Si vous lisez notre article précédent, AISC 360: Conception de connexion de cisaillement, you would have a good sense of how simple connections are designed under AISC 360. A shear connection only has to deliver the beam end reaction. A moment connection has to deliver that reaction and the end moment with it, which brings the supporting column into the problem. In this article we work through an example moment connection between two I-shaped members and go through the design criteria that have to be satisfied. We can also get to the same results directly through the Conception de connexion SkyCiv module, which checks these connections to AISC 360-16 en TSA ou LRFD.
As in the shear connection example, the calculations here use the Allowable Stress Design (ASD) méthode. Si vous n'êtes pas familier avec la différence entre ASD et LRFD dans la conception structurelle, assurez-vous de regardez notre vidéo expliquer cela.
Dans cet exemple, we evaluate the capacity of a Bolted Flange-Plated Fully-Restrained (FR) Moment connection between a W18x50 beam and a W14x99 column, using the dimensions, welds and loads shown below. The connection has to support the beam end vertical reaction and the developed end moment. Compared with a shear connection, the difference is the pair of plates carrying the beam flange forces onto the supporting column flange.
The flange plates turn the beam end moment into a tension and compression couple. The top plate pulls, the bottom plate pushes, and both forces land on the column flange as concentrated forces. That is why a moment connection needs the column local checks that a shear connection does not.
Étant donné:
Charges de niveau de service & Matériau:
Cisaillement vertical de la charge morte (VD) = 7.0 kips
Cisaillement vertical de la charge vive (LV) = 21.0 kips
Moment de la charge morte (MARYLAND) = 42.0 kip-ft
Moment de la charge en direct (ML) = 126.0 kip-ft
Matériau de la plaque: ASTM A36, Fy = 36 KSI, Fu = 58 KSI
Matériau de la poutre et de la colonne: ASTM A992, Fy = 50 KSI, Fu = 65 KSI
Géométrie des poutres et des poteaux:
Beam: L18x50; bf = 7.50 in, tf = 0.570 in, d = 18.0 in, tw = 0.355 in, Sx = 88.9 dans^3
Colonne: L14x99; bf = 14.6 in, tf = 0.780 in, d = 14.2 in, tw = 0.485 in, kdes = 1.38 in
Plaque de bride: 3/4 en épaisseur; 7.0 en x 12.5 en dimensions
Plaque Web: 3/8 en épaisseur; 5.0 en x 9.0 en dimensions
Agencements (Boulons et soudures):
Bride: (8) – 7/8-in.-diameter ASTM F3125 Grade A325-N bolts in standard holes
Plaque Web: (3) – 7/8-in.-diameter ASTM F3125 Grade A325-N bolts in standard holes
70-filets d'électrode ksi. A325 and A490 are grades within ASTM F3125, which consolidated the older standalone bolt specifications.
Calculs de charge:
LRFD Charges (Référence seulement):
Réaction verticale ultime (Ru) = 1.2 (7.0 kips) + 1.6 (21.0 kips) = 42.0 kips
Moment ultime (Mu) = 1.2 (42.0 kip-ft) + 1.6 (126.0 kip-ft) = 252.0 kip-ft
ASD Charges:
Réaction verticale admissible (Ra) = 7.0 kips + 21 kips = 28.0 kips
Moment admissible (Ma) = 42.0 kip-ft + 126 kip-ft = 168.0 kip-ft
Everything below is checked against the ASD loads. Keep the two methods apart: ASD compares service loads to allowable strength, LRFD compares factored loads to design strength, and the LRFD figures above are carried only so you can compare the two.
Solution basée sur le logiciel de conception de connexion SkyCiv:
ERRATUM: La largeur de la plaque d'aile dans cet exemple était 7.0 in mais la largeur utilisée dans les calculs est 7.50 in, d'où la différence de valeurs.
Force de bride
Every check that follows is driven by one number, the force in the flange plate. The end moment is resolved into a couple acting at the plate centroids, so the lever arm is the beam depth plus one plate thickness:
Pde = [ 168.0 kip-ft (12 pouces/pieds) ] / (18.0 in + 0.75 in) = 107.5 kips
Plaque de bride à bride W14x99, Force de soudure
Résistance des soudures d'angle, Ω = 2.0
Taille de la soudure, t = 0.375 in
Fnouveau = 0.6 FEXX [ 1.0 + 0.5 sin1.5 (θ) ]
Où, = l'angle que fait la charge avec l'axe de soudure
= 90, pour les soudures chargées transversalement
= 0, pour les soudures chargées longitudinalement
Résistance par taille unitaire de soudure:
Contrainte de soudure admissible, Feuh = 0.6 (70KSI) / 2.0 = 21 KSI
longueur transversale, lt = 7 in
longueur longitudinale, ll = 0 in
longueur effective totale, l = lt (1.5) + ll (1.0) = 10.5 in
Ce logiciel 1.5 on the transverse length is the directional strength increase, 1.0 + 0.5 sin1.5(90).
(Ra / a) = 21 KSI (10.5 in) = 220.5 kips / in
Taille effective (gorge) de soudure d'angle, a:
0.707 = le cosinus ou le sinus de 45 degrés
a = (0.707) t = 0.265 in
Two welds, one each side of the plate:
Ra = (Ra / a) a (2) = 220.50 (0.265 in) 2 = 116.9 kips
Rapport de capacité de conception, DCR:
charge requise, R = 107.5 kips
capacité globale, Ra = 116.9 kips
DCR = (107.5 / 116.9) = 0.919, d'accord
Contrôles locaux de colonne
These four checks ask whether the W14x99 can accept the flange force without local stiffening. All of them are compared against the same flange force:
Force de bride, Pde = 107.5 kips
- Rendement local du Web, Ω = 1.5
Rn / Ω = [ Fest tw (5k + lb) ] / = 50ksi (0.485in) [ 5(1.38in) + 0.75in ] / 1.5 = 123.7 kips
Ici tw is the column web thickness and lb the bearing length, taken as the flange plate thickness.
Rapport de capacité de conception, DCR:
Force de bride, Pde = 107.5 kips
Capacité globale, Ra = 123.7 kips
DCR = (107.5 / 123.7) = 0.869, d'accord
- Pliage local de bride, Ω = 1.67
Rn / Ω = [ 6.25 FY tF2 ] / Ω = [ 6.25 (50KSI) (0.78in)2 ] / 1.67 = 113.8 kips
Rapport de capacité de conception, DCR:
Force de bride, Pde = 107.5 kips
Capacité globale, Ra = 113.8 kips
DCR = (107.5 / 113.8) = 0.944, d'accord
- Web Local paralysant, Ω = 2.0
Rn / Ω = 0.8 tw2 [ 1 + 3 ( lb / d ) ( tw / tF )1.5 ] ( E FY tF / tw)0.5 / Ω
= 0.8 (0.485in)2 [ 1 + 3 (0.05) (0.62)1.5 ] [ (29000KSI) (50KSI) (0.78in) / 0.485in ] 0.5 / 2.0
= 154.8 kips
Rapport de capacité de conception, DCR:
Force de bride, Pde = 107.5 kips
Capacité globale, Ra = 154.8 kips
DCR = (107.5 / 154.8) = 0.694, d'accord
- Bouclage de compression Web, Ω = 1.67
Rn / Ω = [ 24 tw3 ( E FY )0.5 / h ] / Ω
= 24 (0.485in)3 [ (29000KSI) (50KSI) ] 0.5 / 14.2in (1.67)
= 139.0 kips
The full column depth is used here in place of h, the clear distance between flanges less the fillets, which is conservative.
Rapport de capacité de conception, DCR:
Force de bride, Pde = 107.5 kips
Capacité globale, Ra = 139.0 kips
DCR = (107.5 / 139.0) = 0.773, d'accord
None of the four column local checks governs, so the W14x99 takes the flange force without transverse stiffeners for these limit states. Had any of them exceeded 1.0, the fix would be stiffeners or a doubler plate rather than a larger flange plate, because the capacity that ran out belongs to the column.
Bride W18x50, Rendement à la traction de la plaque à bride
Force de l'élément en tension, Ω = 1.67
Rn / ils ne posent pas le même défi de conception que les connexions de momentY Ag / Ω = (36KSI) (7.5in) (0.75in) / 1.67 = 121.3 kips
Rapport de capacité de conception, DCR:
Force de bride, Pde = 107.5 kips
Capacité globale, Ra = 121.3 kips
DCR = (107.5 / 121.3) = 0.887, d'accord
Bride W18x50, Rendement à la compression de la plaque à bride
Force de l'élément en compression, Ω = 1.67
Rn / ils ne posent pas le même défi de conception que les connexions de momentY Ag / Ω = (36KSI) (7.5in) (0.75in) / 1.67 = 121.3 kips
The compression plate is checked on the gross section because the bolt holes are filled in bearing. It matches the tension yielding value because the plate is short enough between the column face and the first bolt line for slenderness not to reduce it.
Rapport de capacité de conception, DCR:
Force de bride, Pde = 107.5 kips
Capacité globale, Ra = 121.3 kips
DCR = (107.5 / 121.3) = 0.887, d'accord
Bride W18x50, Rupture par traction de la plaque à bride
Force de l'élément en rupture, Ω = 2.0
Facteur de décalage de cisaillement, U du tableau de spécifications AISC D3.1: 1.0
Rn / ils ne posent pas le même défi de conception que les connexions de momentu Ae / Ω = (58KSI) [ 7.5in – 2 (1in) ] (0.75in) (1.0) / 2.0 = 119.6 kips
Two holes are deducted across the plate width. Ce logiciel 1 in deduction is the 7/8 in bolt diameter plus 1/8 in, which is the standard hole allowance used for net area.
Rapport de capacité de conception, DCR:
Force de bride, Pde = 107.5 kips
Capacité globale, Ra = 119.6 kips
DCR = (107.5 / 119.6) = 0.899, d'accord
Tableau récapitulatif de toutes les vérifications des résultats
Vous trouverez ci-dessous le tableau récapitulatif du module de conception de connexion SkyCiv de toutes les vérifications de conception nécessaires effectuées pour cette connexion. Toutes ces vérifications n'ont pas été présentées dans cet article, mais elles sont disponibles au format PDF que vous pouvez télécharger ici: Connexion-Conception-Rapport-EXEMPLE II.B-1-ASD
Of the checks worked through above, flange local bending governs at 0.944. That is the one to watch if the beam end moment grows, and it is a column property, so a heavier flange plate would not help.
De manière similaire, l'exemple de version LRFD peut être trouvé dans ce lien: Connexion-Conception-Rapport-EXEMPLE II.B-1-LRFD
Run This Example Yourself
Enter the W18x50, the W14x99 and the flange plates, and the module returns every check above with its utilization ratio and the clause behind it. Il s'exécute dans le navigateur, with nothing to install.
Références
- AISC 360-16, Spécification pour les bâtiments en acier de construction
- Exemples de conception AISC v14.1 (EXEMPLE II.B-1, pages IIB-2 à 13)
- Logiciel de conception de connexion SkyCiv: https://skyciv.com/structural-software/connection-design/
- Flange plate connection calculator: https://skyciv.com/structural-software/connection-design/flange-plate-connection-calculator/
