LRFD Minimum Flexural Reinforcement Requirements (2019) / Chapter Skim
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25 3.1 Introduction This chapter presents a summary of the experimental and analytical investigations completed for this project. In total, nine beams were tested: two reinforced concrete, three pre-tensioned concrete, three unbonded post-tensioned segmental concrete, and one bonded post-tensioned segmental concrete.
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26 The reinforced concrete girders, RC1 and RC2, were constructed in the Structural Engineering Laboratory at Iowa State University. After the rebar cage was completed, as shown in Figure 3-4, the formwork was constructed.
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27 Figure 3-2. External instrumentation layout used for Girder RC1.
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28 Metal Formwork Wooden Block-out Figure 3-6. Girder RC1 metal formwork rests on the wooden block-out.
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30 reinforcing bars on the basis of the coupon testing at a strain rate of 0.2 in./in./min. Concrete strengths for Girders RC1 and RC2 were evaluated periodically.
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31 Age (days) Compressive Stress (psi)
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32 Nebraska. They were then transported to the Structural Engineering Laboratory at Iowa State University, and a deck was constructed over a length in the midspan region of each girder where flexural cracking was expected to form.
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33 1 2 3 4 5 6 7 8 9 Figure 3-16. Strain gauge locations used in Girder BTC60.
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34 Strain Gauges Figure 3-18. Strain gauges as mounted to prestressed strand in Girder BTC60.
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Figure 3-20. External instrumentation used for Girder BTC60.
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36 screwed into the steel base to sufficiently counteract the shear and uplift forces from the wet concrete. The wooden formwork was also placed against the side steel formwork, which was bolted to the base through a series of angles attached to the formwork base.
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37 Girder Age (days) Compressive Stress, f c (psi)
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38 Percentage of Minimum Flexural Reinforcement Strands Girder f'c,design (%) f'c,experimental (%)
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39 Wooden Block-out Bulkhead Match Cast Pipe Brace Figure 3-32. Typical segment formwork and reinforcement.
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40 Figure 3-35. Application of temporary post-tensioning.
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Figure 3-39. External instrumentation used for Girder UNB1.
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Figure 3-40. External instrumentation used for Girder UNB2.
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Figure 3-41. External instrumentation used for Girder UNB3.
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Figure 3-42. External instrumentation used for Girder BON2.
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45 cells at the anchorage ends. The internal tendons required strain gauges to be secured to the strand before the strand was fed through the girder, and strain gauges for the external tendons were on both sides of the web.
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Age (days) Compressive Strength, f'c (psi)
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Age (days) Compressive Strength, f'c (psi)
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48 0 50,000 100,000 150,000 200,000 250,000 300,000 0 0.01 0.02 0.03 0.04 0.05 St re ss (p si) Strain (in/in)
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49 Material properties of 0.5-in.-diameter prestressing strand: Eps = 31.200 ksi fpy = 251 ksi fpu = 268.5 ksi eu = 0.043 in./in. Additional material tests were conducted on grout specimens for Girder BON2 and the epoxy utilized on all girders.
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50 Girder Height Span Cracking Load (kips) Failure Load (kips)
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51 lack of bonded reinforcement crossing the joints, the overstrength moment ratio is much closer to 1; the actual values ranged from 1.08 to 1.40. If the self-weight was included when the overstrength moment ratio was calculated, as it should be, the corresponding values ranged from 1.05 to 1.29.
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52 Figure 3-53. Girder RC1 deformation at failure.
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53 steel appears to have occurred when the load reached 50 kips and 23 kips for Girders RC1 and RC2, respectively, with Girder RC1 producing a higher resistance because of its larger section. The deflection profiles established for Girders RC1 and RC2 are shown in Figure 3-56 and Figure 3-57, while Figure 3-58 and Figure 3-59 show the recorded longitudinal strains from extreme #5 bars at the midspan of Girders RC1 and RC2, respectively.
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54 applied incrementally, as shown in Figure 3-66. The pausing of the loading allowed visual inspection and marking of the cracks.
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55 then were reloaded after the vibration tests. The displacements recorded during vibration tests never exceeded 0.25 in.
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57 applied incrementally in a quasi-static manner. After each load step, the test was paused, visual inspection was done, and cracks were located and marked on the front (south)
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60 increment of 1 in. without visual inspection, owing to safety concerns.
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61 beam experienced a small stiffness change due to cracking and reached 44.8 kips with a displacement of 1.08 in., which is followed by a drop in strength. This loss is suspected to be due to the beam shifting from the conventional flexural mechanism for transferring load to what appeared to be a hinging mechanism, which is detailed further in Section 3.5.2.
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62 Girder UNB2 was loaded incrementally in designated loading steps. After each load step, testing was paused and visual inspection was completed; during this time, cracks were identified and marked.
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63 The girder was visually inspected for damage after the application of 30, 60, and 90 kips. No further cracking was observed, except for the hairline crack from Day 1.
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64 strand at the midspan location is shown in Figure 3-87, which shows that the initial strain recorded due to prestressing was approximately 6.5 me. The tensile strain when the test was concluded was recorded to be 7.6 me.
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65 Figure 3-84. Girder UNB2 after failure.
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66 Figure 3-87. Load versus prestressing strand strain curve for Girder UNB2.
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67 7 in.4.5 in.
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68 Figure 3-90. Girder UNB3 after failure.
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69 Figure 3-93. Load versus midspan deflection curve for Girder UNB3.
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70 Figure 3-96. Load versus midspan deflection curve for Girder BON2.
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71 of Girder BON2 at various loads. The observed response, which was similar to that of the pre-tensioned girders, exhibited no concerns for experiencing a brittle failure, despite having been designed for less than the requirement for minimum reinforcement in the current AASHTO specifications (AASHTO 2017)
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72 converge after a certain nonlinear stage was reached. In other cases, especially RC and pre-tensioned girders, the analyses underestimated the deflection capacity, sometimes by a significant amount, due to debonding of the reinforcement that took place in the critical section regions.
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73 Figure 3-104. Experimental and calculated load versus displacement curves for Girder UNB2.
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74 crack. The width of the analytical crack is a function of rotation (q)
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75 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Cr ac k W id th (i n.
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76 0 0.0002 0.0004 0.0006 0.0008 0.001 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 St ai n (in ./ in .) Midspan Displacement (in.)
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77 0 0.0002 0.0004 0.0006 0.0008 0.001 0 1 2 3 4 5 St ra in (i n.
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78 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 10 20 30 40 50 60 N or m al iz ed D is pl ac em en t Horizontal Location (ft) 1" Midspan Displacement 3" Midspan Displacement Figure 3-117.
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79 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 10 20 30 40 50 N or m al iz ed D is pl ac em en t Horizontal Location (ft) 1" Midspan Displacement 3" Midspan Displacement Figure 3-118.
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80 Rearrange Equation 3-3 to solve for the applied load (F)
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81 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 Ap pl ie d Lo ad (k ip ) Midspan Displacement (in.)
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82 Span (ft) Member Depth (ft)
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83 ID Span (ft) Member Depth (ft)
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84 rupture stress varied. Even though some variations of the Mo/Mcr ratios exist, the minimum is still 1.64, well above 1.2, which is the current acceptable limit.
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