Load Capacity Of Shallow Embedded Anchor Channels

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Article Article Load Capacity Capacity of Load of Shallow Shallow Embedded Embedded Anchor Anchor Channels Channels 1, and Akanshu Sharma 22 Christoph Mahrenholtz Christoph Mahrenholtz 1,** and Akanshu Sharma 1 Jordahl,12057 12057Berlin, Berlin,Germany Germany Jordahl, Institute of Construction Materialsand andMaterials MaterialsTesting TestingInstitute, Institute,University UniversityofofStuttgart, Stuttgart, Institute of Construction Materials 70569 Stuttgart, Germany; akanshu.sharma@iwb.uni-stuttgart.de 70569 Stuttgart Germany; akanshu.sharma@iwb.uni-stuttgart.de ** Correspondence: Correspondence:christoph.mahrenholtz@jordahl.de christoph.mahrenholtz@jordahl.de 1 2 2 Received: 2020 Received: 88 September September 2020; 2020; Accepted: Accepted: 29 29 October October 2020; 2020; Published: Published: 231November October 2020 Anchorchannels channelsare are cast in concrete the connection of components using Abstract: Anchor cast in concrete and and allowallow the connection of components using channel channel recentthe years, the design value resulted ever thinner concrete elements, bolts. Inbolts. recentInyears, design to valuetoresulted in everinthinner concrete elements, whichwhich often often accommodate the required embedment depth of standard channels. this cannotcannot accommodate the required embedment depth of standard anchor anchor channels. For thisFor reason, reason, may be fitted with short While anchors. Whiledesign existing design provisions allow for the channelschannels may be fitted with short anchors. existing provisions allow for the calculation calculation of the tension capacity also for shallow embedded anchortests channels, tests are to of the tension capacity also for shallow embedded anchor channels, are required torequired determine determine product-specific for theshear economic shear loads design. The presented study product-specific parametersparameters for the economic loads design. The presented study investigated investigated the performance of shallow embedded anchor channels tested in shear. evaluation The detailed the performance of shallow embedded anchor channels tested in shear. The detailed of evaluation of the test data demonstrates that testing of the minimum embedment is conservative the test data demonstrates that testing of the minimum embedment is conservative and that the and that the load-displacement behavior with of channels welded is comparable to that load-displacement behavior of channels weldedwith I-sections is I-sections comparable to that of channels of channels forged headed studs. In addition, a newapproach evaluation with forged with headed studs. In addition, a new evaluation is approach proposed.is proposed. Keywords: anchor anchor channel; shallow embedment; concrete edge breakout; shear capacity 1. Introduction Introduction Anchor channels with channel bolts allow versatile possibilities to conveniently and reliably reinforced concrete structures. Qualified anchoranchor channel–channel bolt-systems connect components componentstoto reinforced concrete structures. Qualified channel–channel boltreliably take up static and cyclic loads even under conditions to be anticipated, e.g., fore.g., the systems reliably take up static and cyclic loads evenextreme under extreme conditions to be anticipated, anchoring of brackets holding curtain wall elements of supertall skyscrapers which are subjected to for the anchoring of brackets holding curtain wall elements of supertall skyscrapers which are high deadto and wind loads 1a). (Figure 1a). subjected high dead and(Figure wind loads Figure 1. (a) The The One, One, Toronto, Toronto, aa supertall supertall skyscraper skyscraper project project with curtain wall wall elements elements anchored anchored to to Figure 1. (a) with curtain the structure using anchor channels; (b) example of anchor channel and channel bolt. the structure using anchor channels; (b) example of anchor channel and channel bolt. CivilEng doi:10.3390/civileng1030015 CivilEng 2020, 2020, 1, 1, 243–252; Firstpage-Lastpage; doi: FOR PEER REVIEW www.mdpi.com/journal/civileng www.mdpi.com/journal/civileng

CivilEng 2020, 1 244 CivilEng 2020, 1, FOR PEER REVIEW 2 Anchor channels which areare cast flush in Anchor channels consist consist of ofanchors anchorseither eitherforged forgedororwelded weldedtotoC-channels C-channels which cast flush reinforced concrete elements and allow, after stripping of the formwork, the installation of matching in reinforced concrete elements and allow, after stripping of the formwork, the installation of T-bolts, aka channel (Figure 1b). These1b). anchor bolt-systems can take can up high matching T-bolts, akabolts channel bolts (Figure Thesechannel–channel anchor channel–channel bolt-systems take tension loads (N in z-direction) and shear loads (V in xand y-direction) by mechanical interlock [1,2], up high tension loads (N in z-direction) and shear loads (V in x- and y-direction) by mechanical making the system verythe robust and very even robust suitableand to withstand explosive loads [3,4], seismicloads loads [3,4], [5,6], interlock [1,2], making system even suitable to withstand explosive and fatigue loads possibility of fixing the channel anychannel locationbolts along of seismic loads [5,6],[7,8]. and The fatigue loads [7,8]. The possibility ofbolts fixingatthe at the anylength location the channel offers higher flexibility to the designer than other cast-in systems such as baseplates with along the length of the channel offers higher flexibility to the designer than other cast-in systems such headed studs.with headed studs. as baseplates The design of of the the anchor anchor channel channel and and channel channel bolt bolt requires requires the the verification verification for for almost almost 20 20 possible possible The design failure modes and partly involves product-specific parameters to be determined by testing. In Europe, failure modes and partly involves product-specific parameters to be determined by testing. In the design for concrete anchors including anchor channels and channel are provided Europe, theprovisions design provisions for concrete anchors including anchor channels andbolts channel bolts are in EN 1992-4 [9],1992-4 i.e., Part of the 2. The design code for concrete in the USA, provided in EN [9],4i.e., PartEurocode 4 of the Eurocode 2. The design code for structures concrete structures in ACI 318 [10], stipulates design rules for single-point concrete anchors. The design rules forrules anchor the USA, ACI 318 [10], stipulates design rules for single-point concrete anchors. The design for channels and channel bolts are notare yet included. For this reason, amendments areare provided in anchor channels and channel bolts not yet included. For this reason, amendments provided AC232 [11], the Acceptance Criteria for anchor channel with channel bolts in the USA, defining required in AC232 [11], the Acceptance Criteria for anchor channel with channel bolts in the USA, defining qualification tests to attain Reports (E(S)R). In Europe, product qualification is required qualification testsEvaluation to attain (Service) Evaluation (Service) Reports (E(S)R). In Europe, product certified by European Technical Assessment (ETA) documents for which qualification tests have to be qualification is certified by European Technical Assessment (ETA) documents for which qualification carried outtoaccording theaccording Europeanto Assessment Document (EAD) 330008-03-0601 Due to the tests have be carriedtoout the European Assessment Document (EAD) [12]. 330008-03-0601 complexity thecomplexity design provisions, structural engineers typicallyengineers use proprietary software to design [12]. Due toofthe of the design provisions, structural typically use proprietary anchor channels and channel bolts (Figure 2a). software to design anchor channels and channel bolts (Figure 2a). (a) (b) Figure 2. Typical Typical design detail of a curtain wall bracket connected to the structure with channel bolts installed in anchor channels: (a) Snapshots of the design software; (b) situation on site. regulations of anchor channels and channel bolts arebolts almost The qualification qualificationand anddesign design regulations of anchor channels and channel areidentical almost in Europeinand the USA, some minor differences still call forstill harmonization [13]. While both identical Europe and though the USA, though some minor differences call for harmonization [13]. standard frameworks do not require product-specific parameters to design for tension loading, they do While both standard frameworks do not require product-specific parameters to design for tension require product-specific to allow the economic design for shear loading. loading, they do require parameters product-specific parameters to allow the economic design for shear loading. To determine the product-specific parameters, tests are carried out on anchor channels installed in determine the product-specific parameters, tests are carried out on anchor channels installed concrete. TestTest datadata presented below verifies that also embedded anchor anchor channelschannels can transfer in concrete. presented below verifies thatshallow also shallow embedded can shear loads safely despite reduced embedment. Shallow Shallow embedded anchor channels are popular transfer shear loads safelytheir despite their reduced embedment. embedded anchor channels are particularly for the connection of curtain wall brackets (Figure 2b) where value engineering led to popular particularly for the connection of curtain wall brackets (Figure 2b) where value engineering thintoconcrete decks,decks, however, interestingly their general load-displacement behavior has not led thin concrete however, interestingly their general load-displacement behavior hasbeen not discussed nor performance data or approval reports published to date. been discussed nor performance data or approval reports published to date. 2. Background on Design Provisions for Concrete Edge Breakout Shear Capacity The design of anchor channels is complex. For those interested in the background of the design for concrete edge breakout shear capacity, the underlying provisions are explained to the required level of

CivilEng 2020, 1, FOR PEER REVIEW 3 2. Background on Design Provisions for Concrete Edge Breakout Shear Capacity CivilEng 2020, 1 245 The design of anchor channels is complex. For those interested in the background of the design for concrete edge breakout shear capacity, the underlying provisions are explained to the required level ofIndetail. In the following, the denomination according to the European framework is detail. the following, the denomination according to the European standardstandard framework is used for used for the parameter US-American denomination is in provided in angle(“h brackets the parameter notation. notation. DeviatingDeviating US-American denomination is provided angle brackets . . . i”). (“⟨ ⟩”). The overall load capacity is defined as the minimum of all capacities determined for the The overall load capacity is defined as the minimum of all capacities determined for the individual individual failure The mostfailure relevant failure mode under shear is theedge concrete edge breakout, failure modes. Themodes. most relevant mode under shear is the concrete breakout, which is which is if the anchorischannel in aand thinwith slaba and with a small edge distance. This critical if critical the anchor channel installedisininstalled a thin slab small edge distance. This situation is situation is typical for the installation of brackets carrying curtain wall elements (Figure 3). typical for the installation of brackets carrying curtain wall elements (Figure 3). Figure 3. Anchor channel with two channel bolts close to an edge with indicated breakout body Figure 3. Anchor channel with two channel bolts close to an edge with indicated breakout body (shaded area) if loaded in shear: (a) Cross-section; (b) top view. (shaded area) if loaded in shear: (a) Cross-section; (b) top view. For the design, the load from the channel bolts is assumed to be distributed by the channel to For the design, the load from the channel bolts is assumed to be distributed by the channel to the anchors for which the design check of concrete edge breakout is carried out. The characteristic the anchors for which the design check of concrete edge breakout is carried out. The characteristic hnominali concrete edge breakout capacity of the individual anchor of a channel loaded perpendicular ⟨nominal⟩ concrete edge breakout capacity of the individual anchor of a channel loaded to the concrete edge is calculated by: perpendicular to the concrete edge is calculated by: 0 VVRk,c ·Ψ Ψch,c,V · Ψch,h,V Rk,c VRk,c ch,s,V · ψ·ch,c,V · ψch,h,V · ψre,V· Ψre,V Rk,c0 · ψ ch,s,V (1a) (1a) hVcb ·Ψ Ψco,V · Ψ·h,V cb VV ⟨V b b· ψ s,Vs,V · ψ· co,V · ψh,V ψc,V· ⟩Ψc,V i (1b) (1b) The modification modificationfactors factorsψch,c,V Ψch,c,V hΨ i, Ψ hΨh,V i, and hΨc,Vaccount i take the intocondition account ⟨ψco,V ⟩,co,V ψch,h,V ⟨ψch,h,V h,V⟩, and ψre,V ⟨ψc,V⟩Ψtake re,V into the condition (uncracked/cracked) andofthe geometry of concrete hca1 i,asc2the hca2 i, h) as (uncracked/cracked) and the geometry concrete member (c1 ⟨ca1⟩, member c2 ⟨ca2⟩, h)(cas detailing 1 well well as the detailing of surface reinforcement hsupplementary reinforcementi. In the context of the of surface reinforcement ⟨supplementary reinforcement⟩. In the context of the tests presented below, tests below, these factors are since the concrete test members used for thesepresented modification factors aremodification 1.0 since the concrete test1.0 members used for qualification are designed qualification are designed reinforcement withdistances sufficiently corner distances c2 hcthe without reinforcement andwithout with sufficiently largeand corner c2 ⟨clarge a2⟩ and heights h to allow a2 i and heights h to allow the development of a full breakout body. The influence of neighboring anchors, development of a full breakout body. The influence of neighboring anchors, i.e., the effect of location i.e., effectof ofadjacent location and loading of adjacent anchors, however, is relevant and is considered by the andthe loading anchors, however, is relevant and is considered by the modification factor: modification factor: ψch,s,V 1/ (1 (1 s/(4c1 2bch)1.5)) (2a) Ψch,s,V 1/(1 (1 s/(4c1 2bch )1.5 )) (2a) 1.5))⟩ ⟨ψ s,V 1/(1 1/(1 (1 s/(4c 2bchch))1.5 hΨs,V (1 s/(4c ))i a1a1 2b (2b) These equations equations assume assume that that the theconditions conditionsbb /hefef 0.7 0.7 and andhhchch/h /hefef 0.4 0.4 hh ⟨hch ch/h /hef ef 0.5⟩ 0.5i are chch/h fulfilled—which is is assumed assumed in in the the following. following. fulfilled—which The core coreofofEquation Equation is basic the basic characteristic ⟨nominal⟩ resistance ⟨strength⟩ against The (1) (1) is the characteristic hnominali resistance hstrengthi against concrete 0 ⟨Vb⟩ of an individual anchor considered. The research forming 0 concrete edge breakout failure V Rk,c edge breakout failure VRk,c hVb i of an individual anchor considered. The research forming the basis the the basis for the design and qualification anchor channels [14] that showed that the shear capacity for design and qualification of anchorofchannels [14] showed the shear capacity VRk,c 0 hVVbRk,c i is0 increasing with the edge distance c1 hca1 i by the power of 1.5. This is the same power applied on the

CivilEng 2020, 1 246 anchor embedment hef to calculate the tension capacity. This approach is also in line with the design of concrete anchors, i.e., post-installed anchors and cast-in headed studs of anchor plates. Results of shear tests on concrete anchors [15] were later used to reason the decrease of the power from 1.5 to 4/3: VRk,c 0 k12 · fck 0.5 · c1 4/3 (3a) hVb αch,V · f’c 0.5 · ca1 4/3 i (3b) This approach disadvantages anchor channels if compared to concrete anchors. It is noteworthy, however, that the concrete edge capacity of concrete anchors, paradoxically, is still calculated as a function of c1 1.5 hca1 1.5 i. The loss of calculated capacity due to the reduction is about 20% for a typical small edge distance of 75 mm and is progressively increasing with larger edge distances. While fck hf’c i is the characteristic hnominali concrete strength for the specific design case, k12 hαch,V i is a semi-empiric factor. Originally, staggered default values were defined for common small, medium, and large anchor channel sizes [16]. Later, the CUAP 06.01/01 [17], the origin of AC232 and EAD 330008-03-0601, defined only one conservative default value equaling to 4.5 h4.0i valid today for all anchor channels. Optional qualification tests are required to determine product-specific values for the shear capacity factor k12 hαch,V i. These qualification tests are introduced in the following section. 3. Qualification Tests to Determine Product-Specific Shear Capacity Factors Equation (3) is rearranged to determine the product-specific shear capacity factor k12 hαch,V i, which has to be determined for every combination of channel type and anchor type. The factor k12 kcr,V hαch,V i refers to cracked concrete, whereas uncracked concrete test members are used for qualification testing. To compensate for the capacity reduction associated with cracked concrete, the equation is divided by 1.4 hmultiplicated by 0.7i [18]. Moreover, AC232 and EAD 330008-01-0601 cap the value of the shear capacity factor to 7.5 to avoid that shear capacity factors are deduced which are—due to the large scatter caused by the concrete—by chance higher than the range of experience: kcr,V 1/1.4 · min{Vk ; 0.75Vm }/(fc,test 0.5 · c1 4/3 · Ψch,s,V ) 7.5 (4a) hαch,V 0.7 · min{Vk ; 0.75Vm }/(fc,test 0.5 · ca1 4/3 · Ψs,V ) 7.5i (4b) Vk stands for the characteristic (5% quantile, determined under the assumption of a normal distribution with 0.9 as the coefficient of confidence) and Vm for the mean failure load of the test series not normalized to the concrete strength (Vk(nom) /f’c 0.5 Vk(test) /fc,test 0.5 ). The term min{Vk ; 0.75Vm } represents a minimum scatter to be assumed even if the tests show a lower scatter. This equals to a 7.4% coefficient of variation for five test repeats (solving Vk 0.75Vm Vm (1 k v/100) 0.75Vm v 25/k, where k 3.401 for n 5 [19]). In principle, neither qualification nor design rules distinguish between forged anchors, which are headed studs, and welded anchors, which are generally pieces of I-sections. For the tests, the anchor channels are cast in concrete test members, parallel to the edge at a distance of c1 hca1 i corresponding to the minimum value for which qualification is sought (Figures 4 and 5). The test member thickness is large enough to avoid an influence on the failure load (h hcr,V ) and to accommodate a support outside the width of the anticipated breakout body (s 5c1 hs 5c1a i). Tie downs counteract the uplifting force due to the eccentrically acting actuator. A balance beam transfers the load equally to the two channel bolts. A load cell and two displacement transducers touching the fixture allow the recording of load and displacement. It is noted that the displacement may also be measured somewhere between the actuator and fixture. The location of measurement influences the recorded load-displacement behavior; this effect is briefly discussed in the next section.

CivilEng CivilEng 2020, 2020, 1, 1 FOR PEER REVIEW 5 247 CivilEng 2020, 1, FOR PEER REVIEW 5 (a) (a) (b) (b) Figure 4. Example photos (a) before and (b) after a shear loading test (concrete breakout removed). Figure Examplephotos photos(a) (a)before before and and (b) (b) after a shear removed). Figure 4. 4. Example shear loading loadingtest test(concrete (concretebreakout breakout removed). Figure5. Testsetup for shear shear Figure 5.5.Test Test setup for shear loading. loading. Figure loading. 4. Test Program toto Study 4. Test Program StudyProduct-Specific Product-SpecificShear Shear Capacity Capacity Factors Factors 4. Test Program to Study Product-Specific Shear Capacity Factors The aim ofofthe product-specificshear shearcapacity capacity factors The aim thetest testprogram program(Table (Table1) 1)was was to to determine determine product-specific factors The aim of the test program (Table 1) was to determine product-specific shear capacity factors & of of shallow embedded anchor channels (h /h 0.35). The results were used for further studies shallow embedded anchor channels (hchch/hefef 0.35). The results were used for further studies on of shallow embedded anchor channels (hch/hef 0.35). The results were used for further studies on onthe theload-displacement load-displacement behavior comparison with amended on standard embedded behavior and and comparison with amended tests ontests standard embedded anchor thechannels load-displacement behavior and comparison with amended tests on standard of embedded anchor (hch/hef(h ch /h 0.35). Moreover, the potential difference in the performance channels with anchor channels . 0.35). Moreover, the potential difference in the performance of channels ef channels (h ch/hef 0.35). Moreover, the potential difference in the performance of channels with welded anchors (40-S, 50-S, 53-S, 55-S, 40-L, 53-L) and forged anchors (53-L ) was investigated. Note with welded anchors (40-S, 50-S, 53-S, 55-S, 40-L, 53-L) and forged anchors (53-L ) was investigated. welded anchors (40-S, 50-S, 53-S, 55-S, 40-L,channels 53-L) and forgedfor anchors (53-L ) was investigated. Note thatthat currently all all commercially available suitable shallow embedment areare fitted with Note currently commercially available channels suitable for shallow embedment fitted with thatwelded currently all commercially available channels suitable for shallow embedment are fitted with anchors. Eachtest testseries seriescomprised comprised five five test test repeats. sizes with two welded anchors. Each repeats. Channels Channelsofoffour fourdifferent different sizes with two welded anchors. Each test series comprised five test The repeats. Channels of different sizes with100 two anchors at a spacing of 250 or 300 mm were tested. edge distance c 1 ⟨cfour 1a⟩ was between 50 and anchors at a spacing of 250 or 300 mm were tested. The edge distance c1 hc1a i was between 50 and anchors at a channel spacingbolt of 250 or 300 mm were tested. The edge distance c1 ⟨c1a⟩edge was breakout between 50 and is 100 diameters were large enough to to ensure that concrete failure 100mm. mm.The The channel bolt diameters were large enough ensure that concrete edge breakout failure is mm. The channel bolt diameters were large enough tocarried ensureout that concrete edge breakout failure is governing. The tests were part of two test campaigns at accredited test labs. governing. The tests were part of two test campaigns carried out at accredited test labs. governing. The tests were part of two test campaigns carried out at accredited test labs. Table 1. Test program. Table 1. Test program. Table 1. Test program. Channel Anchor Embedment Height Width Anchor Edge Channel Anchor Embedment Height Width Anchor Edge Bolt Channel Depth Ratio Ratio Spacing Distance Channel Anchor Embedment Height RatioWidthSpacingAnchorDistanceEdge Bolt Channel Depth Ratio Code*) *) mm hmm ef, mm hch /hh bRatio ch/hef s, mmSpacing s, mmc1 hca1 c1i,⟨c a1⟩, mm efch/hef bch /hef Bolt Channel hef ,Depth Ratio Distance 40-S M16 W4022 57 0.39 0.70 250 50a1⟩, mm 40-S M16 W4022 57 0.39 0.70 250 50 *) hef, mm hch/hef bch/hef s, mm c1 ⟨c 50-S M20 W5030 71 71 0.42 0.42 0.70 0.70 250 250 50 50 50-S M20 W5030 40-S 53-S M16 W4022 250 50 M20 W5334 76 57 0.45 0.39 0.70 0.70 250 75 53-S M20 W5334 76 0.45 0.70 250 75 50-S 55-S M20 W5030 250 50 M20 W5542 84 71 0.50 0.42 0.65 0.70 300 75 55-S M20 W5542 84 0.50 300 M16 W4022 79 76 0.28 0.45 0.51 0.65 50 7575 53-S 40-L M20 W5334 0.70 250 250 53-L M20 W5334 155 79 0.22 0.28 0.34 0.51 250 250 100 50 40-L M16 W4022 55-S 53-L M20 W5542 0.65 250 300 100 75 M20 W5334 155 84 0.22 0.50 0.34 0.34 53-L M20 W5334 155 0.22 250 100 40-L M16 anchorsW4022 79 for shallow0.28 0.51 250 50 *)53-L Code XX-S: short welded embedment depth; M20 W5334to channels 155 0.22 0.34 Code XX-L/L 250 : long anchors 100 Code Code 53-L W5334 155 depth. 0.22 welded/forgedM20 to channels for standard embedment 53-L M20 W5334 155 0.22 0.34 0.34 250 250 100 100

CivilEng 2020, 1, FOR PEER REVIEW 6 *) Code XX-S: short anchors welded to channels for shallow embedment depth; Code XX-L/L : long anchors welded/forged to channels for standard embedment depth. CivilEng 2020, 1 248 5. 5. Test Results Used Test Results Usedfor forEvaluating Evaluatingthe theProduct-Specific Product-SpecificShear ShearCapacity CapacityFactors Factors All anchor channels failed in concrete edge breakout mode. The scatter of theof ultimate load was All anchor channels failed in concrete edge breakout mode. The scatter the ultimate load generally well below the acceptance criteriacriteria of v 20% [12] (Table 2). The2). channels fitted with was generally well below the acceptance of v 20% [12] (Table The channels fittedlong with anchors for standard embedment showedshowed a very low scatter a coefficient of variation of aroundof long anchors for standard embedment a very lowwith scatter with a coefficient of variation 5%, whereas the coefficient of variation of theofchannels fittedfitted withwith short anchors forfor shallow around 5%, whereas the coefficient of variation the channels short anchors shallow embedment was embedment wassignificantly significantlyhigher, higher,between between6.2% 6.2%and and13.6%. 13.6%.The Thetotal totalmean meanand andcharacteristic characteristic values divided ⟩ i valuesVkVare dividedbyby2 2(relating (relatingtoto11anchor) anchor)totocalculate calculatethe theshear shear capacity capacity factors factors kkcr,V hαch,V k are cr,V⟨α ch,V (Equation (4)), taking into account thethe concrete strength fck ⟨f’fck c⟩ and modification factor factor ψch,s,V ⟨ψ s,V⟩ (Equation (4)), taking into account concrete strength hf’c ithe and the modification Ψch,s,V (Equation (2)). Note allthat tested anchor channels successfully passed through thethe complete hΨs,V i (Equation (2)).that Note all tested anchor channels successfully passed through complete qualification qualificationprogram programofofwhich whichthe thepresented presentedtests testsare areananexcerpt. excerpt. Table 2. 2. Test results. Table Test results. Coeff. of of Mean Coeff. Mean Code Code Variation Capacity Capacity Variation v, %v, % V Vmm,,kN kN 40-S 8.4 22.9 22.9 50-S40-S 6.2 8.4 23.8 50-S 6.2 23.8 53-S53-S 8.7 8.7 40.5 40.5 55-S55-S 13.813.8 49.3 49.3 28.3 40-L40-L 5.4 5.4 28.3 67.6 53-L53-L 4.8 4.8 67.6 53-L 5.1 60.3 53-L 5.1 60.3 Characteristic Concrete ConcreteInfl. Infl. Neighb. Shear Capacity Characteristic Neighb. Shear Capacity Factor Capacity Capacity Strength Strength anchor anchor Factor k ch,V⟩ k, kN f fck ⟨f’c⟩, MPa ch,s,V ⟨ψ Vk ,V kN Ψch,s,VψhΨ *)*) kcr,V ⟨αcr,V s,V i s,V⟩ ck hf’c i, MPa hαch,V i 16.4 16.418.8 18.8 28.528.5 26.126.1 23.223.2 56.756.7 49.8 22.0 21.3 22.1 23.3 20.8 17.8 17.8 49.8 22.0 21.3 22.1 23.3 20.8 17.8 17.8 0.97 0.94 0.81 0.88 0.97 0.74 0.74 0.97 0.94 0.81 0.88 0.97 0.74 0.74 6.99 7.0 7.57.0 7.5 7.57.5 7.07.0 7.57.5 7.57.5 7.57.5 6.99 8.02 8.02 8.49 8.49 6.97 6.97 9.37 9.37 12.58 12.58 11.23 11.23 *) Calculation based on Equation (4a); Equation (4b) would result in values different by 2%. *) Calculation based on Equation (4a); Equation (4b) would result in values different by 2%. 80 35 70 30 60 Shear load V, kN Shear load V, kN InIngeneral, curves showed a amixed behavior (Figure 6) 6) general,the theload-displacement load-displacement curves showed mixedductile–brittle ductile–brittle behavior (Figure because the primary brittle concrete edge breakout is combined with the secondary ductile bending because the primary brittle concrete edge breakout is combined with the secondary ductile bending of ofanchor anchorand and channel. channel. The common The set set of of curves curveshave haveaalarge largeband bandofofscatter scatterabout aboutthe thedisplacement, displacement, common forfor this kind of test. The large scatter is the result of the random play between fixture hole and channel this kind of test. The large scatter is the result of the random play between fixture hole and channel bolt, ofofthe bolt,the theslip slipofofthe thebolt boltininthe thechannel channelduring duringloading, loading,elastic elasticdeformation deformation thesteel steelasaswell wellasas slackness within the connecting devices between the actuator and channel bolt if ifthe slackness within the connecting devices between the actuator and channel bolt thedisplacement displacement transducers are not placed directly at the fixture. The displacement, however, is not transducers are not placed directly at the fixture. The displacement, however, is notananacceptance acceptance criterion for the qualification of anchor channel–channel bolt-systems since it is not critical forfor their criterion for the qualification of anchor channel–channel bolt-systems since it is not critical their robust load-bearing behavior. robust load-bearing behavior. 50 40 30 20 53-L mean 10 53-L mean 25 20 15 10 40-L mean 5 40-S mean 0 0 0 1 2 Displacement δ, mm (a) 3 0 1 2 3 Displacement δ, mm (b) Figure Shear load-displacement curves: Comparison channels with anchors made welded Figure 6. 6. Shear load-displacement curves: Comparison of of channels (a)(a) with anchors made ofof welded I-sections (53-L) and forged headed bolts (53-L and ) and with short (40-S) and long (40-L) anchors. I-sections (53-L) and forged headed bolts (53-L ) (b)(b) with short (40-S) and long (4

Article Load Capacity of Shallow Embedded Anchor Channels Christoph Mahrenholtz 1,* and Akanshu Sharma 2 1 Jordahl, 12057 Berlin, Germany 2 Institute of Construction Materials and Materials Testing Institute, University of Stuttgart, 70569 Stuttgart, Germany; akanshu.sharma@iwb.uni-stuttgart.de * Correspondence: christoph.mahrenholtz@jordahl.de Received: 8 September 2020; Accepted: 29 October .

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ASCE 32-01, “Design and Construction of Frost-Protected Shallow Foundations”, contains several different, code approved, methods to design shallow foundations of various types. The reference booklet you downloaded for this course, the HUD “Revised Builder’s Guide to Frost Protected Shallow Foundations” contains design methods for the most

does not offer dynamic well control methods of managing shallow hazards such as methane hydrates, shallow gas and shallow water flows. These negative aspects of "Pump and Dump" are in addition to the environmenta l impact, high drilling fluid (mud) . 3.2.2 Well Control "Modified Driller's Method" . .38 3.3 Dual Gradient .

day I am going to buy a car just like that.'' He thei1 explained : ''You see, mister, Harm can't waJk. I go downtow11. and look at' all e nice Tiiii;-J(S in the store window, and come home and try tc, tell Harry what it is all about, but r tell it very good. Some day J am going to make