SUMMARY OF THE NEW REINFORCED CONCRETE BLAST DESIGN PROVISIONS IN UFC , STRUCTURES TO RESIST THE EFFECTS OF ACCIDENTAL EXPLOSIONS

Transcription

1 SUMMARY OF THE NEW REINFORCED CONCRETE BLAST DESIGN PROVISIONS IN UFC , STRUCTURES TO RESIST THE EFFECTS OF ACCIDENTAL EXPLOSIONS William H. Zehrt, Jr. and Patrick F. Acosta Synopsis: Since its initial publication in 1969, Unified Facilities Criteria (UFC) (formerly Army Technical Manual /Navy Publication NAVFAC-P397/Air Force Manual AFR 88-22) has provided uniquely practical and intuitively straightforward procedures for analyzing and designing blast resistant structures. With its unlimited distribution, UFC is the blast design manual of choice of both government explosives safety experts and private A-E firms throughout the world. This paper summarizes updates to the blast design guidance in chapter 4, reinforced concrete design. Detailed data are presented on the revisions in three areas: dynamic increase factor, design of diagonal tension reinforcement in walls and slabs, and prediction of concrete spall and breach. The paper concludes with a brief discussion of future work. Keywords: design, blast; safety, explosives; concrete, reinforced; spall; breach 8-1

2 William H. Zehrt, Jr. is a safety engineer with the DoD Explosives Safety Board in Alexandria, Virginia. He previously worked for the US Army Engineering and Support Center, Huntsville as a senior structural engineer and branch chief. Bill has extensive experience in blast analysis and design, co-authoring more than 30 technical papers on a wide range of explosives safety topics. He earned BSCE and MSCE degrees from the University of Illinois at Urbana-Champaign and is a registered professional engineer in the state of Alabama. Patrick F. Acosta is a senior structural engineer with the US Army Engineering and Support Center, Huntsville. He is a registered Professional Engineer in the State of Alabama. For the past 18 years, Patrick has been directly involved in the analysis and design of partial and total containment structures to resist the effects of accidental and intentional explosions. INTRODUCTION UFC , Structures to Resist the Effects of Accidental Explosions, (Office of the Deputy Under Secretary of Defense (Installations and Environment) 2008) was first published in 1969 as the tri-service, US Department of Defense (DoD) manual, Army TM /NAVFAC P-397/AFR (TM ) (Department of the Army et al 1969). At the time, it provided engineers with groundbreaking, quantitative procedures for analyzing and designing structures to withstand non-nuclear blast effects. The manual was based upon the results of numerous explosive test programs and accident investigations and included detailed design procedures and step-by-step design examples to illustrate their application. Since reinforced concrete performs particularly well under intense, short duration blast pressures, the manual emphasized the design of reinforced concrete structural elements. During the 1970s and 1980s, understanding of explosive effects and blast resistant construction significantly advanced. In recognition of these advances, DoD funded an extensive revision to the manual. TM , revision 1 (Department of the Army et al. 1990) not only expanded the coverage of reinforced concrete elements but also added detailed analysis and design procedures for structural steel, masonry and other structural materials. Comprehensive examples continued to aid designers in correctly applying these procedures. In recent years, the increased computational capability of mainframe and personal computers has allowed scientists and engineers to gain unprecedented insight into the effects of explosions on both conventional and blast resistant structures. In response, the DoD Explosives Safety Board established a Technical Working Group (TWG) in March 2003 to update TM The TWG provides direction to the revision effort and makes technical decisions related to the manual s content. The TWG charter specifically limits the scope to the incorporation of existing procedures and products; no new research will be funded by the TWG. Due to funding constraints, TWG work has focused on areas with the most potential benefit to the explosives safety community. Several TWG-funded studies evaluated reinforced concrete research and test data published since the development of TM , revision 1. When warranted, TWG members developed revisions to chapter 4 s reinforced concrete guidance for review by the full working group. The resulting draft revisions were disseminated to the explosives safety community at the 2006 DoD Explosives Safety Seminar (Woodson and Zehrt 2006; Zehrt et al. 2006). Draft final revisions were then developed and reviewed by TWG members. As a last step, the final chapter 4 revision was converted to UFC format and incorporated in UFC , published on 5 Dec 2008 (Office of the Deputy Under Secretary of Defense (Installations and Environment) 2008). REVISION SUMMARY A summary of the UFC revisions is provided in Table 1. Due to the extent of these revisions, it is not feasible to discuss each change in this paper. Instead, we will illustrate the scope of the updates by focusing on 8-2

3 changes in three areas: dynamic increase factor (Malvar 1998, Malvar and Crawford 1998); design of diagonal tension reinforcement in walls and slabs (Woodson and Zehrt, 2006; Zehrt et al. 2006); and prediction of concrete spall and breach (Marchand 1994). Dynamic increase factor A structural element subjected to a blast loading exhibits a higher strength than a similar element subjected to a static loading. This increase in the strength is attributed to the rapid rates of strain that occur in dynamically loaded structures. Thus, the dynamic ultimate resistance of an element subjected to a blast load is greater than its static resistance. Both concrete and steel reinforcing bars exhibit greater strength under rapid strain rates. The higher the strain rate, the higher the compressive strength of concrete and the ultimate strength of the reinforcing bar. This phenomenom is accounted for in the design of a blast resistant structure by using dynamic stresses to calculate the dynamic ultimate resistance of reinforced concrete members. The dynamic increase factor (DIF) is defined as the ratio of the dynamic stress to the static stress, e.g., f dy /f y, f du /f u and f' dc /f' c. As previously noted, the DIF depends upon the rate of strain of an element, increasing as the strain rate increases. TM , revision 1 (Department of the Army et al. 1990) provided design curves of the DIF versus strain rate for use in computing the ultimate dynamic compressive strength of 4,000 psi concrete and the dynamic yield stress of ASTM A615 Grade 60 reinforcing bars. UFC (Office of the Deputy Under Secretary of Defense (Installations and Environment) 2008) updates and expands upon these data. New DIF design curves are provided for the ultimate compressive strength of concrete with 2,500 < f c < 5,000 psi (17.2 Mpa < f c < 34.5 MPa) and with f c = 6,000 psi (41.4 MPa) and for the ultimate tensile strength (before cracking) of concrete with f c = 6,000 psi (41.4 MPa). These curves are shown in Fig. 2 and Fig. 3. The new DIF design curves for the yield and ultimate stresses of ASTM A 615 Grade 40, Grade 60 and Grade 75 reinforcing steel are given in Fig. 4. Grade 40 steel is not permitted in new protective construction. Thus, the Grade 40 data are included for comparative purposes and for use in evaluating existing construction. The curves were derived from test data having a maximum strain rate of 300 in./in./second for concrete and 100 in./in./second for steel. Values taken from these design curves are conservative DIF estimates and are safe for design purposes. Design of diagonal tension reinforcement in walls and slabs Non-laced elements make up the bulk of protective concrete construction for explosives safety applications. These elements are generally used to withstand the blast and fragment effects associated with the far design range but also may be designed to resist close-in effects. Non-laced elements may be designed to attain small or large deflections depending upon the protection requirements of the acceptor system. TM , revision 1 (Department of the Army et al. 1990) placed several restrictions on the use of single leg stirrups to withstand the diagonal tensions forces in reinforced concrete slabs. The manual required lacing when the center of an explosive charge was located at scaled distances less than 1.0 ft/lb 1/3 (0.4 m/kg 1/3 ). This requirement was applied to all protection categories and design support rotations and even applied in slabs with sufficient thickness to prevent spalling. In addition, the manual required lacing if the design support rotation exceeded four degrees under flexural action or eight degrees under tensile membrane action. The diagonal tension design requirements in UFC (Office of the Deputy Under Secretary of Defense (Installations and Environment) 2008) are based upon a wide range of explosives testing programs conducted since the early 1960s. Brief summaries of more recent, unclassified research reports and test data follow. 8-3

4 Effects of Stirrups Details on Load-Response Behavior of Slabs (Woodson and Kiger, 1986) Woodson and Kiger analyze data from 10 experiments of one-way, rigidly restrained, concrete slabs under a uniformly distributed pressure. Two of these slabs were reinforced by single leg stirrups with degree bends. These slabs attained maximum support rotations of 14.0-degrees and 14.5 degrees without collapse. Woodson and Kiger conclude that slabs with stirrups can be designed to provide significant ductility. Although laced slabs may allow some further increase in ductility, the authors state that this increase will not be sufficient to justify the additional expense. Shear Reinforcement in Blast-Resistant Design, (Kiger et al, 1988) Kiger et al state that in blast resistant slab designs, the reinforcement normally considered to be diagonal tension reinforcement does not primarily act to resist shear forces. Instead, this reinforcement improves a slab s performance in the large deflection region by tying the two principal mats together. The authors note that the data from several research programs investigating structural response to static and blast loads indicate that reinforced concrete structures can sustain large deflections (rotations in excess of 12 degrees) without failure. None of the tested slabs used lacing for diagonal tension reinforcement. While most slabs had stirrups, some slabs successfully sustained large deflections with no diagonal tension reinforcement at all. Kiger et al further report that in virtually all of the data cited where stirrups were used, the stirrups had a 135-degree bend on one end and a 90-degree bend on the other end. These stirrups performed satisfactorily under both static and high intensity blast loads and were much easier and more economical to install than stirrups with 180-degree bends on each end. Alternative Shear Reinforcement Guidelines for Blast Resistant Design, (Woodson et al, 1990) Woodson et al provide an extensive review of relevant test data (278 tests). These tests measured the performance of reinforced concrete slabs and box-type structures having lacing bars, stirrups, and no diagonal tension reinforcement under both static and dynamic loads. Unfortunately, although the database includes a large number of tests, Woodson et al report significant gaps. Nonetheless, the authors conclude that the laced slabs that were tested did not respond significantly differently than slabs containing a similar amount of diagonal tension reinforcement in the form of single leg stirrups. This research led to the publication of guidance in the 1990 Army Engineer Technical Letter (Department of the Army, US Army Corps of Engineers, 1990) permitting the use of three stirrup configurations (including stirrups) for hardened construction. Lacing and Stirrups in One-Way Slabs, (Woodson, 1992) The overall objective of this study was to better understand the effects of diagonal tension reinforcement details on slab behavior, thereby allowing improvements in protective construction design requirements, enhancing both safety and cost effectiveness. Sixteen one-way reinforced concrete slabs were statically (slowly) loaded with water pressure. All slabs were designed to be loaded in a clamped (laterally and rotationally restrained) condition and may be considered to be approximately ¼-scale models of prototype wall or roof slabs of protective structures. The investigation indicated that one-way slabs typical of protective construction (equal top and bottom steel, restrained at ends) are susceptible to diagonal tension failure when reinforced with approximately 0.5 percent or more principal steel, but with no diagonal tension reinforcement. In comparison, the response and behavior of the slabs reinforced with lacing and with single leg stirrups were very similar, differing only slightly in resistance values. Woodson concludes that single-leg stirrups with a 90-degree bend on one end and a 135-degree bend on the other end are sufficient to prevent diagonal tension failure and to enhance the reserve capacity to the same level as (or, as in some cases of this study, better than) lacing bars. Based upon the foregoing research, UFC significantly revised and expanded the allowable uses of single leg strrups for diagonal tension reinforcement. Further details are provided in the following paragraphs. For the purposes of this section, far range effects occur when the scaled distance from the charge to the wall or slab is greater than or equal to 3.0 ft/lb 1/3 (1.2 m/kg 1/3 ). The scaled distance is calculated by dividing the minimum distance from the center of the explosive charge to the element being designed by the design explosive weight raised to the one-third power. For example, for a stand-off distance of four feet (1.22 m) and a design charge weight of eight pounds (3.63 kg), the scaled distance would be calculated as four divided by (8) 1/3 or 2 ft/lb 1/3 (0.8 m/kg 1/3 ). 8-4

5 In UFC , a non-laced element designed for far range effects may attain deflections corresponding to support rotations up to two degrees under flexural action. Single leg stirrups are not required to attain this deflection. However, diagonal tension reinforcement is required if the shear capacity of the concrete is not sufficient to develop the ultimate flexural strength Per UFC , Type A, Type B or Type C single leg stirrups must be provided when a non-laced element is designed to resist close-in blast effects to prevent local punching shear failure. When the explosive charge is located at scaled distances less than 1.0 ft/lb 1/3 (0.4 m/kg 1/3 ), Type C single leg stirrups or lacing must be employed. For scaled distances greater than 1.0 ft/lb 1/3 (0.4 m/kg 1/3 ) but less than 3.0 (1.2 m/kg 1/3 ), single leg stirrups must be provided, while for scaled distances greater than 3.0 ft/lb 1/3 (1.2 m/kg 1/3 ), diagonal tension reinforcement should be used only if required by analysis. A single leg stirrup consists of a straight bar with a hook at each end. Minimum bar bend requirements for single leg stirrups depend upon both the design support rotation and the scaled distance of the charge from the element, as follows: Type A Single leg stirrup with a 90 degree hook on one end and a 135 degree hook on the other end. Type A stirrups may be used only if the scaled distance from the center of the charge to the element is greater than 1.0 ft/lb 1/3 (0.4 m/kg 1/3 ), the design support rotation is 2-degrees or less, and concrete spalling is prevented. Placement requirements for Type A stirrups are summarized in Fig. 5. For elements designed for blast loading on one-face only, the 90 degree leg shall be placed on the blast face. For elements designed for blast loading on either face, the 90 degree leg shall be alternated between each face. Type B Single leg stirrup with 135-degree hooks on both ends. Type B stirrups may be used only if the scaled distance from the center of the charge to the element is greater than 1.0 ft/lb 1/3 (0.4 m/kg 1/3 ). Type B stirrups are acceptable for all protection categories and thus, may be used for design support rotations up to 12 degrees. Type C Single leg stirrup with a 180-degree hook on each end. Type C stirrups may be used for all charge separation distances allowed by this UFC. It should be emphasized that these separation distances are the minimum clear distance from the surface of the charge to the surface of the element. The normal scaled distances (center of charge to surface of barrier) corresponding to these minimum clear separation distances are equal to approximately 0.25 ft/lb 1/3 (0.1 m/kg 1/3 ). Type C stirrups also are acceptable for all protection categories and thus, may be used for design support rotations up to 12 degrees. Single leg stirrup hooks shall conform to ACI 318. At any particular section of an element, the longitudinal flexural reinforcement is placed to the interior of the transverse reinforcement and the stirrups are bent around the transverse reinforcement (Fig. 5). The required quantity of single leg stirrups is a function of the element's flexural capacity while the size of rebar used is a function of the required area and spacing of the stirrups. The maximum and minimum size of stirrup bars are No. 8 and No. 3, respectively, while the spacing between stirrups is limited to a maximum of d/2 for type I crosssections (concrete effective in resulting moment) or d c /2 for other cross-sections where d is defined as the distance from the extreme compression fiber to the centroid of the tension reinforcement and d c is defined as the distance between the centroids of the compression and the tension reinforcement. The preferable placement of single-leg stirrups is at every flexural bar intersection. However, the transverse flexural reinforcement does not have to be tied at every intersection with a longitudinal bar. A grid system may be established whereby alternate bar intersections in one or both directions are tied within a distance not greater than 2 feet (0.61 m). The choice of the three possible schemes depends upon the quantity of flexural reinforcement, the spacing of the flexural bars and the thickness of the concrete element. For thick, lightly reinforced elements, stirrups may be furnished at alternate bar intersections, 8-5

6 whereas for thin and/or heavily reinforced elements, stirrups will be required at every bar intersection. For those sites where large stirrups are required at every flexural bar intersection, the bar size used may be reduced by furnishing two stirrups at each flexural bar intersection. In this situation, a stirrup is provided at each side of longitudinal bar. Single leg stirrups must be distributed throughout an element. Unlike shear reinforcement in conventionally loaded elements, the stirrups cannot be reduced in regions of low shear stress. The size of the stirrups is determined for the high stress areas and, because of the non-uniformity of the blast loads associated with close-in detonations, this size stirrup is placed across the span length to distribute the loads. For two-way elements, diagonal tension stresses must be resisted in two directions. Prediction of concrete spall and breach Direct spalling is caused by a compression wave traveling through a concrete element, reaching the back face and being reflected as a tension wave. Spalling occurs when the tension is greater than the tensile strength of the concrete. TM , revision 1 (Department of the Army et al, 1990) provided limited guidance for predicting the spall and breach of concrete elements under blast loading. This guidance was limited to evaluating an element s response either to blast overpressure or to impact by a single metal fragment. In comparison, UFC (Office of the Deputy Under Secretary of Defense (Installations and Environment) 2008) allows users to directly assess spall and breach from the detonation of both thin and heavily cased munitions at a wide range of scaled standoff distances. While arena test data for munitions are typically classified, several open distribution documents have been published that provide useful evaluations of a concrete element s response to a cased munition s combined overpressure and fragmentation loads. A brief summary of this supporting research follows. Spall Damage of Structures, (McKay, 1988) McVay conducted 40 spall and breach experiments and collected data from 334 additional tests performed by others. The data were combined to make a large database upon which empirical prediction methods could be made. All of the data were tabulated. Table 2 summarizes the number of tests with scaled distances less than 1.0 that were incorporated into the empirical models. Shear Reinforcement in Blast-Resistant Design, (Kiger et al, 1988) Kiger et al define lacing bars as reinforcing bars that extend in the direction parallel to the principal reinforcement and are bent into a diagonal pattern between mats of principal reinforcement. The lacing bars enclose the transverse reinforcing bars which are placed outside the principal reinforcement. Kiger et al state that in blast resistant designs, the primary purpose of this type of reinforcement, normally considered to be shear reinforcement, is not to resist shear forces but rather to improve performance in the large deflection region by tying the two principal mats together. Review of data from several research programs investigating structural response to static and blast loads over a 10-year period indicated that reinforced concrete structures can sustain large deflections (rotations in excess of 12 degrees) without failure. None of these structures had laced elements. Most had stirrups reinforcement, but some sustained large deflections without failure with no shear reinforcement at all. Kiger et al conclude that shear reinforcement will not help in preventing spall of the concrete cover over the reinforcement. Dynamic Tests of Reinforced Concrete Slabs, (Tancreto, 1988) Tancreto describes results from six scaled tests of reinforced concrete slabs under blast loading. Test objectives included verifying that the then proposed TM , revision 1 breaching restrictions for close-in detonations were sufficient [lacing required at z < 1.0 ft/lb 1/3 (0.4 kg/m 1/3 ) and stirrups required at 1.0 ft/lb 1/3 < z < 3.0 ft/lb 1/3 (0.4 m/kg1/3 < z < 1.2 m/kg1/3)]. In addition, data were obtained on slabs with stirrups and on slabs with no diagonal tension reinforcement to justify a reduction in the scaled standoff distance required to prevent breaching. The test slabs had plan dimensions of 10-6 x 10-6 (3.20 m x 3.20 m) with two-way unsupported spans of 7-6 x 7-6 (2.29 m x 2.29 m). The charge weight in all tests was 60 lbs (27.2 kg) C4 explosive [equivalent to 67.8 lbs (30.7 kg) TNT]. Other test parameters are 8-6

7 summarized in Table 3. Spalling was expected and occurred in all tests. Tancreto concludes that single leg stirrups are adequate for resisting breaching at z = 0.7 ft/lb 1/3 (0.28 m/kg 1/.3 ) Revisiting Concrete Spall and Breach Prediction Curves: Strain Rate (Scale Effect) and Impulse (Pulse Length and Charge Shape) Considerations, (Marchand et al, 1994) Marchand et al note that the prediction of concrete structure spall and breach as generated by tactical weapons ranging in size from small mortars up to large aircraft bombs has traditionally been accomplished through the use of empirically generated prediction curves and algorithms based on data fits to those curves. Marchand et al report the results ofa complete review of all of the pertinent parameters for spall and breach prediction and a similitude analysis. These data are applied to spall and breach threshold analysis. Marchand et al then provide equations and figures that were developed in accordance with their recommended data and scaling approach. Based upon the extensive test data and knowledge base that have been developed in recent years, UFC provides much more detailed spall and breach guidance than previous versions of the manual. The new guidance incorporated in UFC is reviewed in the following paragraphs. Many spall tests have been conducted on the configuration shown in Fig. 6, where a cylindrical charge, cased or bare, is oriented side-on at a stand-off distance from a wall slab and oriented end-on in contact with the ground. Tested variations to this configuration include non-cylindrical charge shapes, charges off the ground, and charges in contact with the slab. Test data for all of these cases have been compiled and analyzed and are plotted in Fig. 7. The test data in this figure are reported in terms of the observed severity of spall, i.e., as either no spall, spall (no breach), or breach. Threshold spall and breach curves are plotted as approximate upper bounds to the spall and breach data points, respectively and may be used in design. The spall threshold curve is given by Eq. 1: h R a b c 0.5 (1) where: h = concrete thickness (ft) R = Range from slab face to charge center of gravity (ft) a = b = c = Ψ = spall parameter (equations 3 and 4) The breach threshold curve is given by Eq. 2: h R 1 a b c 2 (2) where: h = concrete thickness (ft) R = range from slab face to charge center of gravity (ft) a = b = c = Ψ = spall parameter (Eq. 3 and Eq. 4) 8-7

8 The spall parameter for noncontact charges is given by Eq. 3: W adj R f ' c Wadj (3) W adj Wc Equation 4 gives the spall parameter for contact charges: R f ' c Wadj (4) where: Ψ = spall parameter R = range from slab face to center of charge (ft) f c = concrete compressive strength (psi) W adj = adjusted charge weight (lb) W c = steel casing weight (lb) The spall parameter equations have limits of 0.5 Ψ 14. The adjusted charge weight, W adj, is the weight of a hemispherical surface charge that applies an equal explosive impulse at the target to that of the actual charge (see Fig. 6) and is given by Eq. 6: where: W adj = B f C f W (6) W adj = adjusted charge weight (lb) B f = burst configuration factor = 1.0 for surface bursts, 0.5 for free air bursts W = equivalent TNT charge weight (lb) C f = cylindrical charge factor given by Eq. 7 and Eq. 8: where: 1 LD ; (3 /16) R C f L > D and R/W < 2.0 (7) LD 2W 333 C f = 1.0; all other cases (8) L = charge length (ft) D = charge diameter (ft) R = range from slab face to charge center of gravity (ft) W = equivalent TNT charge mass (lb) The burst configuration factor, B f, is used to correct to a surface burst condition, such as the ground in Fig. 6. The charge shape factor, C f, is used to correct to hemispherical charge geometry in the case of close-in cylindrical charges oriented side-on to the slab. These corrections are applicable to both standoff and contact charges. It should 8-8

9 be considered in design that when the munition position is variable, a contact burst may not be worst-case. The spall effect for cased charges can be greatest at a small standoff, particularly for heavy casings. The test data range listed in Table 4 for each parameter shows that the data spans a wide range of subscale and fullscale tests. Although subscale tests predominate in the data base, the applicability of Fig. 7 to large full-scale weapons is enhanced by the fact that concrete strain rate effects are accounted for in the Ψ term. FUTURE WORK Future work will focus on the update and expansion of UFC s content. We anticipate that this work will include the update and expansion of UFC s masonry and structural steel blast design guidance; the revision of the gas pressure calculation procedure for partially blast containment rooms (Bogosian and Zehrt 1998, Tancreto and Zehrt, 1998, Hager et al, 2006), and the addition of new guidance on innovative materials and on retrofit of existing structures. CONCLUSIONS Since its initial publication in 1969, TM /UFC has provided uniquely practical and intuitively straightforward procedures for analyzing and designing blast resistant structures. With its unlimited distribution, UFC is the blast design manual of choice of both government explosives safety experts and private A-E firms through the world. To obtain maximum benefit from recent research advances, pertinent data must be disseminated quickly to the blast design community in an open distribution document. Whenever possible, guidance should be written so it can be understood and applied by a veteran structural designer with little or no blast experience. Although UFC provides updated reinforced concrete design guidance, additional revisions and supplementary coverage of new, innovative systems and materials are sorely needed. The UFC Technical Working Group currently is working to update and expand the masonry design guidance in chapter 6. A major revision to the structural steel design guidance in chapter 5 is scheduled to follow. Referenced standards and reports REFERENCES The standard listed below was the latest edition at the time this document was prepared. Because this document is revised frequently, the reader is advised to contact the proper sponsoring group if it is desired to refer to the latest version. American Concrete Institute 318 Building Code Requirements for Reinforced Concrete This publication may be obtained from this organization: American Concrete Institute Country Club Drive Farmington Hills, MI

10 Cited references ACI Committee 318, 1983, Building Code Requirements for Reinforced Concrete (ACI ), American Concrete Institute, Farmington Hills, MI. Bogosian, D. D. and Zehrt, W. H., Jr., Assessment of Analytical Methods Used to Predict the Structural Response of 12-inch Concrete Substantial Dividing Walls to Blast Loading, Twenty-Eighth DoD Explosives Safety Seminar Proceedings, Orlando, FL, Department of the Army, US Army Corps of Engineers, Response Limits and Shear Design for Conventional Weapons Resistant Slabs, Engineer Technical Letter , Washington, DC, Departments of the Army, the Navy and the Air Force, 1969, Structures to Resist the Effects of Accidental Explosions, Army Technical Manual , Navy Publication NAVFAC P-397, Air Force Manual AFM 88-22, Washington, DC. Departments of the Army, the Navy and the Air Force, 1990, Structures to Resist the Effects of Accidental Explosions, Revision 1, Army Technical Manual , Navy Publication NAVFAC P-397, Air Force Manual AFM 88-22, Washington, DC. Hager, K., Needham, C., and Doolittle, C., Algorithm for Calculating Gas-Pressure Rise-Time for Confined Explosions, Thirty-Second DoD Explosives Safety Seminar Proceedings, Philadelphia, PA, Kiger, S. A., Woodson, S. C., and Dallriva, F. D., Shear Reinforcement in Blast-Resistant Design, Twenty-Third DoD Explosives Safety Seminar Proceedings, Atlanta, GA, Malvar, L. J., Review of Static and Dynamic Properties of Steel Reinforcing Bars, ACI Materials Journal, vol. 95, no. 5, September-October 1998, pp Malvar, L. J. and Crawford, J. E., Dynamic Increase Factors for Steel Reinforcing Bars, Twenty-Eighth DoD Explosive Safety Seminar Proceedings, Orlando, FL, Marchand, K. A., Improving Tools for Spall and Breach Prediction, Final Report to U. S. Army Engineer Waterways Experiment Station, Contract No. DAC39-93-M-7992, June Marchand, K. A., Woodson, S., and Knight, T., Revisiting Concrete Spall and Breach Prediction Curves: Strain Rate (Scale Effect) and Impulse (Pulse Length and Charge Shape) Considerations, Twenty-Sixth DoD Explosives Safety Seminar Proceedings, Miami, FL, McVay, M. K., Spall Damage of Structures, Technical Report SL-88-22, US Army Waterways Experiment Station, Vicksburg, MS, Tancreto, J. E., Dynamic Tests of Reinforced Concrete Slabs, Twenty-Third DoD Explosives Safety Seminar Proceedings, Atlanta, GA, Tancreto, J. E. and Zehrt, W. H., Jr., Design for Internal Quasi-Static Pressures from Partially Contained Explosions, Twenty-Eighth DoD Explosives Safety Seminar Proceedings, Orlando, FL, The Departments of the Army, Air Force, and Navy and the Defense Special Weapons Agency, 2002, Design and Analysis of Hardened Structures to Conventional Weapons Effects, UFC , Distribution authorized to U. S. Government Agencies and their contractors, Washington, DC. 8-10

11 Woodson, S. C., Lacing and Stirrups in One-Way Slabs, Twenty-Fourth DoD Explosives Safety Seminar Proceedings, Anaheim, CA, Woodson, S. C., Gaube, W. H., and Knight, T. C., Alternative Shear Reinforcement Guidelines for Blast Resistant Design, Twenty-Fourth DoD Explosives Safety Seminar Proceedings, St. Louis, MO, Woodson, S. C. and Kiger, S. A., Effects of Stirrups Details on Load-Response Behavior of Slabs, Twenty-Second DoD Explosives Safety Seminar Proceedings, Anaheim, CA, Woodson, S. C. and Zehrt, W. H., Jr., Investigation of Army TM /NAVFAC P-397/AFR Diagonal Tension Requirements at Low Scaled Distances, Thirty-Second DoD Explosives Safety Seminar, Philadelphia, PA, Zehrt, W. H., Jr., Woodson, S. C., and Beck D. C., Investigation of Army TM /NAVFAC P-397/AFR Bar Bend Requirements for Single Leg Stirrups used as Diagonal Tension Reinforcement, Thirty-Second DoD Explosives Safety Seminar Proceedings, Philadelphia, PA,

12 Table 1 Summary of reinforced concrete design changes incorporated in UFC Description Increases maximum design support rotation for non-laced reinforced concrete elements under flexural action to 6-degrees. Increases maximum design support rotation for non-laced reinforced concrete elements under tension membrane action to 12-degrees. Allows use of ASTM A 706 reinforcing bars in lieu of ASTM A 615 reinforcing bars. Updates and expands dynamic increase factor data for concrete and reinforcing bars. Revises dynamic design stresses for elements with a maximum design support rotation, θ m, 5 o < θ m 6 o. Provides new equations for calculating minimum reinforcement ratios for slabs. Equations now explicitly consider the concrete s compressive strength and the reinforcing bar s yield strength. Adds alternate ACI equation for calculating the allowable shear stress on the unreinforced web of an element subjected to flexure only. Revises diagonal tension design requirements for slabs that are based upon the scaled charge distance. Updates minimum design shear stresses. In addition, instead of basing requirements upon close-in and far design ranges, requirements are now based upon the scaled charge distance from an element. Revises the equation for allowable ultimate direct shear force, V d, that may be resisted by the concrete in a slab. Adds new sections on tension design requirements in non-laced slabs, laced slabs and beams (previously provided in section 4-68). Significantly revises reinforcing bar development and lap splice requirements. In general, reinforcing bar development and lap splice lengths now calculated in accordance with ACI 318. Supplementary requirements are noted. References Section 4-9.2, Section 4-9.3, Section 4-16, Section , Section 4-24, Section , Section , Section and Section 4-34 Section and Section Section Section , Figure 4-9a, Figure 4-9b and Figure 4-10 Section (Table 4-2) Section , Table 4-3, Section and Appendix 4A (Example 4A-1, step 6 and Example 4A-4, step 6) Section Section Section and Table 4-4 Section and Section Section 4-20A, Section and Section 4-35A Section 4-21 and subsections, Section 4-64, Section and Section 4-66 subsections Significantly expands allowable uses of single leg stirrups for diagonal Section 4-22 and Section

13 tension reinforcement in slabs. Provides limits on the use of three different single leg stirrup types (designated as Type A, Type B and Type C). Updates figures summarizing design parameters for unlaced and laced elements to incorporate new criteria. Replaces minimum reinforcement ratio guidance with new equations that explicitly consider the concrete s compressive strength and the reinforcing bar s yield strength. Provides new equations for calculating the minimum area of closed ties in columns. Provides new equations for calculating the minimum area of spiral reinforcement in columns. Section completely revised to incorporate UFC s procedures for predicting concrete spall and breach. Since UFC is a limited distribution document, these open distribution procedures were not previously available to the public. Defines Type A, Type B and Type C single leg stirrups and their allowable uses. Section revised to eliminate now duplicate guidance for non-laced slabs, laced slabs and beams (now provided in Section 4-20A, Section and Section 4-35A, respectively). Figure 4-17 and Figure 4-29 Section and Appendix 4A (Example 4A-6, step 4d) Section Section Section 4-55 (including Figure 4-65, Figure 4-65a and Table 4-15a) Section Section 4-68 Figures updated to incorporate changes to design criteria. Figure 4-1, Figure 4-2, Figure 4-18, Figure 4-21, Figure 4-59, Figure 4-83, Figure 4-85, Figure 4-101, Figure and Figure Updates and expands bibliography. Appendix 4C 8-13

14 Table 2 Empirical data base for scaled distances less than 1.0 ft/lb 1/3 (0.4 m/kg 1/3 ) reported by McVay. Scaled Distance Number of Tests (ft/lb 1/3 ) <

15 Table 3 Major test parameters reported by Tancreto. Slab Type Slab Thickness (in.) Flexural Steel (%) Flexural Steel Spacing (in.) Diagonal Tension Reinf. Spacing (in.) Scaled Charge Distance (ft/lb1/3) Type of Diagonal Tension Reinforcement I d/2 d/ Stirrups II d D 0.74 Lacing III d D 0.65 Stirrups IV d/2 D 0.69 Stirrups V d d 1.10 None VI d/2 d/ Stirrups 8-15

16 Table 4 Parametric ranges for spall prediction. Parameter Maximum Minimum Average Standoff distance, R, in Charge weight, W, lb Case length, in Case diameter, in Case thickness, in R/W 1/3, in/lb 1/3 * Concrete thickness, T, in f c, psi Rebar spacing, S, in Reinf. Ratio, ρ *The minimum allowable design value for R/W 1/3 is approximately 0.25 ft/lb 1/3 (0.10 m/kg 1/3 ). 8-16

17 Figure 1 - Design curve for DIF for ultimate compressive strength of concrete, 2,500 psi < f c < 5,000 psi (17.2 Mpa < f c < 34.5 MPa). 8-17

18 Figure 2 Design curves for DIFs for ultimate compressive and tensile strengths of concrete, f c = 6,000 psi (41.4 MPa) in semi-log format. 8-18

19 10 Tension Compression DIF 1 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 Strain Rate (in/in/s) Figure 3 Design curves for DIFs for ultimate compressive and tensile strengths of concrete, f c = 6,000 psi (41.4 MPa) in log-log format. 8-19

20 DYNAMIC INCREASE FACTOR Grade 40 yield Grade 60 yield Grade 75 yield Grade 40 ultimate Grade 60 ultimate Grade 75 ultimate STRAIN RATE (1/S) Figure 4 - Design curves for DIFs for yield and ultimate stresses of ASTM A 615 Grade 40, Grade 60, and Grade 75 reinforcing steel. 8-20

21 Figure 5 Placement requirements for Type A single-leg stirrups. 8-21

22 Figure 6 Typical geometry for spall predictions. Figure 7 - Threshold spall and breach curves for slabs subject to high-explosive bursts in air (standoff and contact charges, cased and bare). 8-22