EXAMPLE 9.2– Part VI PCI Bridge Design Manual 2011/12 Edition EXAMPLE 9.2– Part VI PCI Bridge Design Manual BULB “T” (BT-72) THREE SPANS, COMPOSITE DECK LRFD SPECIFICATIONS Materials copyrighted by Precast/Prestressed Concrete Institute, 2011. All rights reserved. Unauthorized duplication of the material or presentation prohibited.

ALTERNATE SHEAR DESIGN In Version 4 of the LRFD Specifications, AASHTO restored the use of Vci and Vcw from the old Standard Specifications. This was the result of NCHRP Report 549. Concluded that the sectional method (modified compression field) was more accurate. However, even the most accurate method has a COV of 25% While conservative, this method is not unreasonable for design. Modified to cover both prestressed and non prestressed members.

ALTERNATE SHEAR DESIGN 2011/12 Edition Flexural shear – Vci and Web Shear - Vcw The flexural shear capacity, Vci, is the shear force required to cause a flexural crack to “bend over” and become a shear crack. (This is conservative because the cracks bend over long before the strut will crush!). The web shear capacity, Vcw is the shear force that causes a diagonal crack in the web, usually near the support.

ALTERNATE SHEAR DESIGN 2011/12 Edition Flexural shear - Vci It is much easier to understand Vci if you look at the derivation. To find Vci, it is first necessary to determine the shear in the section when the beam cracks. A prestressed beam will form a flexural crack when the moment at a section reaches Mcr. The shear at the section which exists at the time of cracking is called Vcr. Note that the beam cracks due to moment, not shear. Vcr is the shear in the section associated with Mcr.

ALTERNATE SHEAR DESIGN 2011/12 Edition Flexural shear - Vci Experiments have shown that if the shear at the section increases by 0.02(fc’)bvdv, the flexural crack will grow to a shear crack. The flexural shear strength can be written as: Note that this is the same increment as in the old Standard Specification, just changed to KSI units!

ALTERNATE SHEAR DESIGN 2011/12 Edition Flexural shear - Vci The term Vcr is the shear in the section when the section cracks at Mcr. It is assumed that the shear and the moment increase proportionally:

ALTERNATE SHEAR DESIGN 2011/12 Edition Flexural shear - Vci It was assumed that the shear and moment increase proportionally. However, the dead load doesn’t increase proportionally, so subtract it out of the proportionality portion of the equation. The equation becomes:

ALTERNATE SHEAR DESIGN 2011/12 Edition Flexural shear - Vci Mcre must be adjusted to reflect the fact that the dead load effect has been accounted for: Where Sc = composite section modulus fr = modulus of rupture = 0.2√fc’ (5.4.2.6) fcpe = compression stress at the flexural tension fiber due to effective prestressing force Mdnc = moment applied to the non-composite section Snc = non-composite section modulus. 5.8.3.4.3-2

ALTERNATE SHEAR DESIGN 2011/12 Edition Flexural shear - Vci There is a limit placed on Vci : For a composite section, the Commentary of 5.8.3.4.3 permits: Vi = Vu – Vd and Mmax = Mu – Md Where Vu and Mu are the FACTORED total shear and moment while Vd and Md are the UNFACTORED dead load shear and moment. 5.8.3.4.3-1

ALTERNATE SHEAR DESIGN 2011/12 Edition Web shear - Vcw In a beam, there are shear stresses from flexure. The maximum shear stress occurs at the neutral axis. For most beams, there is no normal stress at the neutral axis. However, in a prestressed beam there is a normal stress from the P/A term in the stress equation. In a composite beam, the neutral axis of the composite beam is not the same as in the non-composite beam. At the neutral axis of the composite section, there will also be normal stresses from bending, caused by the prestressing and the dead load applied to the non-composite section.

ALTERNATE SHEAR DESIGN 2011/12 Edition Web shear - Vcw The normal stress fpc is:

ALTERNATE SHEAR DESIGN 2011/12 Edition Web shear - Vcw Vcw can be calculated using the shearing stress equation v = (VcwQ)/(It), where v is the shear stress which causes a maximum principal tensile stress of 4(fc’)½ psi when the normal stress is fpc:

ALTERNATE SHEAR DESIGN 2011/12 Edition Web shear - Vcw In place of the calculation of principal stress, the following approximate equation may be used: 5.8.3.4.3-3 Vp is the vertical component of prestressing force from harped strands. fpc is the axial stress in centroid of the cross section due to effective prestressing force

ALTERNATE SHEAR DESIGN For shear stirrups, the theta angle is needed: 5.8.3.4.3-4 Remember,  is the angle between the longitudinal axis of the beam and the stirrups. For normal, upright stirrups,  = 90o.

ALTERNATE SHEAR DESIGN Check Vci and Vcw at 0.2L Using the values of shear and moment calculated in the table in the Bridge Manual: Mu = 1.25(873+1335-24)+1.5(-42)+1.75(1044) = 4494 k-ft Vu = 1.25(28.8+44.0+5.0)+1.5(10.0)+1.75(113.8) = 311.4 k

ALTERNATE SHEAR DESIGN Next, the UNFACTORED non-composite shear and moment are needed Mdnc = (873+1335-24) = 2184 k-ft Vd = (28.8+44.0+5.0) = 77.8 kips

ALTERNATE SHEAR DESIGN Article 5.8.3.4.3 states that Mmax is the FACTORED moment from all superimposed loads. Vi is the FACTORED shear at the section associated with Mmax. It is NOT necessarily the maximum shear due to superimposed loads at the section!

ALTERNATE SHEAR DESIGN As previously stated, the Commentary of 5.8.3.4.3 states that, for composite sections it is permissible to use: Vi = Vu – Vd Mmax = Mu – Md

ALTERNATE SHEAR DESIGN Now find the cracking moment. From previous calculations: P = 1071 k (after all losses) e = 25.8 inches (at 0.2L = 24 ft)

ALTERNATE SHEAR DESIGN Note that Sc = Sbc and Snc = Sb. Mdnc must be in K – IN!

ALTERNATE SHEAR DESIGN Note that Vi and Vd are in KIPS. Mmax and Mcre must have the same units.

ALTERNATE SHEAR DESIGN 2011/12 Edition Web shear - Vcw The normal stress fpc is:

ALTERNATE SHEAR DESIGN Web shear - Vcw Vcw controls!

ALTERNATE SHEAR DESIGN Assuming #5 @ 24 inches and =90o:

ALTERNATE SHEAR DESIGN Finally: OK!