L-Spandrels: Can Torsional Distress Be Induced by Eccentric Vertical Loading?

Transcription

1 L-Spandrels: Can Torsional Distress Be Induced by Eccentric Vertical Loading? Donald R. Logan, P.E., FPCI CEO/President Stresscon Corp. Colorado Springs, Colo. Current code-required design procedures for eccentrically loaded L-spandrels assume that torsional distress is the mode of failure at ultimate shear-torsion capacity and prescribe appropriate reinforcement to accommodate such distress. The more commonly accepted design procedures vary in complexity, but all result in the need for heavy reinforcement and complex detailing that are expensive with regard to both material and fabrication labor costs. Based on observation of the failure mode of an L-beam in a full-scale torsion test conducted by the author in 1961, and particularly on his diagnosis of the failure modes of L-spandrels in tests conducted in the mid-1980s by Wiss, Janney, Elstner Associates Inc., the author concludes that the face shell spalling and severe spiral cracking associated with torsional distress is not induced in L-spandrels at ultimate failure by eccentric vertical loading. Thus, the current complex design procedures and the complexity and expense of reinforcement resulting from these procedures are not justified. Instead, the ultimate capacity in the end region of L-spandrels is satisfied by the reinforcement required in their inside face to resist outof-plane bending. Concrete shear capacity is checked by the V cw equation and seldom requires additional reinforcement in deep L-spandrels. 46 PCI JOURNAL

2 v v u u u P u u e v v e u P v v Fig. 1. Torsion load test, November 1961, Donald R. Logan, Edw. Campbell Co., Vineland, N.J. Note: = ft; = in. In the formative years of the prestressed concrete industry (the mid-1950s to the mid-1960s), many aspects of the design and behavior of precast concrete structures and various types of structural members were neither well researched nor clearly understood. Investigations and reports of minor and major distress in structures were among the most important sources of the emerging knowledge and understanding of this important new structural material. Many of us, at that time, also conducted informal, inhouse, full-scale load tests of nearly every condition that had not been formally researched at that time. Although informal and unpublished, these tests and their findings resulted in a growing body of knowledge that was shared among our peers through presentations at local and regional seminars and trade associations, in early PCI committee meetings and subsequent informal discussions, and via telephone and written communication. Questions generated more questions and speculations, leading to even more informal load tests. Within these discussions, internal torsion in precast concrete L-beams was not considered to be an important contributor to structural distress and was generally disregarded. In November 1961, the author conducted a full-scale load test on a 20-ft-long (6 m) precast concrete L-beam supporting short double tees loaded to simulate a 40 ft (12 m) roof span (Fig. 1). The purpose of the test was to attempt to detect and evaluate behavioral symptoms of internal torsion as the L-beam was subjected to eccentric vertical loading that was gradually increased to its calculated shear capacity. Torsional behavior in accordance with St. Venant s classical theory would predict, in a brittle material such as concrete, spiral cracking and warping of the surfaces of rectangular sections, resulting in face-shell spalling. However, no measurable twisting was observed and there was no evidence of any of the above symptoms of torsional distress. The primary finding of the test was that the L-beam experienced severe lateral deflection caused by the component of the vertical load acting transversely to the sharply inclined principal weak axis of the L-beam. The Appendix describes March April

3 y Fig. 2. Eccentrically loaded L-spandrel. Inclination of principal angle = θ. Figure 2 shows a typical precast, prestressed concrete L- spandrel which is used to support end bays in parking structures and to provide the exterior architectural surface treatthis informal load test and includes calculations from November 29, 1961, of the torsional stiffness of the gross concrete section and its computed torsional rotation under the applied eccentric load. These results confirmed the observed torsional rigidity of the L-beam section and the section s resistance to torsional rotation. Meanwhile, during the early 1960s and the 1970s, most formal research on torsion focused on the behavior of rectan- R H H u P(typ.) v x Psinθ v (Deck Ties (typ.) u Pcosθ Fig. 3. Eccentrically loaded L-spandrel. Tie-back forces H provide stabilizing couple at the ends of the L-spandrel. The spandrel is tied to the double-tee deck diaphragm. gular beams subjected to applied twisting moments and the observed distress associated with the effects of internal torsion. Empirical design equations were devised to reflect the observed response of concrete rectangular beams subjected primarily to pure torsion and to provide reinforcement and its detailing to accommodate the observed torsional distress. 1 4 The resulting complexity of design formulas and consequent heavy reinforcement and intricate detailing were reflected in section of Building Code Requirements for Reinforced Concrete (ACI ). 5 However, the need for such detailing was difficult to reconcile with the observed behavior of precast L-beams subjected to eccentric vertical loading in limited full-scale tests and in actual structures where failing L-beams showed none of the distress to which the above design and detailing requirements were directed. In the mid-1980s, full-scale testing of L-spandrels by Gary Klein of Wiss, Janney, Elstner Associates Inc. (WJE), 6 sponsored by the Precast/Prestressed Concrete Institute (PCI), confirmed that neither spiral cracking nor face-shell spalling occurred in the L-spandrels tested, and Klein questioned whether the intricate detailing of reinforcing steel should apply to deep L-spandrel sections. Others, including Bob Mast, Jerry Jacques, and the author, concluded that internal torsion could not be induced in L-spandrels by eccentric vertical loading and that the elaborate design procedures as well as the special torsion reinforcement and detailing were not appropriate for this condition. Despite these test results, none of the subsequent editions of ACI 318 addressed the special condition of precast concrete L-spandrels, and the PCI Design Handbook: Precast and Prestressed Concrete 7 continued to require the complex design procedures for L-spandrels and the consequent heavy reinforcement and intricate detailing derived from the earlier research on internal torsion. Understandably, in an industry survey, PCI Producer Members selected simpler design and detailing of L-spandrels as the number one research priority. In response to the results of this survey, the author volunteered to form an ad hoc subcommittee of the PCI Research & Development Committee to study torsion and recommend a research program. Subsequently, the subcommittee proposed that a full-scale testing program be carried out to determine the actual failure mechanism in the end regions of L-spandrels subjected to eccentric vertical loading and to develop appropriate design procedures to accommodate the observed failure mechanism. The recommended program and its rationale were presented to the full Research & Development Committee in October Excerpts from that proposal are included in this article to illustrate the applicable concepts and principles of L-spandrel behavior. Current Practices, Assumptions, and their consequences 48 PCI JOURNAL

4 Fig. 4. Eccentrically loaded L-spandrel without a double-tee deck tie. P sin θ causes the L-spandrel to bend outward, more at the bottom than the top. ment. The spandrel also provides the necessary resistance to bumper loads and the required safety railing height, either directly or through added railing sections attached to the top of the L-spandrel. The principal axes of the section are included as illustrated, and the component of the applied vertical load Psinθ acts transversely to the weak principal axis below the center of gravity of the section, causing complex outward bending of the spandrel. A simple case of an eccentrically loaded L-spandrel in a typical parking structure is shown in Fig. 3. The ends are stabilized at the columns by a connecting force H at the top of the L-spandrel and an equal and opposite connecting force H at the bottom. The purpose of these connections is to prevent the L-spandrel from falling inward as the eccentric loads are applied to its ledge. The L-spandrel is also tied to the precast concrete double-tee floor diaphragm, providing resistance to vehicle bumper loads. Under increasing load, the L-spandrel tends to tilt and warp in response to the eccentrically applied load. Without the double-tee deck tie, the Psinθ component acting against the weak principal axis causes the L-spandrel to bend outward, more at the bottom than at the top (Fig. 4). With the web of the spandrel tied to the deck, the lateral bending becomes more complex, bending inward at the top and outward at the bottom of the L-spandrel, as illustrated in Fig. 5. If eccentric loading of L-spandrels could induce torsional distress, as the current code requirements and design equations assume, its symptoms would become evident as the load approaches the calculated shear/torsion failure level. The symptoms of torsional distress assumed in the coderequired shear/torsion design are illustrated in Fig. 6, wherein the L-spandrel would experience severe spiral cracking in the end regions accompanied by face-shell spalling as its sur- Fig. 5. Eccentrically loaded L-spandrel with the L-spandrel strongly tied to the double-tee deck diaphragm. The top bends inward, and the bottom bends outward. faces warp and distort under the effects of internal torsion. Current code-required design procedures for L-spandrels accommodate such anticipated torsional distress as the assumed failure mode at ultimate shear/torsion capacity. The sixth edition of the PCI Design Handbook, pages 4-57 to 4-65, leads the design engineer through complex procedures and formulas to design a prestressed L-spandrel and to determine the reinforcing steel requirements. For a specific L-spandrel subjected to eccentric vertical loading, the step-by-step design procedures, starting at the end region, where shear and torsion levels are the greatest, are as follows: 1. Check the threshold levels at which torsion design must be considered: where T u > T u(min) (4.4.1) T u(min) = ϕ 0.5λ f ( c x 2 y) γ γ = 1+10 f pc f c 2. Check the applied loading against the maximum torsion permitted for the section: 1 3 K t λ f c x 2 y T n(max) = 2 K 1+ t V u 30C t T u T u ϕ (4.4.2) March April

5 Outside face Inside face Spiral cracking and face shell spalling Fig. 6. Characteristics of torsional distress assumed in current code-required shear/torsion design. where K t = γ f pc f c C t = b w d x 2 y 3. Check the applied loading against the maximum shear permitted for the section: V n(max) = 10λ f c b w d V u 1+ 30C t T 2 ϕ (4.4.3) u K t V u 4. Check torsion carried by the concrete alone: where T c = 0.8λ f c x 2 y( 2.5γ 1.5) V c = 0.6 f c V u d b w d M u 5. Check shear carried by the concrete alone: V c = V c 1+ V c 2 / V u (4.4.5) T c / T u If the applied shear/torsion load exceeds the capacity of the concrete alone, then complex design procedures are required to determine the area of steel reinforcement needed to accommodate the assumed shear/torsion distress. 6. Area of transverse reinforcement: T c = T c 1+ T c / T u V c / V u 2 (4.4.4) T u ϕ T c s (4.4.6) A t = α t x 1 y 1 f y Check again here where s = tie spacing (x 1 + y 1 )/4 or 12 in. α t = [ y 1 /x 1 ] < 1.5 x 1 = short side of closed tie, in. y 1 = long side of closed tie, in. and ( ) = 50 b w s γ min ( ) b w s A v + 2A t f y f y (4.4.7) Fig. 7. Secondary shear/torsion analysis required. Where shear and torsion reduce toward the interior of the span, all procedures must be checked again to determine whether shear/torsion analysis is required. 7. Area of longitudinal reinforcement: A = 2A t ( x 1 + y 1 ) s (4.4.8) 50 PCI JOURNAL

6 Fig. 8. Code-required shear/torsion reinforcement details. Complexity and congestion of reinforcing cage, complying with code-required shear/torsion design and details. Closed ties and stirrups with 135-degree hooks at corners. or A = 400x f y and need not exceed 50 b w f y T u T u + V u 3C t f pc f c 2A t s 200b w f y x 1 + y 1 ( ) (4.4.9) for 2A t s After the end region is checked, all procedures must be checked again at the reduced shear/torsion region inside the first double-tee stem location (Fig. 7). In most typical cases, the concrete capacity is exceeded even at the reduced shear/ torsion level. The reinforcement quantity calculated by the previous equations and the detailing required by section of ACI 318 result in complex L-spandrel reinforcement cages. Figures 8, 9, and 10 illustrate this complexity, which significantly affects material and fabrication labor costs. Fig. 9. Code-required shear/torsion reinforcement details. The top of the reinforcing bar cage shows conflicts and congestion of longitudinal bars, U-bars, closed stirrups, 135-degree hooks, and strand. tied-arch deep beam flexural failure mode, while the outside face showed only the symptoms of lateral bending, apparently caused by the Psinθ component of the eccentrically applied load P acting below the center of gravity of the L-spandrel section. In addition, there was severe 45-degree cracking of the inside face of the web in the end regions, resulting from the out-of-plane bending induced by the tie-back force needed to prevent the L-spandrel from falling inward. Clearly, the complex design procedures and intricate reinforcement detailing, which are intended to accommodate torsional distress, are not appropriate for the failure mode of the L-spandrels observed in the WJE test series. Suggested Rationale for L-Spandrel Design and Detailing In perhaps the most comprehensive study and analysis of, and guide to, the design of spandrels, Charles Raths 8 report- Are the Current Code Assumptions and Their Consequences Justified for L-Spandrels? As illustrated in Fig. 11, the current code requirements are based on the assumption that the warped concrete face shell spalls off and the reinforcement cage-encased core is all that remains to resist the shear and internal torsion imposed at the ends of the L-spandrel. However, in the full-scale tests conducted in the mid-1980s by Gary Klein of WJE, the L-spandrels at failure showed no evidence of torsional distress. Instead, Figure 12 illustrates that the inside face of the L-spandrel showed symptoms of a March April 2007 Fig. 10. Reinforcement cage complexity resulting from coderequired shear/torsion design. Prestressing strand must be threaded through consecutive, fully assembled reinforcing bar cages in a long-line prestressing plant. 1

7 Outside face Inside face Spiral cracking and face shell spalling Fig. 11. Can code-assumed torsional distress be induced by eccentric vertical loading? ed no evidence of internal torsional distress in his study of actual failures of L-spandrels in structures. In his recommended design procedure, Raths use of the term beam end torsion refers to the end couple needed to prevent the L-spandrel from falling inward in response to the eccentrically applied vertical loading. Klein uses the term torsional equilibrium to refer to this stabilizing couple. Perhaps the terminology should be modified to indicate that this couple provides the external mechanism by which internal torsion is induced into the L-spandrel section. The force necessary to tie the L-spandrel back to its support results in severe 45-degree web cracking in response to the out-of-plane bending of the web. In Raths article, this web cracking and its calculation method are accurately described on page 80 and clearly illustrated on page 82. Paradoxically, the use of the term torsion for this stabilizing couple is even less appropriate because the consequent cracking of the web significantly weakens its stiffness to the extent that the web is unable to transmit the end couple (twisting moment) into the remaining L-spandrel cross section. Thus, internal torsional distress within the section is prevented and the cracked web itself becomes the primary mode of ultimate failure. Figures illustrate the failing web bending mechanism and the ultimate failure mode. If this concept correctly identifies the ultimate failure mode of L-spandrels, the design procedure is reduced to the following: 1. Calculate the orthogonal reinforcement required in the inside face of the web of the L-spandrel to resist outof-plane bending in the end region; 2. Calculate the ledge hanger reinforcement required in the inside face of the web to resist the eccentric loads applied to the top surface of the ledge. Compare the result to the vertical component of the orthogonal reinforcement calculated previously, and select whichever reinforcement is greater for the end region; and 3. Check the shear capacity of the concrete as follows: V cw = 3.5 f ( c f pc ) b w d p +V p If the concrete shear capacity is not exceeded, the minimum shear reinforcement is already satisfied by the hanger reinforcement and/or the out-of-plane bending reinforcement. Thus, no additional shear reinforcement would be needed; and Web bending cracks in inside face Outside face Vertical cracks resulting from lateral bending caused by Psinθ component of vertical force acting to inclined vertical axis at bottom of L-spandrel (see Fig. 2) Inside face Tied-Arch Failure mode. Typical flexural failure of deep beam. Fig. 12. Actual failure mode of L-spandrels in Wiss, Janney, Elstner Associates Inc. tests in the mid-1980s. There was no evidence of torsional distress. 52 PCI JOURNAL

8 Fig. 13. L-spandrel failure mechanism (deck tie is omitted for clarity). Eccentric loading begins, but the web is not yet cracked. Web stiffness can induce torsional stresses into L- spandrel cross section. Fig. 14. L-spandrel failure mechanism (deck tie is omitted for clarity). With increasing eccentric loading, out-of-plane bending causes light web cracking. Reduced web stiffness decreases torsional stresses transmitted into L-spandrel cross section. Fig. 15. L-spandrel failure mechanism (deck tie is omitted for clarity). Severe web cracking isolates remaining L-spandrel cross section from torsional effects of end tie-back couple. Fig. 16. L-spandrel failure mechanism (deck tie is omitted for clarity). The ultimate failure mode is out-of-plane fracture of the end region of the L-spandrel. Torsional distress is not induced. 4. None of the shear/torsional formulas are applicable and do not need to be applied. Since the special shear/torsion reinforcement details are no longer required closed ties and 135-degree hooks are unnecessary and additional longitudinal reinforcement is not required. The cage reinforcement and detailing for L-spandrels are greatly simplified, as illustrated in the example shown in Fig. 17. The sequencing and assembly of prefabricated cage components shown in Fig significantly reduce the fabrication labor for a long prestressing line and permit daily cycling of the production line that is not feasible under the current code-required complexity and detailing shown in Fig March April 2007 Conclusions The stabilizing end couple that prevents L-spandrels from falling inward has been referred to in the literature as torsion. It actually consists of external forces that have the potential to twist and warp the torsionally rigid L-spandrel cross section, causing it to deform and show the symptoms of internal torsional distress, provided the following: The connections to the supporting structure itself are strong and rigid enough to induce such internal deformation; and The L-spandrel web, subjected to out-of-plane bending, remains uncracked and is strong enough to transmit the end couple into the L-spandrel cross section. In laboratory tests, the end couple connections can be designed and executed to be strong and rigid, but in actual prac- 3

9 WWR Reinf. At Ends Interior Span Fig. 17. Reinforcement cage configuration to accommodate out-of-plane bending. 3. Set upper cages; supported by upper-face prestressing strands. 1. Install lower reinf. cage in consecutive forms. 2. Run prestressing strand full length of long-line facility, and apply full prestress to all strands. Fig. 18. Simplified cage assembly. 54 PCI JOURNAL

10 4. Set ledge reinf. cage into assem- Fig. 19. Simplified cage assembly. 5. Fully assembled consecutive Fig. 20. Simplified cage assembly. March April 2007

11 tice, the typical precast concrete connections are generally too flexible to perform this function. Even if the connections are sufficiently strong and rigid, fullscale L-spandrel tests and supporting calculations show that the webs of typical L-spandrels do not appear to be capable of transmitting internal torsion into their cross sections. If the external end couple cannot create internal torsional distress in the L-spandrel cross section, then the complex shear/torsion design and detailing are not appropriate and should not apply to the design and fabrication of L-spandrels. Instead, the design for out-of-plane bending and ledge hanger reinforcement satisfies the requirements for the end regions of L- spandrels. Recommendations The L-spandrel configurations described in this article, tested by Klein in the mid-1980s and described by Raths in his 1984 PCI Journal article, are typical of those commonly used within the precast concrete industry. However, the potential range of configurations and limits to which these concepts apply need to be evaluated and defined. Klein and Raths considered variations such as dapped ends and pocketed spandrels. Raths considered other variations, including L-spandrels not tied back at the top, in which the reaction shifts to the inside until it aligns with the applied eccentric loads, requiring the end region of the ledge to act as an inverted corbel to resist the concentrated reaction load. Many other variations in connection methods, configuration of cross section, and location of bearing reaction (such as midheight or eccentric with respect to the center of gravity of the L-section) exist in actual practice and need to be evaluated with respect to the applicability of the previously mentioned concepts. Generally, L-spandrels are relatively deep and their webs are relatively thin. Compact L-beams are shorter and their webs (stems) are thicker. Although their stems may not crack as ultimate capacity of the end regions is reached, the capability of the connections and the supporting structure may still prevent the end couple from transmitting its twisting effect into the cross section and creating internal torsional distress. The applicability of this concept in compact L-beams needs to be evaluated. Author s Update Since this article was written and the concepts presented to the PCI Research & Development Committee on October 15, 2005, the ad hoc L-Spandrel Committee prepared a full report, which was presented to the Research & Development Committee on December 8, That report recommended that a request for proposal (RFP) be sent to appropriate research organizations to conduct the applicable research to achieve the goal of the suggested research statement: Determine through full-scale tests, an appropriate mechanism, derived from the observed performance of test specimens at service load and failure, which will lead to safe but simpler design procedures and detailing requirements for L-spandrels (as postulated in this report). The ad hoc committee report was accepted by the full PCI Research & Development Committee and the RFP was sent to numerous potential research organizations in February Seven outstanding proposals were received by PCI in May The full Research & Development Committee voted on and selected a research team to conduct the necessary research over a two-year period, to be completed no later than November The members of the L-Spandrel Committee, who will serve as the steering committee for the ongoing research conducted by the successful research team, are Bob Mast, Norm Scott, Ned Cleland, Tom D Arcy, Harry Gleich, and Don Logan (chair), with ongoing input by Doug Sutton (Research & Development Committee chair). Each of these people contributed significantly in the preparation of the final report for the Research & Development Committee. The author specifically acknowledges the early contribution of Bob Mast, who envisioned the relationship between the diminishing stiffness of the cracked web and its inability to induce internal torsional distress in the concrete section (a concept independently envisioned by Ugur Ersoy, who described to the author, in September 1999, the confirming results of his early testing of cast-in-place edge beams); Norm Scott for his early speculations regarding the inapplicability of conventional torsion design to L-spandrels and his review of and comments on the author s presentation and proposed report to the Research & Development Committee; the late Jerry Jacques for extensive debate regarding the applicability and limits to these emerging concepts; and Harry Gleich for enthusiastic support and lively debate, for suggesting modifications to the author s original simplified reinforcing scheme, and for proposing cross-sectional dimensions and span lengths to evaluate the concept, at its anticipated limits, through full-scale laboratory tests. Finally, the author expresses appreciation to his associate Chuck Ross, for refining and re-creating the author s original illustrations into digital form, and to George Nasser, PCI Journal editor emeritus, for his suggested modifications during his review of this article. References 1. Zia, Paul, and W. D. McGee Torsion Design of Prestressed Concrete. PCI Journal, V. 19, No. 2 (March April): pp Mitchell, D., and M. P. Collins Detailing for Torsion. ACI Journal, V. 73, No. 9 (September): pp Zia, P., and T. T. C. Hsu Design for Torsion and Shear in Prestressed Concrete. Paper presented at the American Society of Civil Engineers (ASCE) convention, October 16 20, in Chicago, IL, reprint # Collins, Michael P., and Denis Mitchell Shear and Torsion Design of Prestressed and Non-Prestressed Concrete Beams. PCI Journal, V. 25, No. 5 (September October): pp ACI Committee Building Code Requirements for Reinforced Concrete (ACI ). Section 11.6, pp Detroit, MI: American Concrete Institute (ACI). 6. Klein, G. J Design of Spandrel Beams. PCI Journal, V. 31, No. 5 (September October): pp PCI Industry Handbook Committee PCI Design Handbook: Precast and Prestressed Concrete. 6th ed., pp to Chicago, IL: Precast/Prestressed Concrete Institute (PCI). 8. Raths, Charles E Spandrel Beams Behavior and Design. PCI Journal, V. 29, No. 2 (March April): pp PCI JOURNAL

12 Appendix: Full-Scale Load Test of L-Beam, November 1961 Background For a project under consideration in November 1961, the author addressed the following questions: Is torsional rotation of a precast concrete L-beam a significant design consideration, and if so, would the rotation be reduced by tying the top of the L-beam to the top of supported double tees? Can torsional distress be induced in precast L-beams by eccentric vertical loading? Torsional behavior was addressed in textbooks, but the conditions illustrated were primarily related to axles of circular cross sections. Torsional behavior of rectangular sections was also addressed, but for sections composed of ductile materials in which the surface warping was illustrated and calculation methods were developed to measure the effects. In circular sections composed of a brittle material, such as a piece of blackboard chalk, applying a simple twisting motion to the chalk reveals the classic spiral cracking and failure mode. In rectangular sections composed of a brittle material, such as concrete, it was anticipated that warping of the flat surfaces and corners would result in their spalling, tending to reduce the section to a circular shape. Would these symptoms of torsional distress be induced in the precast concrete L-beam to be tested? Test Setup Figure A1 shows the configuration of the L-beam, its cross section, and its support conditions. The short-span double tees (TTs) were utilized to apply the test load, simulating the load applied by 40-ft-long (12 m) double tees carrying 20 psf (0.96 kpa) superimposed dead load and 30 psf (1.4 kpa) snow load. Loading was gradually increased by successively adding cement sacks, appropriately spaced, and the L-beam was reinforced to comply with applicable code equations for flexure and shear. Rotation and lateral deflection of the L-beam at midspan were observed by sighting through a transit set at an off-set distance parallel to the beam length and measured intermittently at midspan by a hand-held tape (accurate to the nearest 1 32 in. [1 mm]). Test Results Rotation Except for the initial seating of the L-beam at the stabilizing end supports, no measurable torsional rotation was observed during the application of increasing loads, even as the loading of the L-beam approached its calculated ultimate capacity. Lateral Deflection There was no connection between the double tees and the L-beam, and the outside face of the L- beam was only lightly reinforced. As the loading increased, the transverse component of the vertical load Wsinθ caused significant lateral deflection, particularly as vertical cracking developed in the outside face. As the load approached the calculated ultimate capacity of the L-beam, the test was discontinued because the double-tee stems at the L-beam midspan were at risk of losing bearing due to the lateral deflection of the L-beam and local spalling of the L-beam ledge. Conclusions Figure A2 is a replica of original hand calculations, which were prepared immediately after the test on November 29, The calculated torsional rotation of the L-beam at mid-span was compared to the calculated end rotation of a 40-ft-long (12 m) TT under the applied service load. The TT end roatation is 10 times greater than the torsional rotation of the L-beam, demonstrating that welding the top of the TTs to the top of the L-beam tends to increase, rather than decrease, the torsional rotation of the L-beam. Torsional rotation of L-beams subjected to eccentric vertical loading appeared to be insignificant due to the unanticipated torsional rigidity of the concrete section. In this case, at superimposed service load, the calculated differential rotational displacement over the depth of the L-beam is in. = in. (0.25 mm), less than in. (0.25 mm), consistent with the March April 2007 absence of measurable rotation during the test. Lateral deflection was substantial, implying the need to tie the TTs to the L-beam and to provide longitudinal reinforcement in the outside face of the L-beam to reduce post-cracking lateral deflection and protect against premature lateral failure. Although unpublished, the test results, calculations, and conclusions were shared with the project engineerof-record in a letter dated November 30, 1961 (Fig. A3), which emphasizes the resistance to rotation (torsional rigidity) of the L-beam section compared with the end rotation of the TT that applies the load to the L-beam. Neither spiral cracking nor face shell spalling was observed, confirming that torsional distress was not induced by the eccentric loading of the L-beam section, as configured in the test setup. 7

13 10 in. 6 in. e = 8 in. v 5 in. 5 in. 3 in in in. u w sin W w cos u = in. 8 in. 24 in. h = 24 in. W v 6.33 in in. b = 10 in. 16 in. Beam specimen cross section Simplified cross section for torsional rotation calculation No connections Neoprene pad Neoprene pad Steel angle brace 4TT16 20 ft-0 in. Concrete support block L-beam 20 ft-0 in. Support system at ends of L-beam Load application system full length of L-beam Torsion load test November 1961 Donald R. Logan, Edw. Campbell Co. Vineland, New Jersey Fig. A1. Torsion load test, November 1961, Donald R. Logan, Edw. Campbell Co., Vineland, N.J., November Note: 1 in. = 25.4 mm; 1 ft = m. 58 PCI JOURNAL

14 Fig. A2. Relationship between L-beam and double-tee rotation (Original hand calculations from November 1961). Note: 1 in. = 25.4 mm; 1 ft = m; 1 psi = kpa; 1 plf = N/m; 1 psf = Pa. March April

15 Fig. A2 Cont. 60 PCI JOURNAL

16 Fig. A3. A letter dated November 30, 1961, from Donald R. Logan to Howard Stevenson regarding the behavior of L-beams.