ICC-ES Evaluation Report Reissued May 1, 2010 This report is subject to re-examination in two years.

Size: px
Start display at page:

Download "ICC-ES Evaluation Report Reissued May 1, 2010 This report is subject to re-examination in two years."

Transcription

1 ICC-ES Evaluatio Report ESR-2502 Reissued May, 200 This report is subject to re-examiatio i two years. (800) (562) A Subsidiary of the Iteratioal Code Coucil DIVISION: 03 CONCRETE Sectio: 035 Cocrete Achorig REPORT HOLDER: POWERS FASTENERS, INC. 2 POWERS LANE BREWSTER, NEW YORK 0509 (94) or (800) egieerig@powers.com EVALUATION SUBJECT: POWERS POWER-STUD+ SD2 ANCHORS IN CRACKED AND UNCRACKED CONCRETE.0 EVALUATION SCOPE Compliace with the followig codes: 2009 Iteratioal Buildig Code (2009 IBC) 2009 Iteratioal Residetial Code (2009 IRC) 2006 Iteratioal Buildig Code (2006 IBC) 2006 Iteratioal Residetial Code (2006 IRC) 2003 Iteratioal Buildig Code (2003 IBC) 2003 Iteratioal Residetial Code (2003 IRC) 997 Uiform Buildig Code (UBC) Property evaluated: Structural 2.0 USES The Powers Power-Stud+ SD2 achor is used to resist static, wid ad seismic tesio ad shear loads i cracked ad ucracked ormal-weight ad structural sad-lightweight cocrete havig a specified compressive stregth, f c, of 2,500 psi to 8,500 psi (7.2 MPa to 58.6 MPa); ad cracked ad ucracked ormal-weight or structural sad-lightweight cocrete over steel deck havig a miimum specified compressive stregth, f c, of 3,000 psi (20.7 MPa). The achorig system complies with achors istalled i hardeed cocrete as described i Sectio 92 of the 2009 ad 2006 IBC ad Sectio 93 of the 2003 IBC. The achorig system is a alterative to cast-i-place achors described i Sectio 9 of the 2009 ad 2006 IBC, Sectio 92 of the 2003 IBC ad Sectios 923. ad of the UBC. The achors may also be used where a egieered desig is submitted i accordace with Sectio R30..3 of the 2009, 2006 ad 2003 IRC. 3.0 DESCRIPTION 3. Power-Stud+ SD2: Power-Stud+ SD2 achors are torque-cotrolled, mechaical expasio achors comprised of a achor body, expasio wedge (clip), washer ad hex ut. The achor body is maufactured from medium carbo steel ad has miimum ich (5 µm) zic platig i accordace with ASTM B 633. The expasio clip is maufactured from AISI Type 36 stailess steel. The washer coforms to ASTM F 844. The hex uts coform to ASTM A 563, Grade A. The Power-Stud+ SD2 achor is illustrated i Figure 2. The achor body is comprised of a high-stregth rod threaded at oe ed ad havig a tapered madrel at the other ed. The tapered madrel is eclosed by a three-sectio expasio clip which freely moves aroud the madrel. The expasio clip movemet is restraied by the madrel taper ad by a collar. The achors are istalled i a predrilled hole with a hammer. Whe torque is applied to the ut of the istalled achor o the threaded ed of the achor body, the madrel at the other ed of the achor is draw ito the expasio clip, forcig it outward ito the sides of the predrilled hole i the base material. Istallatio istructios ad iformatio are set forth i Sectio 4.3, Table ad Figure, ad Figures 3 ad Cocrete: Normal-weight ad structural sad-lightweight cocrete must coform to Sectios 903 ad 905 of the IBC ad UBC, as applicable. 3.3 Steel Deck Paels: Steel deck paels must comply with the cofiguratios i Figure 4 ad have a miimum base-metal thickess of ich (0.899 mm) [20 gage]. Steel deck must comply with the requiremets of ASTM A 653/A 653M SS Grade 36, ad have a miimum yield stregth of 36 ksi (248 MPa). 4.0 DESIGN AND INSTALLATION 4. Stregth Desig: Desig stregth of achors complyig with the 2009 ad 2003 IBC ad 997 UBC as well as Sectio of the 2009 ad 2003 IRC must be determied i accordace with ACI Appedix D ad this report. Desig stregth of achors complyig with the 2006 IBC ad Sectio of 2006 IRC must be i accordace with ACI Appedix D ad this report. ICC-ES Evaluatio Reports are ot to be costrued as represetig aesthetics or ay other attributes ot specifically addressed, or are they to be costrued as a edorsemet of the subject of the report or a recommedatio for its use. There is o warraty by ICC Evaluatio Service, Ic., express or implied, as to ay fidig or other matter i this report, or as to ay product covered by the report. Copyright 200 Page of 2

2 ESR-2502 Most Widely Accepted ad Trusted Page 2 of 2 Desig examples accordig to the 2009 IBC are give i Figures 6 through 8 of this report. Desig parameters are based o the 2009 IBC (ACI 38-08) uless oted otherwise i Sectio 4.. through 4.. of this report. The stregth desig of achors must comply with ACI 38 D.4., except as required i ACI 38 D.3.3. Stregth reductio factors, φ, as give i ACI 38 D.4.4 must be used for load combiatios calculated i accordace with Sectio of the IBC ad Sectio 9.2 of ACI 38 or Sectio 62.2 of the UBC. Stregth reductio factors, φ, as give i ACI 38 D.4.5 must be used for load combiatios calculated i accordace with ACI 38 Appedix C or Sectio of the UBC. The value of f c used i the calculatios must be limited to 8,000 psi (55.2 MPa) maximum, i accordace with ACI 38 D.3.5. Desig parameters are provided i Tables 3 ad 4 of this report. Stregth reductio factors, φ, correspodig to ductile steel elemets may be used except for 3 / 8 -ich-diameter (9.5 mm) achors i shear, which have a stregth reductio factor correspodig to brittle steel elemets. 4.. Requiremets for Static Steel Stregth i Tesio, N sa : The omial steel stregth of a sigle achor i tesio, N sa, is give i Table 3 of this report. The values of N sa for sigle achors give i Table 3 must be used ad ot be derived by calculatio Requiremets for Static Cocrete Breakout Stregth i Tesio, N cb or N cbg : The omial cocrete breakout stregth of a sigle achor or group of achors i tesio, N cb ad N cbg, respectively, must be calculated i accordace with ACI 38 D.5.2, with modificatios as described i this sectio. The basic cocrete breakout stregth of a sigle achor i tesio, N b, must be calculated accordig to ACI 38 D.5.2, usig the values of h ef ad k cr as give i Table 3 of this report. The omial cocrete breakout stregth i tesio i regios where aalysis idicates o crackig i accordace with ACI 38 D must be calculated, with ψ c,n =.0 ad usig the value of k ucr as give i Table 3. For achors istalled i the soffit of structural sad-lightweight or ormal-weight cocrete filled steel deck floor ad roof assemblies, as show i Figure 4, calculatio of the cocrete breakout stregth i accordace with ACI 38 D.5.2 is ot required Requiremets for Static Pullout Stregth i Tesio, N p : The omial pullout stregth of a sigle achor i tesio i accordace with ACI 38 D.5.3 i cracked ad ucracked cocrete, N p,cr ad N p,ucr, respectively, is give i Table 3 of this report. For all desig cases, ψ c,p =.0. I accordace with ACI 38 D.5.3.2, the omial pullout stregth i cracked cocrete must be adjusted by calculatio accordig to Eq-: f N p,f c = N c p,cr 2,500 f N p,f c = N c p,cr 7.2 (lb, psi) (N, MPa) (Eq-) where f c is the specified cocrete compressive stregth ad whereby the expoet = / 2 for all achor diameters with the exceptio of the 3 / 8 -ich-diameter (9.5 mm) achor size, where = / 3. I regios where aalysis idicates o crackig i accordace with ACI 38 D.5.3.6, the omial pullout stregth i tesio must be adjusted by calculatio accordig to Eq-2: N p,f c = N p,ucr f c 2,500 (lb, psi) (Eq-2) f N p,f c = N c p,ucr (N, MPa) 7.2 where f c is the specified cocrete compressive stregth ad whereby the expoet = / 2 for all achors. Where values for N p,cr or N p,ucr are ot provided i Table 3, the pullout stregth i tesio eed ot be evaluated. The omial pullout stregth i tesio of the achors istalled i the soffit of structural sad-lightweight or ormal-weight cocrete filled steel deck floor ad roof assemblies, as show i Figure 4, is provided i Table 3. I accordace with ACI 38 D.5.3.2, the omial pullout stregth i cracked cocrete must be calculated accordig to Eq-, whereby the value of N p,deck,cr must be substituted for N p,cr ad the values of 3,000 psi or 20.7 MPa must substitute for 2,500 psi or 7.2 MPa i the deomiator. I regios where aalysis idicates o crackig i accordace with ACI , the omial stregth i ucracked cocrete must be calculated accordig to Eq-2, whereby the value of N p,deck,ucr must be substituted for N p,ucr ad the values of 3,000 psi or 20.7 MPa must substitute for 2,500 psi or 7.2 MPa i the deomiator Requiremets for Static Steel Shear Capacity, V sa : The omial steel stregth i shear, V sa, of a sigle achor i accordace with ACI 38 D.6..2 is give i Table 4 of this report ad must be used i lieu of the values derived by calculatio from ACI 38, Eq. D-20. The shear stregth V sa,deck of achors istalled i the soffit of structural sad-lightweight or ormal weight cocrete filled steel deck floor ad roof assemblies, as show i Figure 4, is give i Table Requiremets for Static Cocrete Breakout Stregth i Shear, V cb or V cbg : The omial cocrete breakout stregth of a sigle achor or group of achors i shear, V cb or V cbg, respectively, must be calculated i accordace with ACI 38 D.6.2, with modificatios as described i this sectio. The basic cocrete breakout stregth of a sigle achor i shear, V b, must be calculated i accordace with ACI 38 D usig the value of l e ad d a (d o ) give i Table 4. For achors istalled i the soffit of structural sad-lightweight or ormal-weight cocrete o steel deck floor ad roof assemblies, as show i Figure 4, calculatio of the cocrete breakout stregth i accordace with ACI 38 D.6.2 is ot required Requiremets for Static Cocrete Pryout Stregth i Shear, V cp or V cpg : The omial cocrete pryout stregth, V cp or V cpg, must be calculated i accordace with ACI 38 D.6.3, modified by usig the value of k cp provided i Table 4 ad the value of N cb or N cbg as calculated i accordace with Sectio 4..2 of this report. For achors istalled i the soffit of structural sad-lightweight or ormal-weight cocrete o steel deck floor ad roof assemblies, as show i Figure 4, calculatio of the cocrete pryout stregth i accordace with ACI 38 D.6.3 is ot required.

3 ESR-2502 Most Widely Accepted ad Trusted Page 3 of Requiremets for Seismic Desig: Geeral: For load combiatios icludig seismic, the desig must be performed accordig to ACI 38 D.3.3, as modified by Sectio of the 2009 IBC, of the 2006 IBC or the followig: CODE 2003 IBC ad 2003 IRC UBC ACI 38 SECTION D.3.3 SEISMIC REGION Moderate or high seismic risk Moderate or high seismic risk CODE EQUIVALENT DESIGNATION Seismic Desig Categories C,D,E ad F Seismic Zoes 2B, 3 ad 4 The omial steel stregth ad omial cocrete breakout stregth for achors i tesio, ad the omial cocrete breakout stregth ad pryout stregth for achors i shear, must be calculated accordig to ACI 38 D.5 ad D.6, respectively, takig ito accout the correspodig values i Tables 3 ad 4 of this report. The achors comply with ACI 38 D. as ductile steel elemets ad must be desiged i accordace with ACI D.3.3.4, D or D or ACI D or D.3.3.5, as applicable, except for 3 / 8 -ich-diameter (9.5 mm) achors i shear, which comply with ACI 38 D. as brittle steel elemets ad must be desiged i accordace with ACI 38 D or D Seismic Tesio: The omial steel stregth ad omial cocrete breakout stregth for achors i tesio must be calculated accordig to ACI 38 D.5. ad D.5.2, as described i Sectios 4.. ad 4..2 of this report ad i accordace with ACI 38 D The appropriate value for pullout stregth i tesio for seismic loads, N eq or N p,deck,cr, described i Table 3 of this report, must be used i lieu of N p. The values of N eq or N p,deck,cr ca be adjusted for cocrete stregth as follows: N eq,f c = N eq f c 2,500 f N eq,f c = N c eq 7.2 (lb, psi) (N, MPa) (Eq-3) where f c is the specified cocrete compressive stregth ad whereby the expoet = / 2 for all achor diameters with the exceptio of the 3 / 8 -ich-diameter (9.5 mm) achor size where = / 3. I additio, for structural sadlightweight or ormal-weight cocrete filled steel deck floor ad roof assemblies, the value of 3,000 psi or 20.7 MPa must be substituted for the value of 2,500 psi or 7.2 MPa i the deomiator. Where values of N eq are ot provided i Table 3 of this report, the pullout stregth i tesio for seismic loads does ot gover ad eed ot be evaluated Seismic Shear: The omial cocrete breakout stregth ad pryout stregth for achors i shear must be calculated accordig to ACI 38 D.6.2 ad D.6.3, as described i Sectios 4..5 ad 4..6 of this report ad i accordace with ACI 38 D The appropriate value for omial steel stregth i shear for seismic loads, V eq or V sa,deck, described i Table 4 of this report must be used i lieu of V sa Iteractio of Tesile ad Shear Forces: For achors or groups of achors that are subject to the effects of combied tesio ad shear forces, the desig must be performed i accordace with ACI 38 D Requiremets for Critical Edge Distace: I applicatios where c < c ac ad supplemetal reiforcemet to cotrol splittig of the cocrete is ot preset, the cocrete breakout stregth i tesio for ucracked cocrete, calculated accordig to ACI 38 D.5.2, must be further multiplied by the factor ψ cp,n give by the followig equatio: ψ cp,n = c c ac (Eq-4) whereby the factor ψ cp,n eed ot be take as less tha.5h ef. For all other cases ψ cp,n =.0. I lieu of ACI 38 c ac Sectio D.8.6, values of c ac provided i Table of this report must be used Requiremets for Miimum Member Thickess, Miimum Achor Spacig ad Miimum Edge Distace: I lieu of ACI 38 D.8.3, values of c mi ad s mi as give i Table of this report must be used. I lieu of ACI 38 D.8.5, miimum member thickesses, h mi as give i Table must be used. For achors istalled through the soffit of steel deck assemblies, the achors must be istalled i accordace with Figure 4A or 4B, as applicable, ad shall have a axial spacig alog the flute equal to the greater of 3h ef or.5 times the flute width. 4.. Structural Sad-lightweight Cocrete: For ACI 38-08, whe achors are used i structural sad-lightweight cocrete, the modificatio factor λ for cocrete breakout stregth must be take as 0.6. I additio, the pullout stregth N p,cr, ad N eq must be multiplied by 0.6, as applicable. For ACI 38-05, the values N b, N eq, N p,cr, ad V b determied i accordace with this report must be multiplied by 0.60, i lieu of ACI 38 D.3.4. For achors istalled i the soffit of structural sad-lightweight cocrete-filled steel deck ad floor ad roof assemblies, this reductio is ot required. 4.2 Allowable Stress Desig (ASD): 4.2. Geeral: Desig values for use with allowable stress desig load combiatios calculated i accordace with Sectio of the IBC ad Sectio 62.3 of the UBC, shall be established usig the followig equatios: T allowable,asd = V allowable,asd = φn α φv α (Eq-5) (Eq-6) where: T allowable,asd = Allowable tesio load (lbf or kn) V allowable,asd = Allowable shear load (lbf or kn) φn = Lowest desig stregth of a achor or achor group i tesio as determied i accordace with ACI 38 Appedix D, Sectio 4. of this report ad 2009 IBC Sectio or 2006 IBC Sectio , as applicable (lbf or N). φv = Lowest desig stregth of a achor or achor group i shear as determied i accordace with ACI 38 Appedix D,

4 ESR-2502 Most Widely Accepted ad Trusted Page 4 of 2 Sectio 4. of this report ad 2009 IBC Sectio or 2006 IBC Sectio , as applicable (lbf or N). α = Coversio factor calculated as a weighted average of the load factors for the cotrollig load combiatio. I additio, α shall iclude all applicable factors to accout for o-ductile failure modes ad required over-stregth. The requiremets for member thickess, edge distace ad spacig, as described i this report, must apply. A example of allowable stress desig values for illustrative purposes is show i Table 5 ad Figure 5 of this report Iteractio of Tesile ad Shear Forces: The iteractio shall be calculated ad cosistet with ACI 38 D.7 as follows: For shear loads V 0.2V allowable,asd, the full allowable load i tesio shall be permitted. For tesio loads T 0.2T allowable,asd, the full allowable load i shear shall be permitted. For all other cases: T T V +.2 (Eq-7) allowable V allowable 4.3 Istallatio: Istallatio parameters are provided i Table, Figure ad Figure 4. Achor locatios must comply with this report ad the plas ad specificatios approved by the code official. The Power-Stud+ SD2 must be istalled accordig to maufacturer s published istallatio istructios ad this report. Achors must be istalled i holes drilled ito the cocrete usig carbide-tipped masory drill bits complyig with ANSI B The omial drill bit diameter must be equal to that of the achor size. The miimum drilled hole depth is give i Table. The predrilled hole must be cleaed free of dust ad debris. The achor must be hammered ito the predrilled hole util the proper omial embedmet depth is achieved. The ut must be tighteed agaist the washer util the torque values specified i Table are achieved. For istallatio i the soffit of cocrete o steel deck assemblies, the hole diameter i the steel deck must ot exceed the diameter of the hole i the cocrete by more tha / 8 ich (3.2 mm). For member thickess ad edge distace requiremets for istallatios ito the soffit of cocrete o steel deck assemblies, see Figure 4A ad 4B. 4.4 Special Ispectio: Special ispectio is required, i accordace with Sectio of the 2009 IBC or Sectio of the 2006 ad 2003 IBC ad, if applicable, Sectio of the UBC. The special ispector must make periodic ispectios durig achor istallatio to verify achor type, achor dimesios, cocrete type, cocrete compressive stregth, hole dimesios, hole cleaig procedure, achor spacig, edge distaces, cocrete member thickess, achor embedmet, tighteig torque ad adherece to the Powers Fasteers' prited istallatio istructios. The special ispector must be preset as ofte as required i accordace with the statemet of special ispectio. Uder the IBC, additioal requiremets as set forth i Sectios 705, 706 ad 707 must be observed, where applicable. 5.0 CONDITIONS OF USE The Powers Power-Stud+ SD2 achors described i this report comply with, or are suitable alteratives to what is specified i, those codes listed i Sectio.0 of this report, subject to the followig coditios: 5. The achors must be istalled i accordace with the maufacturer s published istallatio istructios ad this report. I case of a coflict, this report govers. 5.2 Achor sizes, dimesios, ad miimum embedmet depths are as set forth i this report. 5.3 Achors must be istalled i cracked ad ucracked ormal-weight cocrete ad structural sadlightweight cocrete havig a specified compressive stregth, f c, of 2,500 psi to 8,500 psi (7.2 MPa to 58.6 MPa); ad cracked ad ucracked ormal weight or structural sad-lightweight cocrete over steel deck havig a miimum specified compressive stregth, f c, of 3,000 psi (20.7 MPa). 5.4 The values of f c used for calculatio purposes must ot exceed 8,000 psi (55.2 MPa). 5.5 Stregth Desig values must be established i accordace with Sectio 4. of this report. 5.6 Allowable Stress Desig values must be established i accordace with Sectio 4.2 of this report. 5.7 Achor spacig(s) ad edge distace(s), as well as miimum member thickess, must comply with Table ad Figure Prior to istallatio, calculatios ad details demostratig compliace with this report must be submitted to the code official. The calculatios ad details must be prepared by a registered desig professioal where required by the statutes of the jurisdictio i which the project is to be costructed. 5.9 Sice a ICC-ES acceptace criteria for evaluatig data to determie the performace of achors subjected to fatigue or shock loadig is uavailable at this time, the use of these achors uder such coditios is beyod the scope of this report. 5.0 Achors may be istalled i regios of cocrete where crackig has occurred or where aalysis idicates crackig may occur (f t > f r ), subject to the coditios of this report. 5. Achors may be used to resist short-term loadig due to wid or seismic forces i locatios desigated as Seismic Desig Categories A through F uder the IBC, ad Seismic Zoes 0 to 4 uder the UBC, subject to the coditios of this report. 5.2 Where ot otherwise prohibited i the code, Power-Stud+ SD2 achors are permitted for use with fire-resistace-rated costructio provided that at least oe of the followig coditios is fulfilled: Achors are used to resist wid or seismic forces oly. Achors that support a fire-resistace-rated evelope or a fire-resistace-rated membrae are protected by approved fire-resistace-rated materials, or have bee evaluated for resistace to fire exposure i accordace with recogized stadards. Achors are used to support ostructural elemets. 5.3 Use of zic-coated carbo steel achors is limited to dry, iterior locatios.

5 ESR-2502 Most Widely Accepted ad Trusted Page 5 of Special ispectio must be provided i accordace with Sectio 4.4 of this report. 5.5 Achors are maufactured uder a approved quality cotrol program with ispectios by CEL Cosultig (AA-639). 6.0 EVIDENCE SUBMITTED Data i accordace with the ICC-ES Acceptace Criteria for Mechaical Achors i Cocrete Elemets (AC93), dated February 200, which icorporates requiremets i ACI / ACI , for use i cracked ad ucracked cocrete; icludig optioal suitability Test 2 ad 3 (AC93, Table 4.2) for seismic tesio ad shear; ad quality cotrol documetatio. 7.0 IDENTIFICATION The Power-Stud+ SD2 achors are idetified by dimesioal characteristics ad packagig. A legth letter code head markig is stamped o each achor o the exposed threaded stud ed, alog with a plus sig + ad the umber 2 which are visible after istallatio. Table 2 shows the legth code idetificatio system. Packages are idetified with the achor ame, type ad size; the maufacturer s ame; the ame of the ispectio agecy (CEL); ad the evaluatio report umber (ICC-ES ESR-2502). TABLE A MEAN AXIAL STIFFNESS VALUES, β, FOR POWER-STUD+ SD2 EXPANSION ANCHORS IN NORMAL-WEIGHT CONCRETE Cocrete State Uits 3 / 8 Nomial Achor Size (ich) / 2 5 / 8 3 / 4 Ucracked cocrete Cracked cocrete lbf/i. (kn/mm) lbf/i. (kn/mm) 8,650 (,57) 495 (87) 7,70 (,258) 570 (00) 5,690 (998) 645 (3) 4,200 (737) 720 (26) Mea values show; actual stiffess varies cosiderably depedig o cocrete stregth, loadig ad geometry of applicatio.

6 ESR-2502 Most Widely Accepted ad Trusted Page 6 of 2 TABLE POWER-STUD+ SD2 ANCHOR INSTALLATION SPECIFICATIONS ANCHOR PROPERTY AND SETTING INFORMATION NOTATION UNITS 3 / 8 / 2 NOMINAL ANCHOR SIZE (ich) 5 / 8 3 / 4 Outside diameter of achor d a [d o ] 3 i (mm) (9.5) (2.7) (5.9) (9.) Miimum diameter of hole clearace i fixture d h i. 7 / 6 9 / 6 / 3 6 / 6 (mm) (.) (4.3) (7.5) (20.6) Nomial drill bit diameter d bit i. 3 / 8 / 2 5 / 8 3 / 4 ANSI ANSI ANSI ANSI Miimum omial embedmet depth Effective embedmet Miimum cocrete member thickess Critical edge distace 2 Miimum edge distace 2 Miimum spacig distace 2 Miimum hole depth 2 Miimum overall achor legth Istallatio torque h om h ef h mi c ac c mi s mi h o l ach T ist i. 2 3 / 8 2 / / / / 8 4 / / 4 (mm) (60) (64) (83) (98) (24) (4) (46) i (mm) (5) (5) (83) (83) (08) (95) (27) i. 4 4 / / / / 4 6 / (mm) (02) (4) (52) (46) (46) (46) (65) (203) (78) (254) i. 6 / / (mm) (65) (203) (254) (203) (400) (254) (305) (305) i. 2 / / / 4 4 / 4 4 / / 2 (mm) (64) (02) (70) (02) (70) (08) (08) (27) (4) i. 3 / / 4 4 / (mm) (89) (52) (52) (02) (52) (08) (08) (52) (52) i. 2 5 / / / 4 5 / / 4 (mm) (67) (70) (02) (08) (33) (27) (59) i / 4 4 / / / 4 7 (mm) (76) (95) (4) (2) (52) (59) (78) ft.-lb (N-m) (27) (54) (8) (49) Torque wrech / socket size - i. 9 / 6 3 / 4 5 / 6 / 8 Nut height - I. 2 / 64 7 / 6 35 / 64 4 / 64 For SI: ich = 25.4 mm, ft-lbf =.356 N-m. The embedmet depth, h om, is measured from the outside surface of the cocrete member to the embedded ed of the achor prior to tighteig. 2 For istallatios through the soffit of steel deck ito cocrete see the istallatio details i Figure 4A ad 4B of this report. I additio, achors shall have a axial spacig alog the flute equal to the greater of 3h ef or.5 times the flute width. 3 The otatio i brackets is for the 2006 IBC. FIGURE POWER-STUD+ SD2 ANCHOR DETAIL Before (Left Picture) ad After (Right Picture) Applicatio of Istallatio Torque FIGURE 2 POWER-STUD+ SD2 ANCHOR ASSEMBLY TABLE 2 POWER-STUD+ SD2 LENGTH CODE IDENTIFICATION SYSTEM Legth ID markig o threaded stud head A B C D E F G H I J K L M N O P Overall achor legth, l ach, (iches) From / / / / / / / / 2 9 Up to but ot icludig 2 2 / / / / / / / / 2

7 ESR-2502 Most Widely Accepted ad Trusted Page 7 of 2..) Usig the proper drill bit size, drill a hole ito the base material to the required depth. The toleraces of the drill bit used should meet the requiremets of ANSI Stadard B ) Remove dust ad debris from hole usig a had pump, compressed air or a vacuum to remove loose particles left from drillig. 3.) Positio the washer o the achor ad thread o the ut. If istallig through a fixture, drive the achor through the fixture ito the hole. Be sure the achor is drive to the miimum required embedmet depth, h om. 4.) Tighte the achor with a torque wrech by applyig the required istallatio torque, T ist. e: the threaded stud will draw up durig tighteig of the ut; the expasio wedge (clip) remais i origial positio. FIGURE 3 POWER-STUD+ SD2 INSTALLATION INSTRUCTIONS FIGURE 4A POWER-STUD+ SD2 INSTALLATION DETAIL FOR ANCHORS IN THE SOFFIT OF CONCRETE OVER STEEL DECK FLOOR AND ROOF ASSEMBLIES (SEE DIMENSIONAL PROFILE REQUIREMENTS) FIGURE 4B POWER-STUD+ SD2 INSTALLATION DETAIL FOR ANCHORS IN THE SOFFIT OF CONCRETE OVER STEEL DECK FLOOR AND ROOF ASSEMBLIES (SEE DIMENSIONAL PROFILE REQUIREMENTS) 2,3 Achors may be placed i the upper flute or lower flute of the steel deck profiles i accordace with Figure 4A provided the miimum hole clearace is satisfied. Achors i the lower flute of Figure 4A profiles may be istalled with a maximum -ich offset i either directio from the ceter of the flute. The offset distace may be icreased proportioally for profiles with lower flute widths greater tha those show provided the miimum lower flute edge distace is also satisfied. 2 Achors may be placed i the lower flute of the steel deck profiles i accordace with Figure 4B provided the miimum hole clearace is satisfied. Achors i the lower flute of Figure 4B profiles may be istalled with a maximum / 8 -ich offset i either directio from the ceter of the flute. The offset distace may be icreased proportioally for profiles with lower flute widths greater tha those show provided the miimum lower flute edge distace is also satisfied. 3 Achors may be placed i the upper flute of the steel deck profiles i accordace with Figure 4B provided the cocrete thickess above the upper flute is miimum 3 / 4 -ich a miimum hole clearace 3 / 4 -ich is satisfied.

8 ESR-2502 Most Widely Accepted ad Trusted Page 8 of 2 TABLE 3 TENSION DESIGN INFORMATION FOR POWER-STUD+ SD2 ANCHOR IN CONCRETE (For use with load combiatios take from ACI 38, Sectio 9.2),2 Desig Characteristic atio Uits 3 / 8 Nomial Achor Size (ich) / 2 5 / 8 3 / 4 Achor category, 2 or 3 - Miimum specified yield stregth (eck) STEEL STRENGTH IN TENSION 4 f y ksi (N/mm 2 ) (662) (586) (586) (483) Miimum specified ultimate stregth (eck) f uta ksi (N/mm 2 ) (827) (73) (73) (620) Effective tesile stress area (eck) A se,n i [A se ] 2 (mm 2 ) (35.6) (65.0) (04.5) (53.2) Steel stregth i tesio N sa lbf 6,625 0,445 3,080 2,230 (kn) (29.5) (46.5) (58.2) (94.4) Reductio factor for steel stregth 3 φ Effective embedmet CONCRETE BREAKOUT STRENGTH IN TENSION 8 h ef i (mm) (5) (5) (83) (83) (08) (95) (27) Effectiveess factor for ucracked cocrete k ucr Effectiveess factor for cracked cocrete k cr Modificatio factor for cracked ad ucracked cocrete 5 Ψ c,n -.0 See ote 5.0 See ote 5.0 See ote 5.0 See ote 5 Critical edge distace c ac i. (mm) See Table Reductio factor for cocrete breakout stregth i tesio 3 φ (Coditio B) Characteristic pullout stregth, ucracked cocrete (2,500 psi) 6 Characteristic pullout stregth, cracked cocrete (2,500 psi) 6 PULLOUT STRENGTH IN TENSION (NON-SEISMIC APPLICATIONS) 8 N p,ucr N p,cr lbf 2,775 See 6,65 See See See See (kn) (2.3) ote 7 (29.4) ote 7 ote 7 ote 7 ote 7 lbf 2,65 See 4,375 See 4,980 See 7,795 (kn) (9.6) ote 7 (9.5) ote 7 (22.4) ote 7 (35.) Reductio factor for pullout stregth 3 φ (Coditio B) PULLOUT STRENGTH IN TENSION FOR SEISMIC APPLICATIONS 8 Characteristic pullout stregth, seismic (2,500 psi) 6,9 lbf 2,65 See 4,375 See 4,980 See 7,795 N eq (kn) (9.6) ote 7 (9.5) ote 7 (22.4) ote 7 (35.) Reductio factor for pullout stregth 3 φ (Coditio B) PULLOUT STRENGTH IN TENSION FOR STRUCTURAL SAND LIGHTWEIGHT AND NORMAL-WEIGHT CONCRETE OVER STEEL DECK Characteristic pullout stregth, ucracked cocrete over steel deck, accordig to Figure 4A 6.0 Characteristic pullout stregth, cracked cocrete over steel deck, accordig to Figure 4A 6.0 Characteristic pullout stregth, ucracked cocrete over steel deck, accordig to Figure 4B 6.0 Characteristic pullout stregth, cracked cocrete over steel deck, accordig to Figure 4B 6.0 N p,deck,ucr N p,deck,cr N p,deck,ucr N p,deck,cr lbf,855 2,065 3,930 4,665 7,365 4,900 (kn) (8.3) (9.2) (7.5) (20.8) (32.8) (2.8) lbf,445,465 2,600 3,305 3,490 3,470 (kn) (6.4) (6.5) (.6) (4.7) (5.5) (5.4) lbf (kn) lbf (kn),600 (7.),250 (5.6) 2,025 (9.0),435 (6.4) Reductio factor for pullout stregth 3 φ (Coditio B) For SI: ich = 25.4 mm, ft-lbf =.356 N-m, ksi = N/mm 2, lbf = kn The data i this table is iteded to be used with the desig provisios of ACI 38 Appedix D; for achors resistig seismic load combiatios the additioal requiremets of ACI 38 D.3.3 shall apply. 2 Istallatio must comply with published istructios ad details. 3 All values of φ were determied from the load combiatios of IBC Sectio 605.2, ACI 38 Sectio 9.2 or UBC Sectio If the load combiatios of ACI 38 Appedix C or IBC Sectio are used, the appropriate value of φ must be determied i accordace with ACI 38 D.4.5. For reiforcemet that meets ACI 38 Appedix D requiremets for Coditio A, see ACI 38 D.4.4 for the appropriate φ factor. 4 The Power-Stud+ SD2 is cosidered a ductile steel elemet i tesio as defied by ACI 38 D.. Tabulated values for steel stregth i tesio are based o test results per ACI ad must be used for desig. 5 For all desig cases Ψ c,n =.0. The appropriate effectiveess factor for cracked cocrete (k cr ) or ucracked cocrete (k ucr ) must be used. 6 For all desig cases Ψ c,p =.0. For the calculatio of N p, see Sectio 4..3 of this report. 7 Pullout stregth does ot cotrol desig of idicated achors. Do ot calculate pullout stregth for idicated achor size ad embedmet. 8 Achors are permitted to be used i structural sad-lightweight cocrete i accordace with Sectio 4.. of this report. 9 Tabulated values for characteristic pullout stregth i tesio are for seismic applicatios are based o test results per ACI 355.2, Sectio Values for N p,deck are for structural sad-lightweight cocrete (f' c, mi = 3,000 psi) ad additioal lightweight cocrete reductio factors eed ot be applied. I additio, evaluatio for the cocrete breakout capacity i accordace with ACI 38 D.5.2 is ot required for achors istalled i the deck soffit (flute). For 2003 IBC code basis, f uta replaces f ut ; N sa replaces N s ; Ψ c,n replaces Ψ 3 ; ad N eq replaces N p,seis. 2 The otatio i brackets is for the 2006 IBC.

9 ESR-2502 Most Widely Accepted ad Trusted Page 9 of 2 TABLE 4 SHEAR DESIGN INFORMATION FOR POWER-STUD+ SD2 ANCHOR IN CONCRETE (For use with load combiatios take from ACI 38, Sectio 9.2),2 Desig Characteristic atio Uits 3 / 8 / 2 Nomial Achor Diameter 5 / 8 3 / 4 Achor category, 2 or 3 - Miimum specified yield stregth (threads) Miimum specified ultimate stregth (threads) f uta 0 f y STEEL STRENGTH IN SHEAR 4 ksi (N/mm 2 ) (530) (469) (469) (386) ksi (N/mm 2 ) (662) (585) (585) (496) i Effective tesile stress area (threads) A se,v [A se ] (mm 2 ) (50.0) (65.7) (04.9) (25.8) Steel stregth i shear 5 V sa 0 lbf 2,90 4,640 9,800 0,75 (kn) (9.7) (20.6) (44.) (45.3) Reductio factor for steel stregth 3 φ Load-bearig legth of achor (h ef or 8d o, whichever is less) CONCRETE BREAKOUT STRENGTH IN SHEAR 6 i. Nomial achor diameter d a [d o ] (mm) (9.5) l e 0 i (mm) (5) (5) (83) (83) (08) (95) (27) (2.7) Reductio factor for cocrete breakout stregth i 3 φ (Coditio B) shear Coefficiet for pryout stregth (.0 for h ef < 2.5 i., 2.0 for h ef 2.5 i.) Effective embedmet PRYOUT STRENGTH IN SHEAR (5.9) (9.) k cp h ef i. (mm) 2.00 (5) (5) (83) (83) (08) (95) (27) Reductio factor for pryout stregth 3 φ (Coditio B) STEEL STRENGTH IN SHEAR FOR SEISMIC APPLICATIONS Steel stregth i shear, seismic 7 V lbf,955 4,640 6,530 6,635 eq 0 (kn) (8.7) (20.6) (29.0) (29.5) Reductio factor for steel stregth i shear, seismic 3 φ STEEL STRENGTH IN SHEAR FOR STRUCTURAL SAND-LIGHTWEIGHT AND NORMAL-WEIGHT CONCRETE OVER STEEL DECK 9 Steel stregth i shear, cocrete over steel deck, accordig to Figure 4A 8 Steel stregth i shear, cocrete over steel deck, accordig to Figure 4B 8 V sa,deck V sa,deck lbf 2,70 3,85 5,040 4,05 6,670 4,325 (kn) (9.7) (7.0) (22.4) (7.9) (29.7) (9.2) lbf (kn) 2,70 (9.7) 2,880 (2.8) Reductio factor for steel stregth i shear, cocrete 3 φ over steel deck For SI: ich = 25.4 mm, ft-lbf =.356 N-m, ksi = N/mm 2, lbf = kn. The data i this table is iteded to be used with the desig provisios of ACI 38 Appedix D; for achors resistig seismic load combiatios the additioal requiremets of ACI 38 D.3.3 shall apply. 2 Istallatio must comply with published istructios ad details. 3 All values of φ were determied from the load combiatios of IBC Sectio 605.2, ACI 38 Sectio 9.2 or UBC Sectio If the load combiatios of Appedix C or UBC Sectio are used, the appropriate value of φ must be determied i accordace with ACI 38 D.4.5. For reiforcemet that meets ACI 38 Appedix D requiremets for Coditio A, see ACI 38 D.4.4 for the appropriate φ factor. 4 The Power-Stud+ SD2 is cosidered a ductile steel elemet as defied by ACI 38 D. except for the 3 / 8 -ich-diameter achors i shear. 5 Tabulated values for steel stregth i shear are based o test results per ACI 355.2, Sectio 9.4 ad must be used for desig. These tabulated values are lower tha calculated results usig equatio D-20 i ACI (38-05) ad ACI 38 D Achors are permitted to be used i structural sad-lightweight cocrete i accordace with Sectio 4.. of this report. 7 Tabulated values for steel stregth i shear are for seismic applicatios are based o test results per ACI 355.2, Sectio Values for V sa,deck are for structural sad-lightweight cocrete (f c, mi = 3,000 psi) ad additioal lightweight cocrete reductio factors eed ot be applied. I additio, evaluatio for the cocrete breakout capacity i accordace with ACI 38 D.6.2 ad the pryout capacity i accordace with Sectio D.6.3 is ot required for achors istalled i the deck soffit (flute). 9 Shear loads for achors istalled through steel deck ito cocrete may be applied i ay directio. 0 For 2003 IBC code basis,f uta replaces f ut ; V sa replaces V s ; l e replaces l ; ad V eq replaces V sa,seis. The otatio i brackets is for the 2006 IBC.

10 ESR-2502 Most Widely Accepted ad Trusted Page 0 of 2 TABLE 5 EXAMPLE ALLOWABLE STRESS DESIGN VALUES FOR ILLUSTRATIVE PURPOSES,2,3,4,5,6,7,8,9 Nomial Achor Diameter (i.) Nomial Embedmet Depth (i.) Effective Embedmet (i.) Allowable Tesio Load (pouds) 3 / / ,220 / 2 5 / 8 3 / 4 2 / , / , / , / ,65 4 / , / ,890 For SI: ich = 25.4 mm, ft-lbf =.356 N-m. Sigle achor with static tesio load oly. 2 Cocrete determied to remai ucracked for the life of the achorage. 3 Load combiatios from ACI 38 Sectio 9.2 (o seismic loadig cosidered). 4 30% dead load ad 70% live load, cotrollig load combiatio.2d +.6L. 5 Calculatio of weighted average for α =.2(0.3) +.6(0.7) = f c = 2,500 psi (ormal weight cocrete). 7 c a = c a2 c ac. 8 h h mi. 9 Values are for Coditio B where supplemetary reiforcemet i accordace with ACI 38 D.4.4 is ot provided. FIGURE 5 EXAMPLE STRENGTH DESIGN CALCULATION INCLUDING ASD CONVERSION FOR ILLUSTRATIVE PURPOSES

11 ESR-2502 Most Widely Accepted ad Trusted Page of 2 Give: Two 3 / 8 Power-Stud+ SD2 achors Cocrete compressive stregth: (f c ) = 4,000 psi No supplemetal reiforcemet: (Coditio B per ACI D.4.4 c) Assume cracked cocrete, o seismic, o loadig eccetricity ad a rigid plate h a = 5.0 i. h ef = 2.0 i. s a = 4.5 i. c a = c a,mi = 6.0 i. c a2.5c a Calculate the factored resistace desig stregth i tesio ad equivalet allowable stress desig load for the cofiguratio. Calculatio i accordace with ACI (ACI 38-05) ad this report: Code Ref. Report Ref. Step. Verify miimum member thickess, spacig ad edge distace: h a = 5.0 i. h mi = 4.0 i. OK s a = 4.5 i. s mi = 3.5 i. OK c a,mi = 6.0 i. c mi = 2.5 i. OK Step 2. Calculate steel stregth of achor group i tesio: N sag = N sa = 2 6,625 lbs. = 3,250 lbs. Calculate steel capacity: φn sag = ,250 lbs. = 9,937 lbs. Step 3. Calculate cocrete breakout stregth of achor group i tesio: =,,,, D.8 Table D Table 3 D.5.2. (b) 4..2 Step 3a. Calculate A Nco ad A Nc A Nco = 9h 2 ef = 9 (2.0) 2 = 36.0 i. 2 D.5.2. (b) Table A c = (3.0 h ef ) (3.0 h ef + s a ) = ( ) (( ) + 4.5) = 63.0 i. 2 A Nc = 63.0 i. 2 Step 3b. Calculate ψ ec,n = ( ).0 ; e N = 0 ψ ec,n =.0 Step 3c. Calculate ψ ed,n =.0 if c a,mi.5h ef ; ψ ed,n = ,. if c a,mi <.5h ef c a,mi = 6.0 i..5h ef = 3.0 i. ψ ed,n =.0 D D Table Step 3d. Calculate ψ c,n =.0 D Table 3 Step 3e. Calculate ψ cp,n =.0 (cracked cocrete) D Step 3f. Calculate N b = h. = 7 (.0) 4, = 3,04 lbs. D Table 3 Step 3g. Calculate cocrete breakout stregth of achor group i tesio: N cbg = (63.0/36.0) ,04 = 5,32 lbs. Calculate cocrete breakout capacity = φn cbg = ,32 = 3,459 lbs. Step 4. Calculate omial pullout stregth of a sigle achor i tesio: N p = ψ c,p N p,f c Step 4a. Calculate ψ c,p =.0 (cracked cocrete) Step 4b. Calculate N p,f c = N p,cr. = 2,65. = 2,528 lbs. Calculate pullout capacity: φn p = ,528.0 =,643 lbs. Step 5. Determie cotrollig resistace stregth of the achor group i tesio: φn = mi,, = φn p = 3,287 lbs. Step 6. Calculate allowable stress desig coversio factor for loadig coditio: Assume cotrollig load combiatio:.2d +.6L ; 50% Dead Load, 50% Live Load α =.2(50%) +.6(50%) =.40 Step 7. Calculate allowable stress desig value:, = D.5.2. (b) 4..2 D.5.3. D D D.4.. D Table Table Table =,. = 2,347 lbs FIGURE 6 EXAMPLE STRENGTH DESIGN CALCULATION FOR TENSION CAPACITY

12 ESR-2502 Most Widely Accepted ad Trusted Page 2 of 2 Give: Two 3 / 8 Power-Stud+ SD2 achors Cocrete compressive stregth: (f c ) = 4,000 psi No supplemetal reiforcemet: (Coditio B per ACI D.4.4 c) Assume cracked cocrete, o seismic, o loadig eccetricity ad a rigid plate h a = 5.0 i. h ef = 2.0 i. s a = 4.5 i. c a = c a,mi = 6.0 i. c a2.5c a Calculate the factored resistace desig stregth i shear ad equivalet allowable stress desig load for the cofiguratio. Calculatio i accordace with ACI (ACI 38-05) ad this report: Code Ref. Report Ref. Step. Verify miimum member thickess, spacig ad edge distace: h a = 5.0 i. h mi = 4.0 i. OK s a = 4.5 i. s mi = 3.5 i. OK c a,mi = 6.0 i. c mi = 2.5 i. OK Step 2. Calculate steel stregth of achor group i shear: V sag = V sa = 2 2,90 lbs. = 4,380 lbs. Calculate steel capacity: φv sag = ,380 lbs. = 2,625 lbs. Step 3. Calculate cocrete breakout stregth of achor group i shear: =,,,, D.8 Table D Table 4 D.6.2. (b) 4..5 Step 3a. Calculate A Vco ad A Vc A Vco = 4.5 (c a ) 2 = 4.5 (6.0) 2 = 62.0 i. 2 D.6.2. Table A Vc = (h a ) (3 c a + s a ) = (5.0)((3 6.0) + 4.5) = 2.5 i. 2 Step 3b. Calculate ψ ec,v = ( ).0 ; e V = 0 ψ ec,v =.0 Step 3c. Calculate ψ ed,v =.0 if c a2.5c a ; ψ ed,v = if c a2 <.5c a c a2.5 c a ψ ed,v =.0 D D Table Step 3d. Calculate ψ c,v =.0 (cracked cocrete, o supplemetal or edge reiforcemet) D Step 3e. Calculate ψ h,v =. ; for members where h a <.5c a h a = 5.0 <.5c a = 9.0 ψ h,v =.. =.34 D (ACI oly) - Step 3f. Calculate V b =7. ( ). = (.0) 4000(6.0). = 5,569 lbs. Step 3g. Calculate cocrete breakout stregth of achor group i shear: V cbg = (2.5/62.0) ,569 = 5,82 lbs. Calculate cocrete breakout capacity = φv cbg = ,82 = 3,627 lbs. Step 4. Calculate omial pryout stregth of a achor group i shear: Vcpg = kcpncbg =.0 5,32 lbs = 5,32 lbs. Calculate pryout capacity: φv cpg = ,32 lbs. = 3,724 lbs. Step 5. Determie cotrollig resistace stregth i shear: φv = mi,, = φv sag = 2,625 lbs. Step 6. Calculate allowable stress desig coversio factor for loadig coditio: Assume cotrollig load combiatio:.2d +.6L ; 50% Dead Load, 50% Live Load α =.2(30%) +.6(70%) =.40 Step 7. Calculate allowable stress desig value:, = D Table 4 D.6.2. (b) 4..5 D.6.3. (b) D.4.. D Table =,. =,875 lbs FIGURE 7 EXAMPLE STRENGTH DESIGN CALCULATION FOR SHEAR CAPACITY

13 ICC-ES Evaluatio Report ESR-2502 Supplemet Reissued May, 200 This report is subject to re-examiatio i two years. (800) (562) A Subsidiary of the Iteratioal Code Coucil DIVISION: 03 CONCRETE Sectio: 035 Cocrete Achorig REPORT HOLDER: POWERS FASTENERS, INC. 2 POWERS LANE BREWSTER, NEW YORK 0509 (94) or (800) egieerig@powers.com EVALUATION SUBJECT: POWERS POWER-STUD + SD2 ANCHORS IN CRACKED AND UNCRACKED CONCRETE.0 EVALUATION SCOPE Compliace with the followig codes: 2007 Florida Buildig Code Buildig 2007 Florida Buildig Code Residetial Property evaluated: Structural 2.0 PURPOSE OF THIS SUPPLEMENT This supplemet is issued to idicate that the Powers Power-Stud + SD2 Achors i Cracked ad Ucracked Cocrete described i the master report comply with the 2007 Florida Buildig Code Buildig ad the 2007 Florida Buildig Code Residetial, whe desiged ad istalled i accordace with the master evaluatio report. Use of the Powers Power-Stud + SD2 Achors i Cracked ad Ucracked Cocrete as described i the master evaluatio report to comply with the High Velocity Hurricae Zoe Provisios of the 2007 Florida Buildig Code Buildig has ot bee evaluated, ad is outside the scope of this supplemet. For products fallig uder Florida Rule 9B-72, verificatio that the report holder s quality assurace program is audited by a quality assurace etity approved by the Florida Buildig Commissio for the type of ispectios beig coducted is the resposibility of a approved validatio etity (or the code official whe the report holder does ot possess a approval by the Commissio). This supplemet expires cocurretly with the master report reissued o May, 200. ICC-ES Evaluatio Reports are ot to be costrued as represetig aesthetics or ay other attributes ot specifically addressed, or are they to be costrued as a edorsemet of the subject of the report or a recommedatio for its use. There is o warraty by ICC Evaluatio Service, Ic., express or implied, as to ay fidig or other matter i this report, or as to ay product covered by the report. Copyright 200 Page of

Tension zone applications, i.e., cable trays and strut, pipe supports, fire sprinklers Seismic and wind loading

Tension zone applications, i.e., cable trays and strut, pipe supports, fire sprinklers Seismic and wind loading General Information Mechanical Anchors General Information Power-Stud + SD1 Wedge Expansion Anchor Product Description The Power-Stud+ SD1 anchor is a fully threaded, torque-controlled, wedge expansion

More information

Edward C. Robison, PE, SE. 02 January Architectural Metal Works ATTN: Sean Wentworth th ST Emeryville, CA 94608

Edward C. Robison, PE, SE. 02 January Architectural Metal Works ATTN: Sean Wentworth th ST Emeryville, CA 94608 Edward C. Robison, PE, SE ks ATTN: Sean Wentworth 1483 67 th ST Emeryville, CA 94608 02 January 2013 SUBJ: 501 CORTE MADERA AVE, CORTE MADERA, CA 94925 BALCONY GUARD BASE PLATE MOUNTS The guards for the

More information

C. C. Fu, Ph.D., P.E.

C. C. Fu, Ph.D., P.E. ENCE710 C. C. Fu, Ph.D., P.E. Shear Coectors Desig by AASHTO RFD (RFD Art. 6.10.10) I the egative flexure regios, shear coectors shall be rovided where the logitudial reiforcemet is cosidered to be a art

More information

Example 1 - Single Headed Anchor in Tension Away from Edges BORRADOR. Calculations and Discussion

Example 1 - Single Headed Anchor in Tension Away from Edges BORRADOR. Calculations and Discussion Example 1 - Single Headed Anchor in Tension Away from Edges Check the capacity of a single anchor, 1 in. diameter, F1554 Grade 36 headed bolt with heavy-hex head installed in the top of a foundation without

More information

DIVISION: METALS SECTION: METAL FASTENINGS SECTION: STEEL DECKING REPORT HOLDER: PNEUTEK, INC.

DIVISION: METALS SECTION: METAL FASTENINGS SECTION: STEEL DECKING REPORT HOLDER: PNEUTEK, INC. ICC ES Report ICC ES () 7 () www.icc es.org Most Widely Accepted and Trusted ESR 1 Reissued /1 This report is subject to renewal /. DIVISION: METALS SECTION: METAL FASTENINGS SECTION: 1 STEEL ING REPORT

More information

Anchor Bolt Design (Per ACI and "Design of Reinforcement in Concrete Pedestals" CSA Today, Vol III, No. 12)

Anchor Bolt Design (Per ACI and Design of Reinforcement in Concrete Pedestals CSA Today, Vol III, No. 12) Anchor Bolt Design (Per ACI 318-08 and "Design of Reinforcement in Concrete Pedestals" CSA Today, Vol III, No. 12) Design Assumptions: Base Units and Design 1. Tension is equally distributed among all

More information

Failure Theories Des Mach Elem Mech. Eng. Department Chulalongkorn University

Failure Theories Des Mach Elem Mech. Eng. Department Chulalongkorn University Failure Theories Review stress trasformatio Failure theories for ductile materials Maimum-Shear-Stress Theor Distortio-Eerg Theor Coulomb-Mohr Theor Failure theories for brittle materials Maimum-Normal-Stress

More information

Case Study in Steel adapted from Structural Design Guide, Hoffman, Gouwens, Gustafson & Rice., 2 nd ed.

Case Study in Steel adapted from Structural Design Guide, Hoffman, Gouwens, Gustafson & Rice., 2 nd ed. Case Std i Steel adapted from Strctral Desig Gide, Hoffma, Gowes, Gstafso & Rice., d ed. Bildig descriptio The bildig is a oe-stor steel strctre, tpical of a office bildig. The figre shows that it has

More information

Case Study in Steel adapted from Structural Design Guide, Hoffman, Gouwens, Gustafson & Rice., 2 nd ed.

Case Study in Steel adapted from Structural Design Guide, Hoffman, Gouwens, Gustafson & Rice., 2 nd ed. ARCH 631 Note Set F014ab Case Std i Steel adapted from Strctral Desig Gide, Hoffma, Gowes, Gstafso & Rice., d ed. Bildig descriptio The bildig is a oe-stor steel strctre, tpical of a office bildig. The

More information

DIVISION: METALS SECTION: STEEL DECKING SECTION: STEEL ROOF DECKING REPORT HOLDER: NEW MILLENNIUM BUILDING SYSTEMS, LLC

DIVISION: METALS SECTION: STEEL DECKING SECTION: STEEL ROOF DECKING REPORT HOLDER: NEW MILLENNIUM BUILDING SYSTEMS, LLC 0 Most Widely Accepted and Trusted ICC ES Report ICC ES 000 (800) 423 6587 (562) 699 0543 www.icc es.org ESR 2657 Reissued 05/2017 This report is subject to renewal 03/2018. DIVISION: 05 00 00 METALS SECTION:

More information

Principle Of Superposition

Principle Of Superposition ecture 5: PREIMINRY CONCEP O RUCUR NYI Priciple Of uperpositio Mathematically, the priciple of superpositio is stated as ( a ) G( a ) G( ) G a a or for a liear structural system, the respose at a give

More information

A through-bolt expansion wedge anchor with controlled torque, for use in non cracked concrete.

A through-bolt expansion wedge anchor with controlled torque, for use in non cracked concrete. A through-bolt expansion wedge anchor with controlled torque, for use in non cracked concrete. ETA assessed option 7 anchor. Stainless steel 316 (A4) grade, with 316 (A4) grade stainless steel expansion

More information

FAILURE CRITERIA: MOHR S CIRCLE AND PRINCIPAL STRESSES

FAILURE CRITERIA: MOHR S CIRCLE AND PRINCIPAL STRESSES LECTURE Third Editio FAILURE CRITERIA: MOHR S CIRCLE AND PRINCIPAL STRESSES A. J. Clark School of Egieerig Departmet of Civil ad Evirometal Egieerig Chapter 7.4 b Dr. Ibrahim A. Assakkaf SPRING 3 ENES

More information

SHAFTS: STATICALLY INDETERMINATE SHAFTS

SHAFTS: STATICALLY INDETERMINATE SHAFTS SHAFTS: STATICALLY INDETERMINATE SHAFTS Up to this poit, the resses i a shaft has bee limited to shearig resses. This due to the fact that the selectio of the elemet uder udy was orieted i such a way that

More information

Evaluation of Anchor Bolt Clearance Discrepancies

Evaluation of Anchor Bolt Clearance Discrepancies Evaluatio of Achor Bolt Clearace Discrepacies Cotract # DTRT1GUTC1 with USDOT Office of the Assistat Secretary for Research ad Techology (OST-R) Fial Report July 016 Pricipal Ivestigator: Ia E. Hosch,

More information

The target reliability and design working life

The target reliability and design working life Safety ad Security Egieerig IV 161 The target reliability ad desig workig life M. Holický Kloker Istitute, CTU i Prague, Czech Republic Abstract Desig workig life ad target reliability levels recommeded

More information

SHAFTS: STATICALLY INDETERMINATE SHAFTS

SHAFTS: STATICALLY INDETERMINATE SHAFTS LECTURE SHAFTS: STATICALLY INDETERMINATE SHAFTS Third Editio A.. Clark School of Egieerig Departmet of Civil ad Eviromet Egieerig 7 Chapter 3.6 by Dr. Ibrahim A. Assakkaf SPRING 2003 ENES 220 Mechaics

More information

A through-bolt expansion wedge anchor with controlled torque, for use in cracked and non cracked concrete.

A through-bolt expansion wedge anchor with controlled torque, for use in cracked and non cracked concrete. A through-bolt expansion wedge anchor with controlled torque, for use in cracked and non cracked concrete. ETA assessed option 1 anchor. Galvanised carbon steel, with 316 (A4) stainless steel expansion

More information

Accuracy of prediction methods for the improvement of impact sound pressure levels using floor coverings

Accuracy of prediction methods for the improvement of impact sound pressure levels using floor coverings Accuracy of predictio methods for the improvemet of impact soud pressure levels usig floor coverigs Daiel GRIFFIN 1 1 Marshall Day Acoustics, Australia ABSTRACT The improvemet of impact soud pressure levels

More information

SNAP Centre Workshop. Basic Algebraic Manipulation

SNAP Centre Workshop. Basic Algebraic Manipulation SNAP Cetre Workshop Basic Algebraic Maipulatio 8 Simplifyig Algebraic Expressios Whe a expressio is writte i the most compact maer possible, it is cosidered to be simplified. Not Simplified: x(x + 4x)

More information

1 Input data. Profis Anchor Company: Specifier: Address: Phone I Fax: Page: Project: Sub-Project I Pos. No.

1 Input data.   Profis Anchor Company: Specifier: Address: Phone I Fax:   Page: Project: Sub-Project I Pos. No. 1 Specifier's comments: Design of Typical Baseplate B1 according to Max. forces in Node No. (5984), LC19 (1.2D+1.6S+0.8WY CASE B) 1 Input data Anchor type and diameter: HIT-HY 200 + HIT-V (8.8) M24 Seismic/Filling

More information

Exponents. Learning Objectives. Pre-Activity

Exponents. Learning Objectives. Pre-Activity Sectio. Pre-Activity Preparatio Epoets A Chai Letter Chai letters are geerated every day. If you sed a chai letter to three frieds ad they each sed it o to three frieds, who each sed it o to three frieds,

More information

Applying Performance Based Plastic Design Method to Steel Moment Resisting Frame in Accordance with the Indian Standard Code

Applying Performance Based Plastic Design Method to Steel Moment Resisting Frame in Accordance with the Indian Standard Code Iteratioal Joural of Egieerig ad Techology Volume 2 No. 3, March, 2012 Applyig Performace Based Plastic Desig Method to Steel Momet Resistig Frame i Accordace with the Idia Stadard Code Sejal P. Dalal

More information

Analysis of Experimental Measurements

Analysis of Experimental Measurements Aalysis of Experimetal Measuremets Thik carefully about the process of makig a measuremet. A measuremet is a compariso betwee some ukow physical quatity ad a stadard of that physical quatity. As a example,

More information

Client: Client No 1. Location: Location No 1

Client: Client No 1. Location: Location No 1 1 of 3 JOINT CONIGURATION AND DIMENSIONS: bolted ed plate coectio (ustiffeed) Referece clauses: Resistaces for the exteded ed plate coectio. Assumptio: The desig momets i the to beams are equal ad opposite.

More information

Power supplies for parallel operation Power supplies

Power supplies for parallel operation Power supplies Power supplies Power supplies for parallel operatio U 1 2 U Parallel operatio of switchmode power supplies Techical details for passive curret-sharig The aim of operatig switchmode power supplies (SMPS)

More information

EVALUATION OF GLASS FIBER/EPOXY INTERFACIAL STRENGTH BY THE CRUCIFORM SPECIMEN METHOD

EVALUATION OF GLASS FIBER/EPOXY INTERFACIAL STRENGTH BY THE CRUCIFORM SPECIMEN METHOD EVALUATION OF GLASS FIBER/EPOX INTERFACIAL STRENGTH B THE CRUCIFORM SPECIMEN METHOD Ju KOANAGI, Hajime KATO, Akihiro KASHIMA, uichi IGARASHI, Keichi WATANABE 3, Ichiro UENO 4 ad Shiji OGIHARA 4 Istitute

More information

Reliability of steel flexural members according to EC in serviceability limit state

Reliability of steel flexural members according to EC in serviceability limit state NSCC2009 Reliability of steel flexural members accordig to EC i serviceability limit state D. Hofi & A. Mårtesso Divisio of Structural Egieerig, Lud Uiversity, Lud, Swede ABSTRACT: To achieve a relatively

More information

Provläsningsexemplar / Preview TECHNICAL REPORT INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE

Provläsningsexemplar / Preview TECHNICAL REPORT INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE TECHNICAL REPORT CISPR 16-4-3 2004 AMENDMENT 1 2006-10 INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE Amedmet 1 Specificatio for radio disturbace ad immuity measurig apparatus ad methods Part 4-3:

More information

U8L1: Sec Equations of Lines in R 2

U8L1: Sec Equations of Lines in R 2 MCVU U8L: Sec. 8.9. Equatios of Lies i R Review of Equatios of a Straight Lie (-D) Cosider the lie passig through A (-,) with slope, as show i the diagram below. I poit slope form, the equatio of the lie

More information

Trusted SECTION: POST COLUMBIA, PANELS. Conformity! ICC-ES Evaluation. Copyright 2015

Trusted SECTION: POST COLUMBIA, PANELS. Conformity! ICC-ES Evaluation. Copyright 2015 0 ICC ES Report ICC ES (800) 423 6587 (562) 699 0543 www.icc es.orgg 000 Most Widely Accepted and Trusted ESR 1169 Reissued 06/2015 This report is subject to renewal 06/2016. DIVISION: 05 00 00 METALS

More information

A CONFINEMENT MODEL OF HIGH STRENGTH CONCRETE

A CONFINEMENT MODEL OF HIGH STRENGTH CONCRETE 3 th World Coferece o Earthquake Egieerig Vacouver, B.C., Caada August -6, 24 Paper No. 873 A CONFINEMENT MODEL OF HIGH STRENGTH CONCRETE Nobutaka NAKAZAWA, Kazuhiko KAWASHIMA 2, Gakuho WATANABE 3, Ju-ichi

More information

Max. thick. of part to be fixed. Min. thick. of base material. anchor depth. Anchor mechanical properties

Max. thick. of part to be fixed. Min. thick. of base material. anchor depth. Anchor mechanical properties zin oated steel version 1/6 High seurity, high performane fixing for use in raked and non-raked onrete ETA European Tehnial Assessment ETA Option 1-05/0044 d T inst T inst d f t fix APPLICATIO Safety ritial

More information

Respon Spektrum Gempa

Respon Spektrum Gempa Mata Kuliah : Diamika Struktur & Pegatar Rekayasa Kegempaa Kode : TSP 302 SKS : 3 SKS Respo Spektrum Gempa Pertemua 10 TIU : Mahasiswa dapat mejelaska feomea-feomea diamik secara fisik. TIK : Mahasiswa

More information

Reliability and Availablity

Reliability and Availablity Reliability ad Availablity This set of otes is a combiatio of material from Prof. Doug Carmichael's otes for 13.21 ad Chapter 8 of Egieerig Statistics Hadbook. NIST/SEMATECH e-hadbook of Statistical Methods,

More information

1 Input data. Profis Anchor Company: Specifier: Address: Phone I Fax: Page: Project: Sub-Project I Pos. No.

1 Input data.   Profis Anchor Company: Specifier: Address: Phone I Fax:   Page: Project: Sub-Project I Pos. No. 1 Specifier's comments: Check of Existing Base plate (B6)- According to max. forces on Node No. 11979, LC 1.4(D.L.+WX) 1 Input data Anchor type and diameter: HIT-HY 200 + HIT-V-F (8.8) M27 Seismic/Filling

More information

Chapter 12 - Quality Cotrol Example: The process of llig 12 ouce cas of Dr. Pepper is beig moitored. The compay does ot wat to uderll the cas. Hece, a target llig rate of 12.1-12.5 ouces was established.

More information

1 Input data. 2 Overall Result. 3 Geometry. PROFIS Anchor Channel Company: Specifier: Address: Phone Fax:

1 Input data. 2 Overall Result. 3 Geometry.   PROFIS Anchor Channel Company: Specifier: Address: Phone Fax: Phone Fax: Specifier's comments: 1 1 Input data Channel type; bolt HAC-60 148/350 F; HBC-C 8.8F, M16 x 2.0 in. Channel filled w/ HIT-HY 100 no Effective embedment depth h ef = 5.827 in. Channel specification

More information

A statistical method to determine sample size to estimate characteristic value of soil parameters

A statistical method to determine sample size to estimate characteristic value of soil parameters A statistical method to determie sample size to estimate characteristic value of soil parameters Y. Hojo, B. Setiawa 2 ad M. Suzuki 3 Abstract Sample size is a importat factor to be cosidered i determiig

More information

Median and IQR The median is the value which divides the ordered data values in half.

Median and IQR The median is the value which divides the ordered data values in half. STA 666 Fall 2007 Web-based Course Notes 4: Describig Distributios Numerically Numerical summaries for quatitative variables media ad iterquartile rage (IQR) 5-umber summary mea ad stadard deviatio Media

More information

1036: Probability & Statistics

1036: Probability & Statistics 036: Probability & Statistics Lecture 0 Oe- ad Two-Sample Tests of Hypotheses 0- Statistical Hypotheses Decisio based o experimetal evidece whether Coffee drikig icreases the risk of cacer i humas. A perso

More information

Ray-triangle intersection

Ray-triangle intersection Ray-triagle itersectio ria urless October 2006 I this hadout, we explore the steps eeded to compute the itersectio of a ray with a triagle, ad the to compute the barycetric coordiates of that itersectio.

More information

Scholars' Mine. Missouri University of Science and Technology. Ling-En Hsiao. Wei-wen Yu Missouri University of Science and Technology,

Scholars' Mine. Missouri University of Science and Technology. Ling-En Hsiao. Wei-wen Yu Missouri University of Science and Technology, Missouri Uiversity of Sciece ad Techology Scholars' Mie Ceter for Cold-Formed Steel Structures Library Wei-We Yu Ceter for Cold-Formed Steel Structures 8-1-1989 Load ad resistace factor desig of cold-formed

More information

Student s Printed Name:

Student s Printed Name: Studet s Prited Name: Istructor: XID: C Sectio: No questios will be aswered durig this eam. If you cosider a questio to be ambiguous, state your assumptios i the margi ad do the best you ca to provide

More information

Problem Cosider the curve give parametrically as x = si t ad y = + cos t for» t» ß: (a) Describe the path this traverses: Where does it start (whe t =

Problem Cosider the curve give parametrically as x = si t ad y = + cos t for» t» ß: (a) Describe the path this traverses: Where does it start (whe t = Mathematics Summer Wilso Fial Exam August 8, ANSWERS Problem 1 (a) Fid the solutio to y +x y = e x x that satisfies y() = 5 : This is already i the form we used for a first order liear differetial equatio,

More information

Hilti HSV-F Stud anchor

Hilti HSV-F Stud anchor Product Data Sheet Hilti Anchor version Benefits torque-controlled mechanical expansion allows immediate load application HSV-F Carbon steel, hot dipped galvanised, min 42 microns coating thickness setting

More information

Reliability and Queueing

Reliability and Queueing Copyright 999 Uiversity of Califoria Reliability ad Queueig by David G. Messerschmitt Supplemetary sectio for Uderstadig Networked Applicatios: A First Course, Morga Kaufma, 999. Copyright otice: Permissio

More information

ETAG 001 Edition 2012

ETAG 001 Edition 2012 European Organisation for Technical Approvals Europäische Organisation für Technische Zulassungen Organisation Européenne pour l Agrément Technique ETAG 001 Edition 2012 GUIDELIE FOR EUROPEA TECHICAL APPROVAL

More information

11 Correlation and Regression

11 Correlation and Regression 11 Correlatio Regressio 11.1 Multivariate Data Ofte we look at data where several variables are recorded for the same idividuals or samplig uits. For example, at a coastal weather statio, we might record

More information

The z-transform. 7.1 Introduction. 7.2 The z-transform Derivation of the z-transform: x[n] = z n LTI system, h[n] z = re j

The z-transform. 7.1 Introduction. 7.2 The z-transform Derivation of the z-transform: x[n] = z n LTI system, h[n] z = re j The -Trasform 7. Itroductio Geeralie the complex siusoidal represetatio offered by DTFT to a represetatio of complex expoetial sigals. Obtai more geeral characteristics for discrete-time LTI systems. 7.

More information

Senvion SE Franz-Lenz-Str. 1, Osnabrück, Germany

Senvion SE Franz-Lenz-Str. 1, Osnabrück, Germany Iteratioal Wid Egieerig Coferece IWEC 014 WAVE INDUCED FATIGUE LOADS ON MONOPILES - NEW APPROACHES FOR LUMPING OF SCATTER TABLES AND SITE SPECIFIC INTERPOLATION OF FATIGUE LOADS M. SEIDEL Sevio SE Fraz-Lez-Str.

More information

KMXP Linear Position Sensor

KMXP Linear Position Sensor Liear Positio Sesor SPECIFICATIONS AMR liear positio sesor DFN x6 package, very compact Small wall thickess for large air gaps High operatig temperature of 50 C O the edge solderig possible Movig a KMXP

More information

FACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING. Lectures

FACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING. Lectures FACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING Lectures MODULE 5 STATISTICS II. Mea ad stadard error of sample data. Biomial distributio. Normal distributio 4. Samplig 5. Cofidece itervals

More information

6.003 Homework #3 Solutions

6.003 Homework #3 Solutions 6.00 Homework # Solutios Problems. Complex umbers a. Evaluate the real ad imagiary parts of j j. π/ Real part = Imagiary part = 0 e Euler s formula says that j = e jπ/, so jπ/ j π/ j j = e = e. Thus the

More information

TEACHER CERTIFICATION STUDY GUIDE

TEACHER CERTIFICATION STUDY GUIDE COMPETENCY 1. ALGEBRA SKILL 1.1 1.1a. ALGEBRAIC STRUCTURES Kow why the real ad complex umbers are each a field, ad that particular rigs are ot fields (e.g., itegers, polyomial rigs, matrix rigs) Algebra

More information

Section 9.2. Tests About a Population Proportion 12/17/2014. Carrying Out a Significance Test H A N T. Parameters & Hypothesis

Section 9.2. Tests About a Population Proportion 12/17/2014. Carrying Out a Significance Test H A N T. Parameters & Hypothesis Sectio 9.2 Tests About a Populatio Proportio P H A N T O M S Parameters Hypothesis Assess Coditios Name the Test Test Statistic (Calculate) Obtai P value Make a decisio State coclusio Sectio 9.2 Tests

More information

Machine Learning for Data Science (CS 4786)

Machine Learning for Data Science (CS 4786) Machie Learig for Data Sciece CS 4786) Lecture & 3: Pricipal Compoet Aalysis The text i black outlies high level ideas. The text i blue provides simple mathematical details to derive or get to the algorithm

More information

MOST PEOPLE WOULD RATHER LIVE WITH A PROBLEM THEY CAN'T SOLVE, THAN ACCEPT A SOLUTION THEY CAN'T UNDERSTAND.

MOST PEOPLE WOULD RATHER LIVE WITH A PROBLEM THEY CAN'T SOLVE, THAN ACCEPT A SOLUTION THEY CAN'T UNDERSTAND. XI-1 (1074) MOST PEOPLE WOULD RATHER LIVE WITH A PROBLEM THEY CAN'T SOLVE, THAN ACCEPT A SOLUTION THEY CAN'T UNDERSTAND. R. E. D. WOOLSEY AND H. S. SWANSON XI-2 (1075) STATISTICAL DECISION MAKING Advaced

More information

a b c d e f g h Supplementary Information

a b c d e f g h Supplementary Information Supplemetary Iformatio a b c d e f g h Supplemetary Figure S STM images show that Dark patters are frequetly preset ad ted to accumulate. (a) mv, pa, m ; (b) mv, pa, m ; (c) mv, pa, m ; (d) mv, pa, m ;

More information

R. van Zyl 1, A.J. van der Merwe 2. Quintiles International, University of the Free State

R. van Zyl 1, A.J. van der Merwe 2. Quintiles International, University of the Free State Bayesia Cotrol Charts for the Two-parameter Expoetial Distributio if the Locatio Parameter Ca Take o Ay Value Betwee Mius Iity ad Plus Iity R. va Zyl, A.J. va der Merwe 2 Quitiles Iteratioal, ruaavz@gmail.com

More information

MATH/STAT 352: Lecture 15

MATH/STAT 352: Lecture 15 MATH/STAT 352: Lecture 15 Sectios 5.2 ad 5.3. Large sample CI for a proportio ad small sample CI for a mea. 1 5.2: Cofidece Iterval for a Proportio Estimatig proportio of successes i a biomial experimet

More information

Drive Technology \ Drive Automation \ System Integration \ Services. Data Sheet. Functional Safety Safety Characteristics for BE..

Drive Technology \ Drive Automation \ System Integration \ Services. Data Sheet. Functional Safety Safety Characteristics for BE.. Drive Techology \ Drive Automatio \ System Itegratio \ Services Data Sheet Fuctioal Safety Safety Characteristics for BE.. Brake Editio 12/2010 17062810 / EN SEW-EURODRIVE Drivig the world Data Sheet Safety

More information

6.867 Machine learning, lecture 7 (Jaakkola) 1

6.867 Machine learning, lecture 7 (Jaakkola) 1 6.867 Machie learig, lecture 7 (Jaakkola) 1 Lecture topics: Kerel form of liear regressio Kerels, examples, costructio, properties Liear regressio ad kerels Cosider a slightly simpler model where we omit

More information

N14/5/MATHL/HP1/ENG/TZ0/XX/M MARKSCHEME. November 2014 MATHEMATICS. Higher Level. Paper pages

N14/5/MATHL/HP1/ENG/TZ0/XX/M MARKSCHEME. November 2014 MATHEMATICS. Higher Level. Paper pages N4/5/MATHL/HP/ENG/TZ0/XX/M MARKSCHEME November 04 MATHEMATICS Higher Level Paper 0 pages N4/5/MATHL/HP/ENG/TZ0/XX/M This markscheme is the property of the Iteratioal Baccalaureate ad must ot be reproduced

More information

t distribution [34] : used to test a mean against an hypothesized value (H 0 : µ = µ 0 ) or the difference

t distribution [34] : used to test a mean against an hypothesized value (H 0 : µ = µ 0 ) or the difference EXST30 Backgroud material Page From the textbook The Statistical Sleuth Mea [0]: I your text the word mea deotes a populatio mea (µ) while the work average deotes a sample average ( ). Variace [0]: The

More information

62. Power series Definition 16. (Power series) Given a sequence {c n }, the series. c n x n = c 0 + c 1 x + c 2 x 2 + c 3 x 3 +

62. Power series Definition 16. (Power series) Given a sequence {c n }, the series. c n x n = c 0 + c 1 x + c 2 x 2 + c 3 x 3 + 62. Power series Defiitio 16. (Power series) Give a sequece {c }, the series c x = c 0 + c 1 x + c 2 x 2 + c 3 x 3 + is called a power series i the variable x. The umbers c are called the coefficiets of

More information

Algebra of Least Squares

Algebra of Least Squares October 19, 2018 Algebra of Least Squares Geometry of Least Squares Recall that out data is like a table [Y X] where Y collects observatios o the depedet variable Y ad X collects observatios o the k-dimesioal

More information

Design Data 16. Partial Flow Conditions For Culverts. x S o Q F = C 1 = (3) A F V F Q = x A x R2/3 x S o n 1/2 (2) 1 DD 16 (07/09)

Design Data 16. Partial Flow Conditions For Culverts. x S o Q F = C 1 = (3) A F V F Q = x A x R2/3 x S o n 1/2 (2) 1 DD 16 (07/09) Desig Data 16 Partial Flow Coditios For Culverts Sewers, both saitary ad storm, are desiged to carry a peak flow based o aticipated lad developmet. The hydraulic capacity of sewers or culverts costructed

More information

Process Level Gauges

Process Level Gauges TC Fluid Cotrol is the Exclusive UK Supplier of Kliger Level Gauges Kliger origially iveted the Reflex level gauge ad the Group has sice developed ito a world market leader i liquid level moitorig equipmet.

More information

Example: Find the SD of the set {x j } = {2, 4, 5, 8, 5, 11, 7}.

Example: Find the SD of the set {x j } = {2, 4, 5, 8, 5, 11, 7}. 1 (*) If a lot of the data is far from the mea, the may of the (x j x) 2 terms will be quite large, so the mea of these terms will be large ad the SD of the data will be large. (*) I particular, outliers

More information

Properties and Hypothesis Testing

Properties and Hypothesis Testing Chapter 3 Properties ad Hypothesis Testig 3.1 Types of data The regressio techiques developed i previous chapters ca be applied to three differet kids of data. 1. Cross-sectioal data. 2. Time series data.

More information

Finally, we show how to determine the moments of an impulse response based on the example of the dispersion model.

Finally, we show how to determine the moments of an impulse response based on the example of the dispersion model. 5.3 Determiatio of Momets Fially, we show how to determie the momets of a impulse respose based o the example of the dispersio model. For the dispersio model we have that E θ (θ ) curve is give by eq (4).

More information

Module 5 EMBEDDED WAVELET CODING. Version 2 ECE IIT, Kharagpur

Module 5 EMBEDDED WAVELET CODING. Version 2 ECE IIT, Kharagpur Module 5 EMBEDDED WAVELET CODING Versio ECE IIT, Kharagpur Lesso 4 SPIHT algorithm Versio ECE IIT, Kharagpur Istructioal Objectives At the ed of this lesso, the studets should be able to:. State the limitatios

More information

Efficient GMM LECTURE 12 GMM II

Efficient GMM LECTURE 12 GMM II DECEMBER 1 010 LECTURE 1 II Efficiet The estimator depeds o the choice of the weight matrix A. The efficiet estimator is the oe that has the smallest asymptotic variace amog all estimators defied by differet

More information

Analysis of MOS Capacitor Loaded Annular Ring MICROSTRIP Antenna

Analysis of MOS Capacitor Loaded Annular Ring MICROSTRIP Antenna Iteratioal OPEN AESS Joural Of Moder Egieerig Research (IJMER Aalysis of MOS apacitor Loaded Aular Rig MIROSTRIP Atea Mohit Kumar, Suredra Kumar, Devedra Kumar 3, Ravi Kumar 4,, 3, 4 (Assistat Professor,

More information

6 Sample Size Calculations

6 Sample Size Calculations 6 Sample Size Calculatios Oe of the major resposibilities of a cliical trial statisticia is to aid the ivestigators i determiig the sample size required to coduct a study The most commo procedure for determiig

More information

2C09 Design for seismic and climate changes

2C09 Design for seismic and climate changes 2C09 Desig for seismic ad climate chages Lecture 02: Dyamic respose of sigle-degree-of-freedom systems I Daiel Grecea, Politehica Uiversity of Timisoara 10/03/2014 Europea Erasmus Mudus Master Course Sustaiable

More information

Ma 530 Introduction to Power Series

Ma 530 Introduction to Power Series Ma 530 Itroductio to Power Series Please ote that there is material o power series at Visual Calculus. Some of this material was used as part of the presetatio of the topics that follow. What is a Power

More information

ME 375 FINAL EXAM Friday, May 6, 2005

ME 375 FINAL EXAM Friday, May 6, 2005 ME 375 FINAL EXAM Friay, May 6, 005 Divisio: Kig 11:30 / Cuigham :30 (circle oe) Name: Istructios (1) This is a close book examiatio, but you are allowe three 8.5 11 crib sheets. () You have two hours

More information

Optimally Sparse SVMs

Optimally Sparse SVMs A. Proof of Lemma 3. We here prove a lower boud o the umber of support vectors to achieve geeralizatio bouds of the form which we cosider. Importatly, this result holds ot oly for liear classifiers, but

More information

Statistics 511 Additional Materials

Statistics 511 Additional Materials Cofidece Itervals o mu Statistics 511 Additioal Materials This topic officially moves us from probability to statistics. We begi to discuss makig ifereces about the populatio. Oe way to differetiate probability

More information

Microscopic traffic flow modeling

Microscopic traffic flow modeling Chapter 34 Microscopic traffic flow modelig 34.1 Overview Macroscopic modelig looks at traffic flow from a global perspective, whereas microscopic modelig, as the term suggests, gives attetio to the details

More information

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,

More information

PILOT STUDY ON THE HORIZONTAL SHEAR BEHAVIOUR OF FRP RUBBER ISOLATORS

PILOT STUDY ON THE HORIZONTAL SHEAR BEHAVIOUR OF FRP RUBBER ISOLATORS Asia-Pacific Coferece o FRP i Structures (APFIS 2007) S.T. Smith (ed) 2007 Iteratioal Istitute for FRP i Costructio PILOT STUDY ON THE HORIZONTAL SHEAR BEHAVIOUR OF FRP RUBBER ISOLATORS T.B. Peg *, J.Z.

More information

Physics 7440, Solutions to Problem Set # 8

Physics 7440, Solutions to Problem Set # 8 Physics 7440, Solutios to Problem Set # 8. Ashcroft & Mermi. For both parts of this problem, the costat offset of the eergy, ad also the locatio of the miimum at k 0, have o effect. Therefore we work with

More information

Overview. p 2. Chapter 9. Pooled Estimate of. q = 1 p. Notation for Two Proportions. Inferences about Two Proportions. Assumptions

Overview. p 2. Chapter 9. Pooled Estimate of. q = 1 p. Notation for Two Proportions. Inferences about Two Proportions. Assumptions Chapter 9 Slide Ifereces from Two Samples 9- Overview 9- Ifereces about Two Proportios 9- Ifereces about Two Meas: Idepedet Samples 9-4 Ifereces about Matched Pairs 9-5 Comparig Variatio i Two Samples

More information

TESTING GEOGRIDS. Test Procedure for. TxDOT Designation: Tex-621-J 1. SCOPE 2. DEFINITION 3. SAMPLING 4. DETERMINING APERTURE SIZE

TESTING GEOGRIDS. Test Procedure for. TxDOT Designation: Tex-621-J 1. SCOPE 2. DEFINITION 3. SAMPLING 4. DETERMINING APERTURE SIZE est Procedure for xdo Desigatio: ex-621- Effective Date: August 1999 1. SCOPE 1.1 Use this method to sample ad test geogrid materials used i costructio. 1.2 Characteristics Covered aperture size percet

More information

Standard BAL-001-0a Real Power Balancing Control Performance

Standard BAL-001-0a Real Power Balancing Control Performance A. Itroductio. Title: Real Power Balacig Cotrol Performace 2. Number: BAL-00-0a 3. Purpose: To maitai Itercoectio steady-state frequecy withi defied limits by balacig real power demad ad supply i real-time.

More information

Depending on the application and the anchor type one of the following two concepts can be applied: Partial safety factor concept.

Depending on the application and the anchor type one of the following two concepts can be applied: Partial safety factor concept. Anchor design Safety concept Depending on the application and the anchor type one of the following two concepts can be applied: For anchors for use in concrete having an European Technical Approval (ETA)

More information

EXAMINATIONS OF THE ROYAL STATISTICAL SOCIETY

EXAMINATIONS OF THE ROYAL STATISTICAL SOCIETY EXAMINATIONS OF THE ROYAL STATISTICAL SOCIETY GRADUATE DIPLOMA, 016 MODULE : Statistical Iferece Time allowed: Three hours Cadidates should aswer FIVE questios. All questios carry equal marks. The umber

More information

U8L1: Sec Equations of Lines in R 2

U8L1: Sec Equations of Lines in R 2 MCVU Thursda Ma, Review of Equatios of a Straight Lie (-D) U8L Sec. 8.9. Equatios of Lies i R Cosider the lie passig through A (-,) with slope, as show i the diagram below. I poit slope form, the equatio

More information

Castiel, Supernatural, Season 6, Episode 18

Castiel, Supernatural, Season 6, Episode 18 13 Differetial Equatios the aswer to your questio ca best be epressed as a series of partial differetial equatios... Castiel, Superatural, Seaso 6, Episode 18 A differetial equatio is a mathematical equatio

More information

Markscheme May 2015 Calculus Higher level Paper 3

Markscheme May 2015 Calculus Higher level Paper 3 M5/5/MATHL/HP3/ENG/TZ0/SE/M Markscheme May 05 Calculus Higher level Paper 3 pages M5/5/MATHL/HP3/ENG/TZ0/SE/M This markscheme is the property of the Iteratioal Baccalaureate ad must ot be reproduced or

More information

Section 7. Gaussian Reduction

Section 7. Gaussian Reduction 7- Sectio 7 Gaussia eductio Paraxial aytrace Equatios eractio occurs at a iterace betwee two optical spaces. The traser distace t' allows the ray height y' to be determied at ay plae withi a optical space

More information

TESTING OF THE FORCES IN CABLE OF SUSPENSION STRUCTURE AND BRIDGES

TESTING OF THE FORCES IN CABLE OF SUSPENSION STRUCTURE AND BRIDGES TSTING OF TH FORCS IN CABL OF SUSPNSION STRUCTUR AND BRIDGS Zhou, M. 1, Liu, Z. ad Liu, J. 1 College of the Muicipal Techology, Guagzhou Uiversity, Guagzhou. Guagzhou Muicipal ad Ladscape gieerig Quality

More information

IMPACT OF THE VARIATION OF STORAGE VOLUMES IN CASCADING MULTI-TANK RAINWATER HARVESTING SYSTEMS

IMPACT OF THE VARIATION OF STORAGE VOLUMES IN CASCADING MULTI-TANK RAINWATER HARVESTING SYSTEMS IMPACT OF THE VARIATION OF STORAGE VOLUMES IN CASCADING MULTI-TANK RAINWATER HARVESTING SYSTEMS 1 S. Sedaayake 2 K. J. C. Kumara 1 Departmet of Civil Egieerig, South Asia Istitute of Techology ad Medicie

More information

CHAPTER 10 INFINITE SEQUENCES AND SERIES

CHAPTER 10 INFINITE SEQUENCES AND SERIES CHAPTER 10 INFINITE SEQUENCES AND SERIES 10.1 Sequeces 10.2 Ifiite Series 10.3 The Itegral Tests 10.4 Compariso Tests 10.5 The Ratio ad Root Tests 10.6 Alteratig Series: Absolute ad Coditioal Covergece

More information

Non-anaemic iron deficiency and fatigue

Non-anaemic iron deficiency and fatigue Appedices to the Article, Iro deficiecy without aaemia is a potetial cause of fatigue: meta-aalyses of radomised cotrolled trials ad cross-sectioal studies by Katsuhiko Yokoi ad Aki Koomi Appedix A Formulae

More information

Standard BAL Real Power Balancing Control Performance

Standard BAL Real Power Balancing Control Performance A. Itroductio. Title: Real Power Balacig Cotrol Performace 2. Number: BAL-00-3. Purpose: To maitai Itercoectio steady-state frequecy withi defied limits by balacig real power demad ad supply i real-time.

More information

Appendix: The Laplace Transform

Appendix: The Laplace Transform Appedix: The Laplace Trasform The Laplace trasform is a powerful method that ca be used to solve differetial equatio, ad other mathematical problems. Its stregth lies i the fact that it allows the trasformatio

More information