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12 Pages

### Term%20Project%20Shear

Course: SE 151A, Spring 2012
School: UCSD
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Word Count: 604

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Project Term Shear Slide 1 ACI &amp; AASHTO ACI and AASHTO have different approaches (and notation) for the design for shear ACI uses an empirical, and simple, approach based on a 45 degree angle truss model. Factor = 0.75. AASHTO follows the latest developments and uses an approach based on strain compatibility and equilibrium (modified compression field theory). The critical diagonal crack does not...

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Project Term Shear Slide 1 ACI & AASHTO ACI and AASHTO have different approaches (and notation) for the design for shear ACI uses an empirical, and simple, approach based on a 45 degree angle truss model. Factor = 0.75. AASHTO follows the latest developments and uses an approach based on strain compatibility and equilibrium (modified compression field theory). The critical diagonal crack does not have to be at 45 degrees. Factor = 0.90. In our term project we will use a simplified version of AASHTO and will set the angle of the diagonal crack at 45 degrees Term Project Shear Slide 2 Effective Girder (Beam) Dimensions For shear design, effective dimensions are used to explicitly account for shear flow through a section. LRFD 5.8.2.9 The effective shear depth, dv, is the distance between the resultant compressive and tension forces. However, dv needs not be taken less than the greater of: 90% of the distance from the extreme compression fiber to the center of action of the reinforcing steel (jd=0.9d) 72% of the total section height In your project make dv = min(0.9d+, 0.9d-) The effective web width, bv, is the minimum web width anywhere across the section Term Project Shear Slide 3 AASHTO: Shear Design Approach Variable angle truss mechanism Vn = Vc + Vs Vc = 0.083 fc' bw d (normal weight concrete) and Vs = Av fyt jd up to a point s tan ( ) Coefficient and angle are determined u sing strain compatibility and equilibrium (outside the scope of 151A) For simplicity we will make = 45o and = 2 = 0.9 C s A v fy jd T jd /tan() Term Project Shear Slide 4 Shear Force Limit (Diagonal Compression Failure) ACI-318 11.4.7.9: Maximum shear resiste d in a section: Vn = 0.25 fc' bv dv Term Project Shear Slide 5 Design Cases Vu Vn Factored demand Factored capacity Any design will fall within the following 5 possible cases: Vu 1 2 3 4 v. high low low moderate high 5 v. (diagonal compression failure) Vu >0.25fc bvdv shear cannot be resisted Increase fc, bv and/or dv 0.25fc bvdv Vu > 0.125fc bvdv - Shear reinforcement as per truss mechanism Reduced stirrup spacing: s min(0.4dv, 300 mm) 0.125fc bvdv Vu > Vc - Shear reinforcement as per truss mechanism Stirrup spacing: s min(0.8dv, 600 mm) Vc Vu > Vc/2 - provide minimum shear reinforcement Stirrup spacing: s min(d/2, 600 mm) Vu Vc/2 - shear reinforcement is not needed Term Project Shear Slide 6 Design Cases Case 1 Vu very low shear force demand: Vc shear reinforcement is not needed 2 Design case typically found in solid slabs and in column footings: Term Project Shear Slide 7 Design Cases Case 2 low shear force demand: Vc Vu > Vc provide minimum shear reinforcement 2 A v,min = 0.083 fc' fyt bv s s min ( 0.8dv , 600mm ) Term Project Shear Slide 8 Design Cases Case 3 moderate shear force demand: 0125 fc' bv dv Vu > Vc shear reinforcement as per truss mechanism. . Vu ( Vc + Vs ) Vu d Vc but for =45o Vs = Av fyt s V s 1 Av u Vc dv fyt Vs s min ( 0.8dv , 600mm ) Term Project Shear Slide 9 Design Cases Case 4 high shear force demand: 0.25 fc' bv dv Vu > 0125 fc' bv dv shear reinforcement as per trus s mechanism. . Vu ( Vc + Vs ) Vu d Vc but for =45o Vs = Av fyt s V s 1 Av u Vc dv fyt Vs s min( 0.4dv , 300mm ) Term Project Shear Slide 10 Girder Flange Under Transverse Shear (Section 5b) A significant portion of the shear force is from the concrete flange dead load. Assume conservatively, the critical value for Vu is at the face of the girder Vu Vu Most likely Vu will check Case for shear reinforcement) 1 ok (i.e. no need Shear Force Envelope (absolute value) Term Project Shear Slide 11 Term Project Shear Slide 12
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