Design Recommendations

Based on findings presented in this dissertation as part of the TxDOT project 0- 6416, recommendations for the design of inverted-T beams are presented.

5.5.1 Ledge Geometry

It is recommended to extend beam ledges beyond the edge of loading plates in the longitudinal direction for a distance at least equal to the ledge depth. Cut-off ledges are not recommended in inverted-T bent caps since they were found to reduce the shear

Vte st

Observed

Failure Mode Vpre d

Vte st / Vpre d Design Controlling Element Vpre d Vte st / Vpre d Design Controlling Element

kips kips ratio kips ratio

03a DL1-42-1.85-06 741 Direct-Strut Crushing 464 1.60 STNI at support 710 1.04 Tension chord 03b DL1-42-2.50-06 622 Sectional Shear 353 1.76 Intermediate tie 353 1.76 Intermediate tie 10a DL1-42-1.85-03 626 Direct-Strut Crushing 468 1.34 STNI at support 555 1.13 Hanger tie 10b DL1-42-2.50-03 510 Sectional Shear 235 2.17 Intermediate tie 235 2.17 Intermediate tie 11a SL3-42-1.85-03 571 Direct-Strut Crushing 409 1.39 STNI at support 558 1.02 Tension chord 12a SL3-42-1.85-06 744 Direct-Strut Crushing 424 1.76 STNI at support 528 1.41 Tension chord 17b DL3-42-1.85-03 629 Flexure Failure 359 1.75 STNI at support 495 1.27 Tension chord 18a SL1-42-2.50-03 498 Sectional Shear 269 1.85 Intermediate tie 269 1.85 Intermediate tie

Confined support Unconfined support

strength, the diagonal cracking load, and the conservatism of design provisions for the specimens tested.

It is recommended to use long ledges whenever possible. Long ledges increase the strength of the specimens, delay the appearance of diagonal cracking, and increase the conservatism of strength design provisions.

5.5.2 Strength Design

Strut-and-tie modeling as proposed by TxDOT project 5253 and implemented in this work is recommended for the design of all inverted-T bent caps. STM provisions were found to produce more accurate strength estimates (over 30% more accurate overall) than the sectional shear design methods coupled with special ledge design procedures. STM procedures produced much higher accuracy for deep beams and performed on par with sectional design methods for non-deep beams. The proposed STM procedures inherently account for all the different failure modes of interest in inverted-T beams. Thus the procedures provide a single rational and simple design approach for the design of inverted-T beams.

It is recommended to evaluate the shear span of inverted-T beams as the distance between centers of support and the nearest concentrated load; consistent with the definition provided in ACI 318-11 (Art. 11.7.1). Since STM procedures were demonstrated to be equally valid for deep and non-deep beams (by any definition of shear span), such a definition change will improve the accuracy in the design of a portion of the beams that are defined differently by the two competing shear span definitions, while producing comparable accuracy to the sectional design methods for the other portion.

One should note that if STM is used for all inverted-T-beam designs, the definition of shear span becomes a moot point for the differentiation between deep and non-deep beams.

5.5.3 Serviceability

It is recommend to limit shear forces in inverted-T beams to the limits evaluated using Equation 5-1 under un-factored service loads. It is left to the designer to determine what percentage of the live load to include in the service load calculations.

Minimum transverse reinforcement ratios of 0.3% distributed evenly in each direction of the web must be provided to adequately restrain the width of diagonal cracks at service load levels. The minimum transverse reinforcement ratios will also allow for sufficient force redistributions for the struts to reach their full capacity.

5.6 SUMMARY

Data from the experimental program were used to compare the accuracy of the sectional AASHTO and TxDOT design provisions for inverted-T bent caps with that of STM provisions of the TxDOT project 5253 as implemented in this dissertation for inverted-T beams. Strut-and-tie modeling is recommended for the design of all inverted-T beams after producing improved accuracy and reduced unnecessary conservatism compared with sectional shear design methods; especially for deep beams. Additionally, shear span definitions of AASHTO LRFD (2012) and ACI 318-11 were compared, showing that ACI definition results in more accurate strength estimations for inverted-T beams with up to three point loads.

Ledge geometry recommendations were made for inverted-T beam design. Cut- off ledges are not recommended due to reduced conservatism in strength design compared with longer ledges and reduced first-cracking load. Deep and long ledges are recommended whenever possible, due to strength and serviceability benefits observed in the experimental results.

Data from the literature and evaluation database were used to evaluate the main variables influencing the diagonal cracking load. Shear span-to-depth ratio, concrete tensile strength, and section size were shown to be the main variables affecting the diagonal cracking load of inverted-T deep beams. An empirical equation proposed by TxDOT project 5253 was shown to give reasonably conservative estimates of cracking

design of inverted-T beams to limit shear stresses under service loads to below the estimated diagonal cracking load using the proposed equation. The provision should reduce but not eliminate the probability of inclined cracking under service loads. Minimum transverse steel ratios of 0.3% evenly distributed in each direction of the web are recommended to adequately restrain the diagonal crack widths under service load and to allow for enough force redistribution for struts to reach their full capacity. Finally, the application of STM for inverted-T specimens was discussed in light of test results.