Simplified Shear Design of Structural Concrete Members: Appendixes (2005)

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C-1 Appendix C: Shear Database This appendix presents the shear database (SDB). The appendix begins with an introduction to the evolution and development of the database, describing the distribution of data in the SDB and suggesting where additional experimental research is required. In Section C.2, the effects of different parameters on the shear stresses at failure are presented. C.1 Presentation of Shear Database The development of a comprehensive database of shear test results was undertaken in order to provide the research and design communities with a resource for identifying research needs and for developing improved design code provisions. The resulting database is the largest database so far created and it provides new insights into the factors that affect shear strength. It can be used for the evaluation and comparison of different models for shear behavior and different relationships for shear strength. Existing empirical design code provisions do not provide uniform levels of safety against failure. One reason is because only a small portion of the existing test results are typically used to evaluate or develop code provisions. Another is that the types of members in the test database do not well represent the types of structures that will be designed using the provisions. One of the complications in developing this shear database was that only a brief summary of experimental test results are typically published in technical journals. There is often insufficient information on geometric details and material characteristics. For this reason, it takes a considerable amount of time for researchers to do literature surveys, and consequently researchers often examine only a limited number of test results before engaging in an experimental research program. Researchers often repeat previous experiments and focus on studying a relatively limited number and range of governing factors. The development of this database was a joint effort by the University of Illinois and the University of Stuttgart, Germany, undertaken with the objective of making research results more accessible and more comparable and, thus, providing a basis for improving the design code. In the creation of this database, about 600 papers or reports summarizing the results of experiment research on the shear resistance of concrete beams were identified. From 108 of the papers processed to date, 2187 individual beam test results have been extracted and subsequently utilized to evaluate the strength relationships used in various shear models, code provisions and other empirical equations. The shear database (SDB) includes tabularized data on both reinforced and prestressed concrete members. Information on the material, geometry, and test data from each experiment are shown in Table C- 1. C.1.1 Shear Test Data for Reinforced Concrete Members Fig. C-1 provides an overview of the 1444-member reinforced concrete (RC) database. Of these members, 1379 beams were rectangular, 10 were I-shaped, and 55 were T-shaped; 385

C-2 beams had stirrups while 1059 of them did not. The vast majority of the tests (1268 of 1444, or about 90 %) consisted of simply supported beams subjected to one or two concentrated loads. 88 loading cases consisted of simply supported beams subjected to uniform loads; 96 cases consisted of continuous beams subjected to point loads. There are only two test results recorded for continuous beams that were subjected to uniform loads. The distribution of parameter values for the entire 1444-member RC database is shown in Fig. C-2. Only 409 of the test results were for beams with concrete strengths greater than 8000 psi and only 83 were for beams with depths greater than 30 inches. Almost half of the beams had shear span to depth ratios (a/d) less than 2.5. Such beams are generally considered as deep beams, and only 191 beams contained less than 1% longitudinal reinforcement. A total of 409 RC High Strength Concrete (HSC), greater than 8000 psi, shear tests were extracted from 39 publications. The distribution of parameter values for the 409 beam RC HSC database is shown in Fig. C-3. In this bar chart, a second parameter is also reported in order to provide a more detailed description of the database. For example, 48 beams are shown to have cylinder compressive strengths, f′c, between 8000 and 9000 psi, and among these, 29 beams were less than 10 inches in depth, 17 beams were between 10 and 20 inches in depth, and 2 beams were between 20 and 30 inches in depth. Only 14 % of the HSC RC beams were greater than 20 inches in depth and only 5 % of the HSC RC beams were greater than 30 inches in depth. C.1.2 Shear Test Data for Prestressed Concrete Members Fig. C-4 provides an overview of the 743-member prestressed concrete (PC) database. Of these members, 167 beams were rectangular, 535 were I-shaped, and 41 were T-shaped; 282 of the members contained shear reinforcement while 461 did not. For the loading conditions, 729 beams were simply supported and subjected to point loads; 6 beams were simply supported and subjected to uniformly distributed loads; 4 tests were on continuous beams subjected to point loads; and 4 tests were on continuous beams subjected to uniformly distributed loads. The distribution of parameter values for this database is shown in Fig. C-5. Only 115 beams had concrete compressive strengths greater than 8000 psi and only 67 beams were more than 30 inches deep. A total of 611 beams had a shear span to depth ratio (a/d) greater than 2.5 and 312 beams contained less than 1% longitudinal reinforcement. Among the 115 HSC PC (greater than 8000 psi) members, 17 were noted to fail in flexure and 5 were reported with inadequate information for inclusion in the database. Thus, only 93 HSC PC shear tests could be included in the subsequent analysis. The distribution of parameter values for the 115-member HSC PC database is shown Fig. C- 6. The maximum cylinder compressive strength for all tests was about 14,000 psi. Only 31 out of 115 HSC PC beams were greater than 20 inches in depth and only 23 of them were greater than 30 inches in depth. About half of the HSC PC beams were heavily reinforced and most of the HSC PC beams had shear span to depth ratios greater than 2.5. Unfortunately, however, in the evaluation database, only 25 out of 115 HSC PC beams were greater than 20 inches in depth and only 20 of the HSC PC beam were greater than 30 inches in depth.

C-3 C.2 Effect of Parameters The database was used to investigate the influence of several major parameters on shear strength. In this section, the shear strength, )/( dbVv wuu = or normalized shear strength, )/(/ '' cwucu fdbVfv = , is plotted for each primary parameter and observations are drawn from the analyses. This section presents in turn those observations for RC members without shear reinforcement, RC members with shear reinforcement, PC members without shear reinforcement, and PC members with shear reinforcement, respectively Fig. C-7 shows the ultimate shear stresses of the 1444 RC members in the SDB. The large and lightly reinforced members without shear reinforcement (i.e., inh 35≥ , %0.1≤lρ , 0=vρ ) are shown with rectangular markers. The shear strengths of those members are the lowest among members with the same concrete strength and those shear strengths do not increase as the concrete strengths increase. For members with shear reinforcement, the same plot is less meaningful because shear strength is then strongly dependent on the amount of shear reinforcement. In Fig. C-8, the observed shear stresses at failure are plotted versus the concrete cylinder strength for the 743-member PC database. This plot illustrates that very few tests have been conducted in which specimens were cast with high strength concrete or were very heavily reinforced in shear. In the remaining sections of this chapter, the influences of the major parameters on shear are examined for members with shear span to depth ratios greater than 2.4. Before their results were included in the database, members reported as flexural failure were removed and the flexural capacity of all members was checked against the possibility of flexural failure, i.e., /failure nM M < 1.0. The total number of beams examined in this section is 1359 of which 878 are RC members and 481 are PC members. C.2.1 Reinforced Concrete Members without Shear Reinforcement In this section, 718 RC members without shear reinforcement are studied. C.2.1.1 Concrete Strength In Fig. C-9, the shear strengths of RC members are plotted versus their concrete cylinder strength. Most of the beams had ultimate shear stresses ranging from 50 to 600 psi. In most cases the shear strength increases as the concrete strength increases. However, members greater than 30 inches in depth, with light amounts of longitudinal reinforcement ( 0.2<lρ %), do not follow such this trend as discussed previously in Section A.1.3. In Fig. C-10 the shear strength ratio ( ', /u test cv f ) is plotted versus the concrete cylinder strength. The shear strength ratio clearly decreases with increasing concrete cylinder strength which means that the shear strength ( ,u testv ) itself increases less than in direct proportion to

C-4 concrete strength. In most codes of practice, shear strength is proportional to the concrete strength to an exponent between 0.25 and 0.5. In both Figs. C-9 and C-10 the data points are subdivided into groups with three different depth levels. A size effect can be inferred from the three data point layers although there are some exceptions. C.2.1.2 Effective Depth Fig. C-11 shows shear strengths plotted versus effective depths. Although only a limited number of the test beams were large, the shear strength clearly decreases as the effective depth of the member increases. The shear strengths of the members having effective depths less than about 15 inches are very high. However, most of the small size members having shear strengths greater than about 350 psi contained large amounts of longitudinal reinforcement, i.e., %0.3≥lρ . On the other hand, the lower boundaries of data points are for members with low amounts of longitudinal reinforcement. This means that the longitudinal reinforcement has a significant effect on shear strength. Further, the shear strengths of large and lightly reinforced concrete members are especially low. Many of the major codes and empirical equations account for a size effect in shear. In these expressions, the shear strength decreases as a function of the member depth. However, the expressions vary, ranging from d/1 , d/1 , 3/1/1 d , and 4/1/1 d . The CSA and the AASHTO LRFD consider the size effect relationship for members without shear reinforcement in a somewhat different manner, as was described in Appendix B. These codes consider size effect to be a crack spacing parameter that is related to the distance between cracks and that crack widths are roughly proportional to crack spacing for a given level of longitudinal strain. ACI 318-02 still does not include any consideration of the size effect. . C.2.1.3 Shear Span to Depth Ratio (Moment-shear ratio) In both Figs. C-7 and C-13, shear strengths are plotted versus shear span to depth ratios (or moment-shear ratios). However, different subgroups are used in each of these plots. Many of the test beams had an a/d ratio around 2.5. The shear strengths of members with an a/d ratio of 2.5 are clearly higher than those of the members with an a/d ratio around 3.0. This result is due to the beneficial effect of direct load transfer to the support by arch action. From the Fig. C-12 it can be seen that most members having high shear strengths are heavily reinforced, and from Fig. C-13 that those members are mostly of small size except for some members with an a/d ratio around 2.5. Fig. C-13 also shows that the members having low shear strengths, with an a/d ratio of about 3.0, are of relatively large size. Many code provisions and empirical equations include a variable related to the shear span to depth ratio, or moment to shear ratio, in their predictions of shear capacity. However, the a/d

C-5 ratio can not be clearly defined for members subjected to uniformly distributed load, and thus it is more appropriate to use the moment to shear ratio in design code expressions than an a/d ratio. C.2.1.4 Longitudinal Reinforcement Ratio Fig. C-14 shows a plot of shear strengths versus the longitudinal reinforcement ratios. More than half of the test beams were heavily reinforced (i.e., %0.2≥lρ ). This fact is unfortunate as it is not representative of design practice. Only a small number of test beams contain modest amounts of longitudinal reinforcement, i.e., %0.1≤lρ . As can be seen in Fig. C-14, the shear strength clearly increases as the longitudinal reinforcement increases and members with %0.1≤lρ have lower shear strengths. Further, as the member size becomes larger, the decreases in shear strengths of lightly reinforced members increase. Most building codes or empirical formulae account for the influence of longitudinal reinforcement ratio directly or indirectly. For example, AASHTO LRFD considers the influence of longitudinal reinforcement by using the longitudinal strain, xε , which is a function of the longitudinal reinforcement amount as well as other sectional forces and sectional properties. C.2.2 Reinforced Concrete Members with Shear Reinforcement In this section, 160 RC members with shear reinforcement are studied. Because the shear strength of RC members with shear reinforcement strongly depends on the shear reinforcement strength, the shear reinforcement strength levels are divided into 6 groups in all plots; vyv fρ < 100 psi, 100 ≤ vyv fρ < 150 psi, 150 ≤ vyv fρ < 250 psi, 250 ≤ vyv fρ < 500 psi, 500 ≤ vyv fρ < 1000 psi, vyv fρ ≥ 1000 psi. C.2.2.1 Concrete Strength Fig. C-15 shows the shear strengths of RC members with shear reinforcement plotted versus their concrete cylinder strengths. The shear strengths have a large scatter but depend on the shear reinforcement strength, i.e., vyv fρ . Most of the beams have ultimate shear stresses ranging from 100 to 800 psi but several beams have shear strengths of up to 1700 psi. The shear strengths increase slowly with concrete compressive strength increase, although that trend is not very clear. The influence on the shear strength of concrete compressive strength for RC members with shear reinforcement appears to be relatively smaller than the same influence for RC members without shear reinforcement.

C-6 C.2.2.2 Effective Depth Fig. C-16 shows shear strengths plotted versus the effective depths. The shear strengths of RC members having shear reinforcement amounts less than ≤vyv fρ 150 psi and depths greater than 15 inches are almost constant. The shear strengths of smaller members with similar amounts of shear reinforcement strength are a little higher. RC members with high shear reinforcement amounts do not show any significant size effect. C.2.2.3 Shear Span to Depth Ratio (Moment- Shear Ratio) In Fig. C-17, shear strengths are plotted versus shear span to depth ratios, a/d (or moment- shear ratios). Although strengths for members with a/d ratios of about 2.5 show a large scatter, that result is because of different shear reinforcement strengths. In each subgroup having similar shear reinforcement strengths, shear strengths do not vary much with a/d ratio increases but remain almost constant. The a/d ratio does not seem to have a significant influence on the shear strength of RC members with shear reinforcement. C.2.2.4 Longitudinal Reinforcement Ratio Fig. C-18 plots shear strengths versus longitudinal reinforcement ratios. Most of the test beams were heavily reinforced (i.e., %0.2≥lρ ) and only a small number contained low amounts of longitudinal reinforcement (i.e., %0.20.1 or<lρ ). As can be seen in Fig. C-18, for members in each subgroup having similar levels of shear reinforcement, the shear strength clearly increases as the longitudinal reinforcement ratio increases. Further, the increments in shear strength for members with large amounts of shear reinforcement are greater than those for members with lower amounts of shear reinforcement. One of the reasons for this could be that dowel action is enhanced by shear reinforcement. On the other hand, if for test purposes members are heavily reinforced against flexure in order to produce shear failures, then longitudinal strain are smaller than in lightly reinforced members and thus the shear strength increases. C.2.2.5 Shear Reinforcement Fig. C-19 plots shear strength versus the strength of the shear reinforcement. In members with shear reinforcement, a large portion of the shear is carried by the shear reinforcement after diagonal cracking has occurred. Thus, the shear resistance of members with shear reinforcement heavily depends on the amount of shear reinforcement. In most of the major design codes, the shear resistance is limited to avoid concrete web crushing. In Fig. C-20, normalized shear strengths are plotted ( ', /u test cv f ) versus normalized strengths of the shear reinforcement ( '/v vy cf fρ ). Several members have shear strengths greater than '0.25 cf while most of members

C-7 have shear strengths smaller than that value. The shear strength limit (without Vp) in the current AASHTO LRFD is '0.25 cf . C.2.3 Prestressed Concrete Members without Shear Reinforcement In this section, 321 PC members without shear reinforcement are studied. C.2.3.1 Concrete Strength In Fig. C-21 the shear strengths of PC members without shear reinforcement are plotted versus their concrete cylinder strengths, and in Fig. C-22 the normalized ultimate shear strength ratios ( ', /u test cv f ) of those members are plotted versus the ratios of the compressive stresses at the centroids to their concrete cylinder strengths. The ultimate shear stresses of the test beams range from 100 to 1200 psi and the ratios of the compressive stresses at the centroids to their concrete cylinder strengths range from about 0.02 to 0.25. From Fig. C-21 it can be clearly seen that shear strengths increase as concrete strengths increases. On the other hand Fig. C-22 shows that normalized ultimate shear strength ratios ( ', /u test cv f ) also increase as the ratios of the compressive stresses at the centroids to their concrete cylinder strengths ( '/pc cf f ) increase. This result is due to the beneficial effect of the axial compressive stress caused by prestressing. That stress delays the formation of cracking and also reduces crack width. In most codes of practice, the compressive stresses due to prestressing are taken into account. However, the methods used vary widely. In both AASHTO LRFD and CSA 2004, the longitudinal strain becomes smaller as the axial compressive stress increases and this results in greater shear strength. ACI 318-02, Eurocode EC2 (2003), and the German Code (DIN, 2001) account for the prestress directly by using the axial stress at the centroid of the section. The Japanese Code (JSCE Standards, 1986) considers the decompression moment at the extreme fiber to account for axial load as well as prestress effects. C.2.3.2 Effective Depth Fig. C-23 shows shear strengths plotted versus effective depths. Unfortunately, there were only two beams having effective depths greater than 20 inches and thus the influence of effective depth on shear strength is not observable from the database. C.2.3.3 Shear Span to Depth Ratio (Moment-Shear Ratio) Fig. C-24 shows shear strengths versus shear span to depth ratios (or moment-shear ratios) for all PC members (592 beams). Fig. C-25 shows the same plots for members with shear span to depth ratios greater than 2.4.

C-8 From Fig. C-24 it can be seen that the shear span to depth ratio (moment-shear ratio) has a strong influence on the shear strengths of members with a/d ratios less than about 2.5 while it has less influence on strengths for members with a/d ratios greater than about 2.5. This result is because, for short shear span to depth ratios, a large portion of shear force can be directly transmitted to the support without crossing a shear crack. Typical sectional analysis based models or codes give very conservative predictions in these cases. Thus, all analysis in this report use only results for members with a/d ratios greater than 2.4. C.2.3.4 Longitudinal Reinforcement Ratio Fig. C-26 shows shear strengths versus the longitudinal reinforcement ratios. Shear strengths clearly increase as the longitudinal reinforcement ratio increases. As observed for RC members without shear reinforcement, PC members with %0.1≤lρ also have very low shear strengths. PC members with high longitudinal prestressing steel ratios have large compressive stresses and thus higher shear strengths. On the other hand, if members are heavily reinforced against flexure to ensure shear failure for test purposes, the longitudinal strains are smaller than for lightly reinforced members; thus, the shear strength increases. C.2.4 Prestressed Concrete Members with Shear Reinforcement In this section, results for 160 PC members with shear reinforcement are examined. Because the shear strength of PC members with shear reinforcement depends strongly on the strength of the shear reinforcement strength as is the case for RC members with shear reinforcement, shear reinforcement strength levels are again divided into 6 groups in all plots; vyv fρ < 100 psi, 100 ≤ vyv fρ < 150 psi, 150 ≤ vyv fρ < 250 psi, 250 ≤ vyv fρ < 500 psi, 500 ≤ vyv fρ < 1000 psi, vyv fρ ≥ 1000 psi. C.2.4.1 Concrete Strength Fig. C-27 shows the shear strengths of PC members with shear reinforcement plotted versus their concrete cylinder strengths. The shear strengths show a large scatter but they depend on the shear reinforcement strength, i.e., vyv fρ . Shear strengths increase slowly as concrete compressive strengths increase unlike the situation for PC members without shear reinforcement. Thus, the influence of concrete compressive strength on the shear strength of PC members with shear reinforcement appears to be somewhat smaller than for PC members without shear reinforcement.

C-9 C.2.4.2 Effective Depth Fig. C-28 shows the shear strengths of PC members with shear reinforcement plotted versus their effective depths. Although only a limited number of the members were large, there appears to be no size effect for PC members with shear reinforcement. In the AASHTO LRFD, it is assumed that there is no size effect for members having at least minimum shear reinforcement. This assumption seems reasonable, at least for PC members with shear reinforcement, from the data plotted in Fig. C-28. C.2.4.3 Shear Span to Depth Ratio (Moment-shear ratio) Fig. C-29 shows shear strengths versus the shear span to depth ratios (or moment-shear ratios) for PC members with shear reinforcement and with shear span to depth ratios greater than 2.4. From Fig. C-29 there is no clearly observable influence of the shear span to depth ratio on shear strength for PC members with shear reinforcement. C.2.4.4 Longitudinal Reinforcement Ratio Fig. C-30 shows shear strengths versus longitudinal reinforcement ratios. For members with similar shear reinforcement strengths, the shear strength clearly increases as the longitudinal reinforcement ratio increases. Members with large amounts of longitudinal prestressing steel will also have large compressive stresses which in turn increases the shear strength. Shear reinforcement also enhances dowelling resistance to shear displacements along the inclined crack. C.2.4.5 Shear Reinforcement Fig. C-31 plots shear strengths versus shear reinforcement strengths. Clearly the shear resistance of members with shear reinforcement depends strongly on the strength of the shear reinforcement. In Fig. C-32, normalized shear strengths are plotted ( ', /u test cv f ) versus the normalized strengths of the shear reinforcement ( '/v vy cf fρ ). While most members have shear strengths smaller than '0.25 cf , some members with large amounts of shear reinforcement have shear strengths greater than '0.25 cf , which is the shear strength limit (without pV ) in the current AASHTO LRFD.

C-10 Table C-1 List of Parameters Collected and Evaluated in Shear Database Note) This table is to illustrate the details of information compiled into SDB. The notations used in this table do not necessarily represent those used in other part of this report. Classification Symbols Content Classification Symbols Content Units units metric/US unit Eps modulus of elasticity of prestressed reinforcement f'c cylinder compressive strength of concrete epsy yield strain of prestressed reinforcement ec net compressive strain of concrete at compressive strength epu rupture strain of prestressed reinforcement fcu cubic compressive strength of concrete rhop ratio of prestressed reinforcement = Aps/bd fcr cracking strength of concrete rhowp ratio of prestressed reinforcement = Aps/bwd fcr-mr modulus of rupture of concrete dp distance from extreme compression fiber to centroid of prestressed tension reinforcement fcr-un uniaxial tensile strength of concrete Aps area of prestressed reinforcement in tension zone fcr-sp split-cylinder tensile strength dbp diameter of prestressed reinforcement fcr-dp double-punch tensile strength Fst applied force in prestressed reinforcement agg maximum aggregate size fst applied stress in prestressed reinforcement gamc density of concrete Fse effective force in prestressed reinforcement (after allowance for all prestress losses) age age of specimen Prestressing Details fse effective stress in prestressed reinforcement (after allowance for all prestress losses) shape rectangular/T-shape/I-shape (con'd) Vp vertical component of effective prestress force at section bslab width of slab fps stress in prestressed reinforcement at nominal strength tslab thickness of slab rhowp' ratio of prestressed reinforcement = A'ps/bwd h overall depth of member d'p distance from extreme compression fiber to centroid of prestressed reinforcement on compression side b width of member A'ps area of prestressed reinforcement in compression zone bw web width of member d'bp diameter of prestressed reinforcement on compression side btop width of top flange F'se effective force in prestressed reinforcement on compression side (after allowance for all prestress losses) bbot width of bottom flange f'se effective stress in prestressed reinforcement on compression side (after allowance for all prestress losses) ttop thickness of top flange Prestress method pre-tension/post-tension tbot thickness of bottom flange Bond bond status of prestressed reinforcement (bonded/unbonded) Ag gross area of section fyv yield strength of vertical reinforcement Ig moment of inertia of gross-section fuv ultimate strength of vertical reinforcement bar type deformed/plain bar Av area of shear reinforcement perpendicular to flexural tension reinforcement fy yield strength of nonprestressed reinforcement sv spacing of vertical web reinforcement fu ultimate tensile strength of nonprestressed reinforcement theta angle between inclined stirrups and longitudinal axis of member Es modulus of elasticity of reinforcement rhov vertical shear reinforcement ratio( =Av/(bw*sv) ) epy yield strain of reinforcement fyh yield strength of horizontal web reinforcement rho ratio of nonprestressed tension reinforcement =As/bd Ah area of shear reinforcement parallel to flexural tension rhow ratio of nonprestressed tension reinforcement =As/bwd sh spacing of horizontal web reinforcement d distance from extreme compression fiber to centroid of nonprestressed reinforcement on the layer of tension side rhoh horizontal shear reinforcement ratio( =Avh/(bw*sh) ) As area of nonprestressed longitudinal reinforcement on flexural tension side having distance d from extreme compression fiber Diagram diagram of setting specimen db bar diameter on the layer of tension side Set-Up support condition & loading form ns number of longitudinal reinforcement on flexural tension side a/d shear span to depth ratio sc side cover Lent entire length of specimen dc distance from extreme compression fiber to centroid of nonprestressed reinforcement on the layer of compression side L distance between center of supports Asc area of nonprestressed longitudinal reinforcement on flexural comepression side having distance dc from extreme i fib a shear span measured from conter of support to center of loading point dbc bar diameter on the layer of compression side a' distance between concentrated load and face of support fpci compressive strength of concrete at time of initial prestress Ln distance between face of supports age@ps days after casting when the prestressing forces were transmitted to the concrete beams Mn nominal moment strength at section yps distance from centroidal axis of gross section, neglecting reinforcement, to prestressed reinforcement in tension Mcr moment causing flexural cracking at section due to externally applied loads (ACI eq. 11-11) yb distance from centroidal axis of gross section, neglecting reinforcement, to extreme fiber in tension Muf bending moment occurring simulataneously with shear force Vult at the cross section considered yt distance from centroidal axis of gross section, neglecting reinforcement, to extreme fiber in compression Vnf shear force when a member reaches its flexural capacity fpc compressive stress in concrete (after allowance for all prestress losses) at centroid of cross section resisting externally applied loads or at junction of web and flange when Vult/Vnf ratio of ultimate shear force to shear force at flexural failure Prestressing Details fpe compressive stress in concrete due to effective prestress forces only (after allowance for all prestress losses) at extreme fiber of section where tensile stress is caused by externally applied loads Vcr cracking shear force strand type type of prestressing steel (1,2,3,4,5,6,7) Vult ultimate shear force 1. seven-wire strand (fpu=270 ksi) vu ultimate shear stress 2. seven-wire strand (fpu=250 ksi) 3. three- and four-wire strand (fpu=250 ksi) Vn,pred nominal shear capacity predicted by codes or other researchers such as ACI, LRFD, and etc. 4. prestressing wire Vult/Vn,pred shear strength ratio of test values to prediction 5. smooth prestressing bars (fpu=145 ksi) L-D load-deflection diagram 6. smooth prestressing bars (fpu=160 ksi) 7. deformed prestressing bars Crack diagram crack diagram fpy yield strength of prestressed reinforcement Failure mode1 failure mode defined by authors fpu ultimate tensile strength of prestressed reinforcement Failure mode2 failure mode defined by ratio of Vult/Vnf (Vult/Vnf<1.0 : shear failure, Vult/Vnf>1.0 : flexural failure) Concrete Properties Cross-Section Longitudinal Reinforcement Test Result Vertical Shear Reinforcement Longitudinal Web Reinforcement Test Set-up

C-11 Beam Shapes Rect. 95% I shape 1% Tee 4% Stirrups w ith stirrup 27% without stirrup 73% Support & Loading SS-PL 87% SS- UDL 6% SE-PL 7% Fig. C-1 General Characteristics of RC Beams in Database (1444 tests) 126 40 43 30 9 96 54 500 106 79 167 97 419 309 58 218 115 261 264 50 265 125 103 163 92 106 64 35 97 39 191 150 66 66 47 142 123 12 48 11 60 52 5 120 73 177 202 86 39 80 107 42 92 40 1059 136 445 872 1203 1444 43 543 1223 1361 1444 191 306 645 820 997 13121083 1163 1404 1444 1.0 126 222 872607 13711311 1444 50 100 150 1147 1347 1444 (no shear reinforcement) 1405 2 3 4 5 6 7 8 9 10 14 19f'c (ksi) : N of Tests : sum : 30 709 969 1035 1083 depth (in) : N of Tests : sum : 5 10 15 20 25 5030 120 962 ρl (%) : N of Tests : sum : 0.5 0.75 1.0 1.25 1.5 1.75 2.0 2.25 2.5 2.75 3.0 3.25 3.5 4.0 5.0 10 40 94 431 495 768 a/d : N of Tests : sum : sum : N of Tests : ρv fy (psi) : 1.5 2.0 2.5 3.0 3.5 4.0 5.0 6.0 10 389 978 1169 200 300 500 1000 1059 1255 Fig. C-2 Distribution of Parameters of RC Beams in Database (1444 tests)

C-12 29 77 17 17 31 10 13 17 35 48 25 17 6 7 2 4 4 3 10 1 10 2 2 3 5 3 41 0 20 40 60 80 100 120 f'c (ksi) N um be r o f T es ts d<60 in d<50 in d<40 in d<30 in d<20 in d<10 in 8 9 10 11 12 13 14 15 16 17 18 25 10 2 100 9 40 16 8 19 20 6 48 5 311 4 57 2 15 3 22 9 57 5 7 7 0 50 100 150 200 Height, h (in) N um be r o f T es ts 18<f'c<19 ksi 17<f'c<18 ksi 16<f'c<17 ksi 15<f'c<16 ksi 14<f'c<15 ksi 13<f'c<14 ksi 12<f'c<13 ksi 11<f'c<12 ksi 10<f'c<11 ksi 9<f'c<10 ksi 8<f'c<9 ksi 5 15 20 25 30 35 40 45 50 5510 60 24 20 30 6 34 21 12 244 14 11 4 56 37 6 15 7 5 5 21 2 12 9 5 1 1 2 4 0 20 40 60 80 100 120 Longitudinal Reinf. Ratio (%) N um be r o f T es ts d<60 in d<50 in d<40 in d<30 in d<20 in d<10 in 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 7~0 5 7 46 32 2818 13 21 20 36 24 8 8 7 8 5 14 15 4 19 34 26 7 0 20 40 60 80 100 120 Shear Span to Depth Ratio ( - ) N um be r o f T es ts d<60 in d<50 in d<40 in d<30 in d<20 in d<10 in 0 1 1.5 2 2.5 3 3.5 4 4.5 5 ~ 6 Fig. C-3 Distribution of Parameters of RC High Strength Concrete Beams in Database (409 tests)

C-13 Beam Shapes Rect. 22% I shape 72% Tee 6% Stirrups w ith stirrup 38% without stirrup 62% Support & Loading SS-PL 97% SS- UDL 1% SE-PL 1% SE- UDL 1% Fig. C-4 General Characteristics of PC Beams in Database (743 tests) 28 59 10 70 4 65 83 276 109 22 39 170 335 114 50 158 109 18 153 34 89 105 33 108 33 199 32 18 76 59 97 25 41 76 33 40 24 6 15 47 27 17 6 22 1 62 23 27 7 461 70 179 446 630 743 10 276 672 731 743 142 312 421 526 686558 607 709 743 28 93 379290 715675 743 50 100 150 537 604 743 (no shear reinforcement) 706 3 4 5 6 7 8 11 14f'c (ksi) : N of Tests : sum : 293 554 depth (in) : N of Tests : sum : 5 10 15 20 25 4535 70 621 ρl (%) : N of Tests : sum : 0.5 0.75 1.0 1.25 1.5 2.0 3.0 3.5 4.0 5.0 10 59 a/d : N of Tests : sum : sum : N of Tests : ρv fy (psi) : 1.5 2.0 2.5 3.0 3.5 4.0 5.0 6.0 10.0 132 578 200 300 500 1000 465 571 2400 663 696 10 Fig. C-5 Distribution of Parameters of PC Beams in Database (743 tests)

C-14 7 5 5 28 23 7 9 4 2 2 2 2 2 2 1 24 2 6 0 10 20 30 40 50 60 f'c (ksi) N um be r o f T es ts d<70 in d<50 in d<40 in d<30 in d<20 in d<10 in 8 9 10 11 12 13 14 15 16 17 18 36 2 12 6 7 24 4 224 2 6 4 1 2 6 2 7 2 2 0 10 20 30 40 50 60 Height, h (in) N um be r o f T es ts 13<f'c<14 ksi 12<f'c<13 ksi 11<f'c<12 ksi 10<f'c<11 ksi 9<f'c<10 ksi 8<f'c<9 ksi 5 15 20 25 30 35 40 45 50 5510 75~ 11 13 24 2 9 11 42 4 2 2 43 8 4 2 22 2 0 10 20 30 40 50 60 Longitudinal Reinf. Ratio (%) N um be r o f T es ts d<70 in d<50 in d<40 in d<30 in d<20 in d<10 in 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 7~0 2 1 5 12 3 7 20 153 6 4 4 2 11 21 4 2 2 4 3 0 10 20 30 40 50 60 Shear Span to Depth Ratio ( - ) N um be r o f T es ts d<70 in d<50 in d<40 in d<30 in d<20 in d<10 in 0 1 1.5 2 2.5 3 3.5 4 4.5 5 ~ 6 Fig. C-6 Distribution of Parameters of PC High Strength Concrete Beams in Database (115 tests)

C-15 0 500 1000 1500 2000 2500 3000 0 5000 10000 15000 20000 f'c (psi) vu te st (p si ) members w ithout shear reinforcement members w ith shear reinforcement large, lightly reinforced members w ithout Av 0 500 1000 1500 2000 2500 3000 0 5000 10000 15000 20000 f'c (psi) vu te st (p si ) members w ithout shear reinforcement members w ith shear reinforcement large, lightly reinforced members w ithout Av Fig. C-7 Ultimate Shear Stress (vu,test) at Failure versus Concrete Compressive Strength (f'c) of RC Members Fig. C-8 Ultimate Shear Stress (vu,test) at Failure versus Concrete Compressive Strength (f'c) of PC Members 0 100 200 300 400 500 600 700 0 3000 6000 9000 12000 15000 18000 f'c (psi) vu ,te st (p si ) d < 10 in, rhol < 2 % d < 10 in, rhol > 2 % 10 in < d < 30 in, rhol < 2 % 10 in < d < 30 in, rhol > 2 % d > 30 in, rhol < 2 % d > 30 in, rhol > 2 % 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0 3000 6000 9000 12000 15000 18000 f'c (psi) vu ,te st / f'c d < 10 in, rhol < 2 % d < 10 in, rhol > 2 % 10 in < d < 30 in, rhol < 2 % 10 in < d < 30 in, rhol > 2 % d > 30 in, rhol < 2 % d > 30 in, rhol > 2 % Fig. C-9 Ultimate Shear Stress (vu,test) at Failure versus Concrete Compressive Strength (f'c) of RC Members without Shear Reinforcement Fig. C-10 Ultimate Shear Strength Ratio (vu,test/f’c) versus Concrete Compressive Strength (f'c) of RC Members without Shear Reinforcement

C-16 0 100 200 300 400 500 600 700 0 20 40 60 80 100 120 d (in) vu ,te st (p si ) rhol < 1 %, f 'c < 6000 psi rhol < 1 %, f 'c > 6000 psi 1 % < rhol < 2 %, f 'c < 6000 psi 1 % < rhol < 2 %, f 'c > 6000 psi rhol > 2 %, f 'c < 6000 psi rhol > 2 %, f 'c > 6000 psi Fig. C-11 Ultimate Shear Stress (vu,test) at Failure versus Effective Depth of RC Members without Shear Reinforcement 0 100 200 300 400 500 600 700 0 2 4 6 8 a/d vu ,te st (p si ) rhol < 1 %, f 'c < 6000 psi rhol < 1 %, f 'c > 6000 psi 1 % < rhol < 3 %, f 'c < 6000 psi 1 % < rhol < 3 %, f 'c > 6000 psi rhol > 3 %, f 'c < 6000 psi rhol > 3 %, f 'c > 6000 psi 0 100 200 300 400 500 600 700 0 2 4 6 8 a/d vu ,te st (p si ) d < 10 in, f 'c < 6000 psi d < 20 in, f 'c > 6000 psi 10 in < d < 20 in, f 'c < 6000 psi 10 in < d < 20 in, f 'c > 6000 psi d > 20 in, f 'c < 6000 psi d > 20 in, f 'c > 6000 psi Fig. C-12 Ultimate Shear Stress (vu,test) at Failure versus Shear Span to Depth Ratio for RC Members without Shear Reinforcement Fig. C-13 Ultimate Shear Stress (vu,test) at Failure versus Shear Span to Depth Ratio for RC Members without Shear Reinforcement

C-17 0 100 200 300 400 500 600 700 0 2 4 6 8 rhol (%) vu ,te st (p si ) d < 10 in, f 'c < 6000 psi d < 10 in, f 'c > 6000 psi 10 in < d < 30 in, f 'c < 6000 psi 10 in < d < 30 in, f 'c > 6000 psi d > 30 in, f 'c < 6000 psi d > 30 in, f 'c > 6000 psi Fig. C-14 Ultimate Shear Stress (vu,test) at Failure versus Longitudinal Reinforcement Ratio for RC Members without Shear Reinforcement 0 200 400 600 800 1000 1200 1400 1600 1800 0 5000 10000 15000 20000 f'c (psi) vu ,te st (p si ) rhovfvy < 100 psi 100 psi < rhovfvy < 150 psi 150 psi < rhovfvy < 250 psi 250 psi < rhovfvy < 500 psi 500 psi < rhovfvy < 1000 psi rhovfvy > 1000 psi Fig. C-15 Ultimate Shear Stress (vu,test) at Failure versus Concrete Compressive Strength (f'c) of RC Members with Shear Reinforcement

C-18 0 200 400 600 800 1000 1200 1400 1600 1800 0 10 20 30 40 50 d (in) vu ,te st (p si ) rhovfvy < 100 psi 100 psi < rhovfvy < 150 psi 150 psi < rhovfvy < 250 psi 250 psi < rhovfvy < 500 psi 500 psi < rhovfvy < 1000 psi rhovfvy > 1000 psi Fig. C-16 Ultimate Shear Stress (vu,test) at Failure versus Effective Depth of RC Members with Shear Reinforcement 0 200 400 600 800 1000 1200 1400 1600 1800 0 1 2 3 4 5 6 7 a/d vu ,te st (p si ) rhovfvy < 100 psi 100 psi < rhovfvy < 150 psi 150 psi < rhovfvy < 250 psi 250 psi < rhovfvy < 500 psi 500 psi < rhovfvy < 1000 psi rhovfvy > 1000 psi Fig. C-17 Ultimate Shear Stress (vu,test) at Failure versus Shear Span to Depth Ratio for RC Members with Shear Reinforcement

C-19 0 200 400 600 800 1000 1200 1400 1600 1800 0 2 4 6 8 10 12 rhol (%) vu ,te st (p si ) rhovfvy < 100 psi 100 psi < rhovfvy < 150 psi 150 psi < rhovfvy < 250 psi 250 psi < rhovfvy < 500 psi 500 psi < rhovfvy < 1000 psi rhovfvy > 1000 psi Fig. C-18 Ultimate Shear Stress (vu,test) at Failure versus Longitudinal Reinforcement Ratio for RC Members with Shear Reinforcement 0 200 400 600 800 1000 1200 1400 1600 1800 0 500 1000 1500 2000 2500 rhovfvy (psi) vu ,te st (p si ) d < 10 in, rhol < 2 % d < 10 in, rhol > 2 % 10 in < d < 25 in, rhol < 2 % 10 in < d < 25 in, rhol > 2 % d > 25 in, rhol < 2 % d > 25 in, rhol > 2 % 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.00 0.10 0.20 0.30 0.40 0.50 0.60 rhovfvy / f'c vu ,te st / f'c d < 10 in, rhol < 2 % d < 10 in, rhol > 2 % 10 in < d < 25 in, rhol < 2 % 10 in < d < 25 in, rhol > 2 % d > 25 in, rhol < 2 % d > 25 in, rhol > 2 % Fig. C-19 Ultimate Shear Stress (vu,test) at Failure versus Strength of Shear Reinforcement for RC Members with Shear Reinforcement Fig. C-20 Normalized Ultimate Shear Stress (vu,test) at Failure versus Normalized Strength of Shear Reinforcement for RC Members with Shear Reinforcement

C-20 0 200 400 600 800 1000 1200 1400 0 3000 6000 9000 12000 15000 f'c (psi) vu ,te st (p si ) d < 10 in, rhol < 2 % d < 10 in, rhol > 2 % 10 in < d < 25 in, rhol < 2 % 10 in < d < 25 in, rhol > 2 % d > 25 in, rhol < 2 % d > 25 in, rhol > 2 % 0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.10 0.20 0.30 0.40 fpc / f'c vu ,te st / f'c d < 10 in, rhol < 2 % d < 10 in, rhol > 2 % 10 in < d < 25 in, rhol < 2 % 10 in < d < 25 in, rhol > 2 % d > 25 in, rhol < 2 % d > 25 in, rhol > 2 % Fig. C-21 Ultimate Shear Stress (vu,test) at Failure versus Concrete Compressive Strength (f'c) of PC Members without Shear Reinforcement Fig. C-22 Normalized Ultimate Shear Strength Ratio (vu,test/ f'c) versus Ratio of Compressive Stress at Centroid to Concrete Compressive Strength (fpc/f'c) of PC Members without Shear Reinforcement 0 200 400 600 800 1000 1200 1400 0 5 10 15 20 25 30 35 d (in) vu ,te st (p si ) rhol < 1 %, f 'c < 6000 psi rhol < 1 %, f 'c > 6000 psi 1 % < rhol < 2 %, f 'c < 6000 psi 1 % < rhol < 2 %, f 'c > 6000 psi rhol > 2 %, f 'c < 6000 psi rhol > 2 %, f 'c > 6000 psi Fig. C-23 Ultimate Shear Stress (vu,test) at Failure versus Effective Depth of PC Members without Shear Reinforcement

C-21 0 500 1000 1500 2000 2500 3000 3500 0 2 4 6 8 a/d vu ,te st (p si ) rhol < 0.1%, f 'c < 6000 psi rhol < 0.1%, f 'c > 6000 psi 0.1 % < rhol < 3 %, f 'c < 6000 psi 0.1 % < rhol < 3 %, f 'c > 6000 psi rhol > 3 %, f 'c < 6000 psi rhol > 3 %, f 'c > 6000 psi 0 200 400 600 800 1000 1200 1400 0 2 4 6 8 a/d vu ,te st (p si ) rhol < 0.1%, f 'c < 6000 psi rhol < 0.1%, f 'c > 6000 psi 0.1 % < rhol < 3 %, f 'c < 6000 psi 0.1 % < rhol < 3 %, f 'c > 6000 psi rhol > 3 %, f 'c < 6000 psi rhol > 3 %, f 'c > 6000 psi Fig. C-24 Ultimate Shear Stress (vu,test) at Failure versus Shear Span to Depth Ratio for All PC Members without Shear Reinforcement Fig. C-25 Ultimate Shear Stress (vu,test) at Failure versus Shear Span to Depth Ratio for PC Members without Shear Reinforcement (a/d >2.4) 0 200 400 600 800 1000 1200 1400 0 2 4 6 8 rhopl (%) vu ,te st (p si ) d < 10 in, f 'c < 6000 psi d < 10 in, f 'c > 6000 psi 10 in < d < 25 in, f 'c < 6000 psi 10 in < d < 25 in, f 'c > 6000 psi d > 25 in, f 'c < 6000 psi d > 25 in, f 'c > 6000 psi Fig. C-26 Ultimate Shear Stress (vu,test) at Failure versus Longitudinal Reinforcement Ratio for PC Members without Shear Reinforcement

C-22 0 500 1000 1500 2000 2500 0 5000 10000 15000 f'c (psi) vu ,te st (p si ) rhovfvy < 100 psi 100 psi < rhovfvy < 150 psi 150 psi < rhovfvy < 250 psi 250 psi < rhovfvy < 500 psi 500 psi < rhovfvy < 1000 psi rhovfvy > 1000 psi Fig. C-27 Ultimate Shear Stress (vu,test) at Failure versus Concrete Compressive Strength (f'c) of PC Members with Shear Reinforcement 0 500 1000 1500 2000 2500 0 20 40 60 80 d (in) vu ,te st (p si ) rhovfvy < 100 psi 100 psi < rhovfvy < 150 psi 150 psi < rhovfvy < 250 psi 250 psi < rhovfvy < 500 psi 500 psi < rhovfvy < 1000 psi rhovfvy > 1000 psi Fig. C-28 Ultimate Shear Stress (vu,test) at Failure versus Effective Depth of PC Members with Shear Reinforcement

C-23 0 500 1000 1500 2000 2500 0 2 4 6 8 a/d vu ,te st (p si ) rhovfvy < 100 psi 100 psi < rhovfvy < 150 psi 150 psi < rhovfvy < 250 psi 250 psi < rhovfvy < 500 psi 500 psi < rhovfvy < 1000 psi rhovfvy > 1000 psi Fig. C-29 Ultimate Shear Stress (vu,test) at Failure versus Shear Span to Depth Ratio for PC Members with Shear Reinforcement 0 500 1000 1500 2000 2500 0 1 2 3 4 5 rhopl (%) vu ,te st (p si ) rhovfvy < 100 psi 100 psi < rhovfvy < 150 psi 150 psi < rhovfvy < 250 psi 250 psi < rhovfvy < 500 psi 500 psi < rhovfvy < 1000 psi rhovfvy > 1000 psi Fig. C-30 Ultimate Shear Stress (vu,test) at Failure versus Longitudinal Reinforcement Ratio for PC Members with Shear Reinforcement

C-24 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 rhovfvy (psi) vu ,te st (p si ) d < 10 in, rhol < 2 % d < 10 in, rhol > 2 % 10 in < d < 30 in, rhol < 2 % 10 in < d < 30 in, rhol > 2 % d > 30 in, rhol < 2 % d > 30 in, rhol > 2 % 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.00 0.10 0.20 0.30 0.40 0.50 0.60 rhovfvy/f'c vu ,te st /f' c d < 10 in, rhol < 2 % d < 10 in, rhol > 2 % 10 in < d < 30 in, rhol < 2 % 10 in < d < 30 in, rhol > 2 % d > 30 in, rhol < 2 % d > 30 in, rhol > 2 % Fig. C-31 Ultimate Shear Stress (vu,test) at Failure versus Strength of Shear Reinforcement for PC Members with Shear Reinforcement Fig. C-32 Ultimate Shear Stress (vu,test) at Failure versus Strength of Shear Reinforcement for PC Members with Shear Reinforcement