Click for next page ( 11


The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement



Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.

OCR for page 10
10 (Comment It may be prudent to reduce Vn by the torsional | Mu | shear when web crushing governs the capacity. Provisions for + 0.5 N u + 0.5 | Vu - Vp | cot - Aps f po dv considering the combined flexural shear and torsional shear are Calculate x = 2 (Es As + E p Aps ) required by Article 12.3.1 of the Segmental Guide Specification and LRFD Equation 5.8.6.5-3 for segmental bridges.) (Equation 5.8.3.4.2-1) using the equivalent factored shear force, Vu, determined in Step 4. Increase web width if Equation 5.8.3.3-2 is not satisfied. (Comment This simply adds the tensions due to flexural Step 4 Calculate Shear Stress shear and to torsion for the exterior web where the flexural shear and torsional shear are additive and appears to be con- Check if torsion must be considered: servative. Collins and Mitchell (1980) pages 399400, use an equivalent longitudinal tension for combined flexural shear Tu > 0.25Tcr (Equation 5.8.2.1-3) and torsion equal to the square root of the sum of the squares of 2 Acp f pc the individually calculated tensions for flexural shear and for Tcr = 0.125 fc 1+ (Equation 5. .8.2.1-4) pc 0.125 fc torsion.) If whole-width design is used, forces acting on the total sec- For Tu > 0.25Tcr, calculate the equivalent factored shear tion are applied. In this case, the shear force is conservatively force, Vu, acting on the web where the flexural shear and the taken as the equivalent factored shear force, Vu, determined torsional shear are additive as follows: in Step 4 multiplied by the total number of webs. Vu = Vu (flexure) + Tuds/(2Ao) (Equation 5.8.2.1-7) (Comment Whole-width design is not specifically addressed and would benefit from clarification in this area.) (Comment Vu is determined for a single girder and Tu is act- ing on the total cross section.) This accounts for the increased longitudinal tensile force General Comment The fifth paragraph of Commentary due to torsion and will be used to determine and from C5.8.2.1 regarding the equivalent factored shear force would Table 5.8.3.4.2-1. benefit from additional clarification. There is a mention of a Using the calculated values of v u /fc and x, find and stress limit for the principal tension at the neutral axis of the sec- from Table 5.8.3.4.2-1. tion but the specific code section was not referenced. Article 5.8.5 provides limits on the principal tensile stress in the webs of seg- Step 6 Determine Required Spacing mental concrete bridges at the Service III limit state and during of Stirrups construction. As the principal stresses are checked using service load, Vu is not applicable. It appears that the intent of the equiv- The amount of transverse reinforcement required for shear alent factored shear force is to consider the increased shear force is found from and resulting shear stress due to torsion in calculating x, , , and Vc. It appears that equivalent factored shear force should not Vu Vn be considered in determining the required shear capacity, Vn, or the required tensile capacity specified in Article 5.8.3.5. (Comment Clarify that the factored flexural shear, not the equivalent factored shear force, is used for Vu, as the transverse Using the equivalent factored shear force, Vu, acting on the reinforcement for torsion is determined separately.) exterior web where the flexural shear and the torsional shear are additive, calculate the shear stress as follows: Vn = Vc + Vs + Vp (Equation 5.8.3.3-1) vu = (Vu - Vp)/(bvdv) (Equation 5.8.2.9-1) Where (Comment Note that vu includes the effects of flexural shear and torsional shear.) Vc = 0.0316 fc bvdv (Equation 5.8.3.3-3) Vs = (Avfydvcot )/s (Equation C5.8.3.3-1) and x and Find Step 5 Calculate vu / fc Av/s = Vs/(fydvcot ) and The amount of transverse reinforcement required for tor- Calculate v u /fc using vu calculated in Step 4. This accounts sion is found from for the increased shear stress due to torsion and will be used to determine and from Table 5.8.3.4.2-1. Tu Tn