Connection and Tension Member Design

Transcription

1 ACH 631 Note Set 17.1 F2015abn Connecton and Tenson Member Desgn Notaton: A = area (net = wth holes, bearng = n contact, etc...) A e = effectve net area fond from the prodct of the net area A n by the shear lag factor U A b = area of a bolt A g = gross area, eqal to the total area gnorng any holes A gv = gross area sbjected to shear for block shear rptre A n = net area, eqal to the gross area sbtractng any holes, as s A net A nt = net area sbjected to tenson for block shear rptre A nv = net area sbjected to shear for block shear rptre ASD = allowable stress desgn d = dameter of a hole f p = bearng stress (see P) f t = tensle stress f v = shear stress F connector = shear force capacty per connector F n = nomnal tenson or shear strength of a bolt F = ltmate stress pror to falre F EXX = yeld strength of weld materal F y = yeld strength F yw = yeld strength of web materal g = gage spacng of staggered bolt holes I = moment of nerta wth respect to netral axs bendng k = dstance from oter face of W flange to the web toe of fllet l = name for length L = name for length L c = clear dstance between the edge of a hole and edge of next hole or edge of the connected steel plate n the drecton of the load L = length of an angle n a connector wth staggered holes LFD = load and resstance factor desgn n = nmber of connectors across a jont N = bearng length on a wde flange steel secton = bearng type connecton wth threads nclded n shear plane p = ptch of connector spacng P = name for axal force vector, as s T = generc load qantty (force, shear, moment, etc.) for LFD desgn a = reqred strength (ASD) n = nomnal vale (capacty) to be mltpled by φ = factored desgn vale for LFD desgn s = longtdnal center-to-center spacng of any two consectve holes S = allowable strength per length of a weld for a gven sze SC = slp crtcal bolted connecton t = thckness of a hole or member t w = thckness of web of wde flange T = throat sze of a weld V = nternal shear force V longtdnal = longtdnal shear force U = shear lag factor for steel tenson member desgn U bs = redcton coeffcent for block shear rptre X = bearng type connecton wth threads exclded from the shear plane y = vertcal dstance π = p ( radans or 180 ) φ = resstance factor = dameter symbol γ = load factor n LFD desgn Ω Σ = safety factor for ASD = smmaton symbol 323

2 ACH 631 Note Set 17.1 F2015abn Connectons Connectons mst be able to transfer any axal force, shear, or moment from member to member or from beam to colmn. Steel constrcton accomplshes ths wth bolt and welds. Wood constrcton ses nals, bolts, shear plates, and splt-rng connectors. Sngle Shear - forces case only one shear drop across the bolt. f v = P A = P πr 2 Doble Shear - forces case two shear changes across the bolt. f v = P P = 2 A 2πr 2 324

3 ACH 631 Note Set 17.1 F2015abn Bearng of a Bolt on a Bolt Hole The bearng srface can be represented by projectng the cross secton of the bolt hole on a plane (nto a rectangle). P f p = = A P td Horzontal Shear n Composte Beams Typcal connectons needng to resst shear are plates wth nals or rvets or bolts n composte sectons or splces. x The ptch (spacng) can be determned by the capacty n shear of the connector(s) to the shear flow over the spacng nterval, p. y y a p p p p = ptch length V longtdn al p nf VQ VQ = Vlongtdn al = p I I VQconnected area p I connector n = nmber of connectors connectng the connected area to the rest of the cross secton F = force capacty n one connector Q connected area = A connected area y connected area y connected area = dstance from the centrod of the connected area to the netral axs Connectors to esst Horzontal Shear n Composte Beams Even vertcal connectors have shear flow across them. The spacng can be determned by the capacty n shear of the connector(s) to the shear flow over the spacng nterval, p. nf p VQ connector connected I area 325 p p p

4 ACH 631 Note Set 17.1 F2015abn Tenson Member Desgn In tenson members, there may be bolt holes that redce the sze of the cross secton. Effectve Net Area: The smallest effectve are mst be determned by sbtractng the bolt hole areas. Wth staggered holes, the shortest length mst be evalated. f = t P A e or T A e A seres of bolts can also transfer a porton of the tensle force, and some of the effectve net areas see redced stress. Connectons n Wood Connectons for wood are typcally mechancal fasteners. Shear plates and splt rng connectors are common n trsses. Bolts of metal bear on holes n wood, and nals rely on shear resstance transverse and parallel to the nal shaft. Bolted Jonts Stress mst be evalated n the member beng connected sng the load beng transferred and the redced cross secton area called net area. Bolt capactes are sally provded n tables and take nto accont the allowable shearng stress across the dameter for sngle and doble shear, and the allowable bearng stress of the connected materal based on the drecton of the load wth respect to the gran (parallel or perpendclar). Problems, sch as rppng of the bolt hole at the end of the member, are avoded by followng code gdelnes on mnmm edge dstances and spacng. 326

5 ACH 631 Note Set 17.1 F2015abn Naled Jonts Becase nals rely on shear resstance, a common problem when nalng s splttng of the wood at the end of the member, whch s a shear falre. Tables lst the shear force capacty per nt length of embedment per nal. Jonted members sed for beams wll have shear stress across the connector, and the ptch spacng, p, can be determned from the shear stress eqaton when the capacty, F, s known. Other Connectors Screws - ange n szes from #6 (0.138 n. shank dameter) to #24 (0.372 n. shank dameter) n lengths p to fve nches. Lke nals, they are best sed laterally loaded n sde gran rather than n wthdrawal from sde gran. Wthdrawal from end s not permtted. Lag screws (or bolts) Smlar to wood screw, bt has a head lke a bolt. It mst have a load hole drlled and nserted along wth a washer. Splt rng and shear plate connectors Grooves are ct n each pece of the wood members to be joned so that half the rng s n each secton. The members are held together wth a bolt concentrc wth the rng. Shear plate connectors have a central plate wthn the rng. Splce plates These are common n pre-manfactred josts and consst of a sheet of metal wth pnched spkes. Framng seats & anchors for nstance, jost hangers and post bases... Connectons n Steel The lmt state for connectons depends on the loads: 1. tenson yeldng 2. shear yeldng 3. bearng yeldng 4. bendng yeldng de to eccentrc loads 5. rptre Hgh strength bolts resst shear (prmarly), whle the connected part mst resst yeldng and rptre. Welds mst resst shear stress. The desgn strengths depend on the weld materals. 327

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7 ACH 631 Note Set 17.1 F2015abn φ = the resstance factor F n = the nomnal tenson or shear strength of the bolt A b = the cross secton area of the bolt φ = 0.75 (LFD) Ω = 2.00 (ASD) A325, A325M F1858 A354 Grade BC A

8 ACH 631 Note Set 17.1 F2015abn For bearng of plate materal at bolt holes: deformaton at bolt hole s a concern = 1.2L tf 2. 4dtF n deformaton at bolt hole s not a concern n c = 1.5L tf 3. 0dtF c / Ω φ a n or n long slotted holes wth the slot perpendclar to the load = Σγ n = 1.0LctF 2. 0dtF n = the nomnal bearng strength F = specfed mnmm tensle strength L c = clear dstance between the edges of the hole and the next hole or edge n the drecton of the load d = nomnal bolt dameter t = thckness of connected materal φ = 0.75 (LFD) Ω = 2.00 (ASD) The mnmm edge desstance from the center of the oter most bolt to the edge of a member s generally 1¾ tmes the bolt dameter for the sheared edge and 1¼ tmes the bolt dameter for the rolled or gas ct edges. The maxmm edge dstance shold not exceed 12 tmes the thckness of thnner member or 6 n. Standard bolt hole spacng s 3 n. wth the mnmm spacng of tmes the dameter of the bolt, d b. Common edge dstance from the center of last hole to the edge s 1¼ n.. 330

9 ACH 631 Note Set 17.1 F2015abn Tenson Member Desgn In steel tenson members, there may be bolt holes that redce the sze of the cross secton. g refers to the row spacng or gage p refers to the bolt spacng or ptch s refers to the longtdnal spacng of two consectve holes Effectve Net Area: The smallest effectve are mst be determned by sbtractng the bolt hole areas. Wth staggered holes, the shortest length mst be evalated. A seres of bolts can also transfer a porton of the tensle force, and some of the effectve net areas see redced stress. The effectve net area, A e, s determned from the net area, A n, mltpled by a shear lag factor, U, whch depends on the element type and connecton confgraton. If a porton of a connected member s not flly connected (lke the leg of an angle), the nconnected part s not sbject to the fll stress and the shear lag factor can range from 0.6 to 1.0: A A U The staggered hole path area s determned by: A = A n g A of all holes s + tσ 4g t s the plate thckness, s s each stagger spacng, and g s the gage spacng. 331 e = n

10 ACH 631 Note Set 17.1 F2015abn For tenson elements: / Ω φ a n or n = Σγ 1. yeldng n = Fy Ag φ = 0.90 (LFD) Ω = 1.67 (ASD) 2. rptre n = F Ae φ = 0.75 (LFD) Ω = 2.00 (ASD) A g = the gross area of the member (excldng holes) A e = the effectve net area (wth holes, etc.) F y = the yeld strength of the steel F = the tensle strength of the steel (ltmate) For shear elements: / Ω φ a n or n = Σγ 1. yeldng n = 0. 6Fy Ag φ = 1.00 (LFD) Ω = 1.50 (ASD) 2. rptre n = 0. 6F Anv φ = 0.75 (LFD) Ω = 2.00 (ASD) A g = the gross area of the member (excldng holes) A nv = the net area sbject to shear (wth holes, etc.) F y = the yeld strength of the steel F = the tensle strength of the steel (ltmate) Welded Connectons Weld desgnatons nclde the strength n the name,.e. E70XX has F y = 70 ks. Welds are weakest n shear and are assmed to always fal n the shear mode. The throat sze, T, of a fllet weld s determned trgonometry by: T = weld sze* * When the sbmerged arc weld process s sed, welds over 3/8 wll have a throat thckness of 0.11 n. larger than the formla. 332

11 ACH 631 Note Set 17.1 F2015abn Weld szes are lmted by the sze of the parts beng pt together and are gven n AISC manal table J2.4 along wth the allowable strength per length of fllet weld, referred to as S. The maxmm sze of a fllet weld permtted along edges of connected parts shall be: Materal less than ¼ n. thck, not greater than the thckness of the materal. Materal ¼ n. or more n thckness, not greater than the thckness of the materal mns 1/16 n., nless the weld s especally desgnated on the drawngs to be blt ot to obtan fllthroat thckness. The mnmm length of a fllet weld s 4 tmes the nomnal sze. If t s not, then the weld sze sed for desgn s ¼ the length. Intermttent fllet welds cannot be less than for tmes the weld sze, not to be less than 1 ½. For fllet welds: for the weld metal: : / Ω φ a n or n = Σγ n = 0. 6FEXX Tl = Sl φ = 0.75 (LFD) T s throat thckness l s length of the weld Ω = 2.00 (ASD) For a connected part, the other lmt states for the base metal, sch as tenson yeld, tenson rptre, shear yeld, or shear rptre mst be consdered. Avalable Strength of Fllet Welds per nch of weld (φs) Weld Sze (n.) E60XX (k/n.) E70XX (k/n.) ¼ ½ ¾ (not consderng ncrease n throat wth sbmerged arc weld process) 333

12 ACH 631 Note Set 17.1 F2015abn Framed Beam Connectons Copng s the term for cttng away part of the flange to connect a beam to another beam sng welded or bolted angles. AISC provdes tables that gve bolt and angle avalable strength knowng nmber of bolts, bolt type, bolt dameter, angle leg thckness, hole type and copng, and the wde flange beam beng connected. For the connectons the lmt-state of bolt shear, bolts bearng on the angles, shear yeldng of the angles, shear rptre of the angles, and block shear rptre of the angles, and bolt bearng on the beam web are consdered. Grop A bolts nclde A325, whle Grop B ncldes A490. here are also tables for bolted/welded dobleangle connectons and all-welded dobleangle connectons. Sample AISC Table for Bolt and Angle Avalable Strength n All-Bolted Doble-Angle Connectons 334

13 ACH 631 Note Set 17.1 F2015abn Lmtng Strength or Stablty States In addton to resstng shear and tenson n bolts and shear n welds, the connected materals may be sbjected to shear, bearng, tenson, flexre and even pryng acton. Copng can sgnfcantly redce desgn strengths and may reqre web renforcement. All the followng mst be consdered: shear yeldng shear rptre block shear rptre - falre of a block at a beam as a reslt of shear and tenson tenson yeldng tenson rptre local web bcklng lateral torsonal bcklng Block Shear Strength (or ptre): : = 0. 6 F A + U F A 0. 6 F A + U n nv bs φ = 0.75 (LFD) nt y gv Ω = 2.00 (ASD) / Ω φ a n or n A nv s the net area sbjected to shear A nt s the net area sbjected to tenson A gv s the gross area sbjected to shear U bs = 1.0 when the tensle stress s nform (most cases) = 0.5 when the tensle stress s non-nform bs F A nt = Σγ Local Bcklng n Steel I Beams Web Crpplng or Flange Bcklng Concentrated forces on a steel beam can case the web to bckle (called web crpplng). Web stffeners nder the beam loads and bearng plates at the spports redce that tendency. Web stffeners also prevent the web from shearng n plate grders. 335

14 ACH 631 Note Set 17.1 F2015abn The maxmm spport load and nteror load can be determned from: P k + N )F n (max end) = ( 2. 5 P = ( 5k + N )F n (nteror) yw φ = 1.00 (LFD) t w yw t w t w = thckness of the web N = bearng length k = dmenson to fllet fond n beam secton tables Ω = 1.50 (ASD) 336