page 182... ...
F-33 Although it is sometimes convenient to design for the highest torsion combined with the highest shear, it is only necessary to design for the highest shear and its concurrent torsion, and the highest torsion and its concurrent shear. 5.8.3.6.2 Torsional Resistance The nominal torsional resistance shall be taken as: 2 cot o t y n A A f T = s θ (5.8.3.6.2-1)
|
From page 183... ...
F-34 Aoh = area enclosed by centerline of exterior closed transverse torsion reinforcement, including area of any holes (in.2) Tu = factored torsional moment (kip-in.)
|
From page 184... ...
F-35 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.05 0.1 0.15 0.2 0.25 Ratio of v/f'c Ra tio o f V s/ Vn Vs Vc Figure F-1 Influence of Shear Stress Design Ratio on Fraction of Shear Supported by Stirrups fv v y v x 1 2 v σ fpc v v v ( fpc, v )
|
From page 186... ...
F-37 Figure F-5 Derivation of Flexure-Shear Cracking Force, ciV (a) Cross section V M M = 0 s 0.5Nv jd cos θ A fv v f2 f2 f2 D jd bw s (b)
|
From page 187... ...
F-38 15 20 25 30 35 40 45 50 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 fpc/ft th et a (d eg s ) Figure F-7 Comparison of the Angle of Inclination of Strut 15 20 25 30 35 40 45 50 0 2 4 6 8 10 12 14 th e ta (de gs )
|
From page 188... ...
F-39 Figure F-9 Flowchart of Simplified Shear Design Procedure START Given: vb , vd , maxM , cf ' , pV , uN , uV , uM , pcf , puf , pA where cf ' is in ksi. Required shear strength for shear reinforcement: cus VVV −= φ/ where 9.0=φ .
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.