Identifying The Problem

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Herbert Woods
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1 FLEXURAL DESIGN, _~ê= development, hooked bars UNIVERSITY OF WISCONSIN STOUT COLLEGE OF SCIENCE, TECHNOLOGY, ENGINEERING, AND MATHEMATICS LECTURE IV Dr. Jason E. Charalambides = = Identifying The Problem =The forensics: We often see concrete reinforcement becoming exposed with concrete sliced and disengaged from the rest of the structural element. Besides the case of poorly cast concrete (e.g. honeycombing etc.), geometric formation and physics/statics may be the reason behind the result.

2 How Does Development Length Work? But as the form of the concrete locks the bars in place, with every application of forces, these forms experience stresses that generate reactions. Thus a significant amount of surfaces of both steel and concrete need to be in contact in order to allow those stresses to be transferred to the volume of the beam. The deeper the rebar, the more surface will be in contact, the better the dissipation of the stress (generated by the tension applied on the steel) within the concrete. Insufficient development length at the top of column. Source: Oct.2009

3 How Does Development Length Work? Nevertheless, the depth of the rebar is not the only factor. Think of this issue in terms of physical scale, as well as numerical scale that pertains to the strength of the materials. Default conditions (see next slide for definition) What if we have very strong rebars and very mild concrete, or vice versa, and what about the location of the bars within the beam (top rebars vs bottom rebars)? α=location factor=1 or 1.3 if top bars β=bar coating factor=1.0 if not coated, or 1.2 or 1.5 (accordingly) if bars are coated λ=concrete density factor=1 or 1.3 if lightweight concrete More Detail in Formula Favorable bar placement conditions require that: Clear cover and clear spacing of bars is db or greater when there are transverse ties or stirrups as it happens in most beams, or Clear cover is more than db and spacing between bars is greater than 2db where ties and stirrups are not present as in the case of slabs For default formula: c=dimension from center of bar to edge of section. Ktr=transverse reinforcement ratio.

4 Graphic Method Graphic Method The Shortest possible graph yields its results from the highest permissible value of [(c+kv)/db]=2.5 The central value referred as Usual is applicable where bars are placed inside stirrups or ties, and the clear spacing between bars as well as edge cover distance is at least as large as a bar diameter and more than 1in. If no stirrups or ties are present but the clear spacing between bars is at least 2 bd, the Usual graph is applicable again. The Worst case gives values 50% higher than the Usual.

Hooked Bars Framing conditions may limit the space to develop tensile strength along a straight bar, imposing a condition where bars may be bent

5 Hooked Bars Framing conditions may limit the space to develop tensile strength along a straight bar, imposing a condition where bars may be bent 90º or hooked. ldh can be much shorter than ld. ldh is measured from outer edge of hook. See following chart: Hooked Bars Cont (Grade 50, & 4ksi conc.)

Development of Bars in Continuous Beams Inside bend radii must be no less than 6db for bars #3 through #8, 8db for bars #9 through #11, and 10db for larger bars.

6 Development of Bars in Continuous Beams Inside bend radii must be no less than 6db for bars #3 through #8, 8db for bars #9 through #11, and 10db for larger bars. Compression bar development length can be much shorter: It can be noted that ldc=ldh for the materials strengths f`c=4ksi and fy=60ksi Development of Bars Through Lap Splices 1. Lap splices are restricted to #11 or smaller 2. Class B Tension Splice length shall be 1.3 ld 3. Class A Tension Splice length=1.0ld may be used if: Fewer than half of the bars are spliced at the same location, or Bar stress developed is less than fy/2 1. Compression Splice Length shall be 30 db but not less than 12 in. 2. Compression splice length for bars higher than Grade 60 shall be (0.9 fy-24)db with fy expressed in ksi. 3. Compression splices within spiral columns may be 75% as long but no less than 12 in.

7 Where is Anchorage Required? Bar Development Anchorage At least 1/3 of bottom bars required for +ve moment must extend at least 6 in into supports of simply supported beams. At least 1/4 of bottom bars required for +ve moment must extend at least 6 in into supports of continuous beams. At least 1/3 of top bars required for -ve moment must extend beyond the point of inflection associated with ve moment. Continuing bars for flexure must extend beyond the point at which they are required for a distance at least 12db or the depth of the member d.

8 No Hassle Bar Detailing Exterior Spans No Hassle Bar Detailing Exterior Spans

9 No Hassle Bar Detailing Interior Spans In Class Example: Steel Grade is 75 and f`c=5ksi. Calculate the ld for both top and bottom bars.

10 Reading Reading: Req: Furlong, Chapt. 5 Recom: McCormac & Nelson, Chapter 7 for this lecture.

> 0. 1 f, they are treated as beam-columns.

> 0. 1 f, they are treated as beam-columns. 223 A- Flexural Members (Beams) of Special Moment Frames Requirements of ACI 21.5 are applicable for special moment frame members proportioned primarily to resist flexure with factored axial forces 0.