Product Technical Guides : US-EN Cast-In Anchor Channel Fastening Technical Guide | Page 382

1. Anchor Channel Systems Code 2. HAC Portfolio 3. HAC Applications Discussion 4. Design Introduction 5. Base material 6. Loading 8. Reinforcing Bar Anchorage 9. Special Anchor Channel Design Calculations Discussion There load combination that is evaluated: Wind Load: 1.2DL + WL/0.6 WL(ASD)=40psfx10.5’x5’=2100lbs Slab depth: 8” WL(Strength level)=2100lbs/0.6=3500lbs The application is statically indeterminate. Use compatibility equations and statics equations to solve for the location of the neutral axis (x). Once x is known, the tension force on each T-bolt can be calculated. Using the compatibility equations, define the tension force acting on both T-bolts (FT-bolts) in terms of the concrete compressive stress under the fixture (σc). Pocket height: 2” DL(ASD)=14psfx10.5’x5’=735lbs Front edge distance : 5” DL(Strength level)=1.2x735lbs=882lbs Side edge distance : 6” Slab depth deducting pocket: 8”-2”=6” T-bolt spacing: 6” Available tolerance along the channel length: (13.8”-(2x0.984”)-6”)/2=2.916” Bracket tolerance: 1.5” in/out Bracket dimension in y-direction: 8.75” Worst position: Bracket out Bracket dimension in x-direction: 1.5” Step 1: Load Combination and Bracket dimension ASCE 7-10 2.3.2 7. Anchor Channel Design Code x ε s γ g is so small that tan( g ) = e c 5”-x e c x = e s (5 - x ) e s = (5 - x ) F T - bolts . L e s = E T - bolts . A T - bolts e c = s c E c . x E c F T - bolts E T - bolts . A T - bolts .(5 - x ) Compatility equations : assume L = " unity " F T - bolts = Figure 14.1.5— Design example – Profis anchor channel - 3D front View Figure 14.1.6— Design example – Profis anchor channel - 3D Back View Step 2: Determination of T-bolt Tension and shear forces Determine the tension loads on the T-bolts. Assume the fixture is rigid. PROFIS Anchor Channel assumes Ec = 30,000 Mpa A T-bolts = (  2)(tensile stress area of T-bolt) = (2)(157 mm 2 )[1in 2 / (25.4 mm) 2 ] = 0.487in 2 (2) HBC-C 8.8F M16x60 are used. E concrete = (  modulus of elasticity for concrete) = 30,000 MPa = 4,351,200 lb/in 2 E T-bolts = (modulus of elasticity for T-bolt) = 29,000,000 lb/in 2 F T - bolts = 13. Field Fixes 14. Design Example (0.487 in 2 ).(29000000 lb / in 2 ).( s c ).(5 - x ) (4351200 lb / in 2 ).( x ) (3.246 in 2 ).( s c ).(5 - x ) x Sum the tension forces and moments F T - bolts = å F + ­= 0 (1).( s c ).( x ).( b ) = 0 2 2 (3.246 in ).( s c ).(5 - x ) (1).( s c ).( x ).( b ) = 0 + 882 - x 2 é (3.246 in 2 ).(5 - x ) ù é é (1).( x ).(10) ù ù - s c . ê s c . ê ê ú = 882 ú ú 2 x û û ë ë ë û é (5).( x 2 ) + 3.246 x - 16.23 ù ú = 882 x ë û s c . ê é ù 882 x ú ®®® Eqn 1 2 + - (5).( x ) 3.246 x 16.23 ë û s c = ê ( A T - bolts ).( E T - bolts ).( s c ).(5 - x ) ( E c ).( x ) Using statics equations, define the concrete stress under the fixture (σc) in terms of the lcompressive ocation of the neutral axis (x). Solve for x via trial and error. Once x is known, the values for σc and FT-bolts can be calculated. Once FT-bolts is known, the tension force on each T-bolt can be determined. The applied shear force is distributed equally on each T-bolt. (3.246 in 2 ).( s c ).(5 - x ) x é ù 882 x (3.246). ê ú .(5 - x ) 2 + - ( 5).( x ) 3.246 x 16.23 ë û = x é 14314.86 - 2862.972 x ù = ê ú ®®® Eqn 2 2 ë (5).( x ) + 3.246 x - 16.23 û F T - bolts = s c . L = 12. Instructions for Use F T - bolts + 882 lb - γ ε c 11. Best Practices Calculations ( F T - bolts )( L ) PL ® AE ( A T - bolts )( E T - bolts ) x 10. Design Software F T - bolts F T - bolts å M = 0 x ù x ù é é (882). ê 2 + ú + (3500). [ 1.5 ] - ( F T - bolts ). ê 5 - ú = 0 3 û ë ë 3 û é 14314.86 - 2862.972 x ù é x ù x ù é (882). ê 2 + ú + (3500). [ 1.5 ] - ê ú . ê 5 - ú = 0 ®®® Eqn 3 2 3 û ë ë (5).( x ) + 3.246 x - 16.23 û ë 3 û After trial and error x=1.779993152175” the solution to Eqn3 leads to 0.0000000221, which is approximately equal to zero. Substituting the value for x into equation 2 will lead to FT-bolts= 1700lbs. Tension force on each t-bolt = 1700lbs/2=850lbs. Shear Force per each t-bolt = Vy=3500lbs/2=1750lbs per t-bolt Figure 14.1.7 — Design example – Section View - Force Resultant 382 Figure 14.1.8 — Design example – Plan View Cast-In Anchor Channel Product Guide, Edition 1 • 02/2019 383