Earthbound Welded Anchor Calculations

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2 Earthbound Welded Anchor Calculations Objective: Find a welded anchor to steel beam connection able to handle inch diameter A193B7 Threaded. Calculate the welding requirements for welding a round cylindrical coupler to an existing W Flange in the field to connect a tiedown system run. Use 2.50" diameter weld anchor for this calculation check. Determine Allowable Load Given Diameter Size: Calculate threaded rod capacity in accordance to AISC 13th Edition from a given rod size diameter below. Dia := in ; Provide nominal rod diameter 6 1 n := ρ := ρ = 0.17 in in n ; To calculate rod stress area, define number ("n") of threads UNC for this rod size. π At := ( Dia ρ 4 )2 At = in 2 π Ab := 4 Dia2 Ab = 0.99 in 2 Fu := Fy := psi psi ; Define ultimate and yield strength of threaded rod material. In this case ASTM A193B7. For reference A307 standard strength rod: Fy=43ksi, Fu=60ksi. For reference A193B7 high strength rod: Fy=105ksi, Fu=125ksi. Fnt := 0.75 Fu At ; Equation J3-1 and Table J3-2. Fnt = lbf ; Strength in LRFD T := 0.7 Fnt T = 48359lbf ;Per ASCE 7, we convert LRFD to ASD using 0.7. Analyze Weld Design: A fillet weld can be loaded in any direction in shear, compression, or tension. However, it always fails in shear. The shear failure of the fillet weld occurs along a plane through the throat of the weld, as shown in the Figure below: L a Throat = a x cos45 o = a a Failure Plane Earthbound Corporation 8/5/2013 Page 1

3 Determine Weld Capacity given Weld Thickness and Weld Length for Coupler Connection: Per AISC Table J2-5 for fillet welds, use Equations J-4 for Base Metal check and J2.2a for Weld Calculation. The following segment is taken from AISC th Edition. Ω := 2.00 ; Define Ω (ASD) per AISC 13th Table J2-5 θ := 90 FEXX := 70 ksi ; Define θ and FEXX electrode strength 5 a := 16 in ; Define Fillet Weld Size. Per AISC Table J2.4, if the material thickness of steel beam member is greater than 3/4", use 5/16" Fillet Weld Size. Throat := acos ( 45 ) Throat = in ; Calculate Throat Thickness per Sketch above ( ) Rn := 0.60 FEXX sin( θ) 1.5 Throat Rn = lbf ; Based on 1/4" fillet weld in CouplerDia := 2.5 in ; Define Coupler Diameter WeldLength := π ( CouplerDia + a) WeldLength = in ; Calc Weld Length by using Circumference of Coupler and adding in weld size to approximate circumferential weld length. Rn WeldLength WeldCapacity := WeldCapacity = 61502lbf ; Calc ASD Weld Capacity Ω ; Since WeldCapacity > Tension Force (T), ok to use 5/16" Fillet E70xx for inch diameter weld anchor is OK. Earthbound Corporation 8/5/2013 Page 2

4 Check Base Metal (Coupler) Tensile Strength. Thickness of base metal = (CouplerDia - Dia) / 2 CouplerDia Dia Thickness := Thickness = in 2 π CouplerDia 2 CouplerArea := Area := 4 π Dia 2 4 ; We use Nominal Area to be conservative. TensileArea := CouplerArea Area TensileArea = in 2 Coupler_Fy := Coupler_Fu := 53.7 ksi 63.8 ksi ; Define Properties of AISI 1018 Steel (weldable!) Check Coupler Strength via Equation J4-1: Ω := 1.67 Rn Rn := Coupler_Fy TensileArea CouplerASD := CouplerASD = lbf Ω Check Coupler Strength via Equation J4-2: MinCouplerStrength := 1.25Fy Ab MinCouplerStrength = lbf ; OK > Tension Force (T) ϕ := 0.75 ; Determine Minimum Coupler Strength based upon 125% of threaded rod yield strength (Fy) per ICC AC391. ϕrn := ϕ Coupler_Fu TensileArea ϕrn = lbf ; OK > MinCouplerStrength Earthbound Corporation 8/5/2013 Page 3

5 Calculate Minimum Thread Engagement Length: Coupler thread should be 1.25 times stronger than the rod yield, therefore it is necessary for the shear area of the threaded feature be at least 2.5 times the tensile area. (Assuming the threaded feature is of the identical material). Formula is based on BS EN ISO 898. First we must solve for nominal Stress Area below: D := Dia D = 1.13 in 6 1 n := ρ := ρ = 0.17 in in n ; Reference Diameter from Above and define number ("n") of threads UNC for this rod size. π At := ( 4 D ρ )2 At = in 2 Solve for Engagement Length which is 2.0 times the tensile area: 2.0 At Le := Le = in 0.5 π ( D ρ) Earthbound Corporation 8/5/2013 Page 4

6 Threaded Fastener Strength Ratio: The previous formula for Le was based upon the male and female thread materials have the same strength. If the Female Strength is lower, i.e. J as calculated below is greater than one (1), then the length of engagement must be increased to prevent the female thread stripping. Fy = psi Fy J := J = ; Fy = yield from above. Coupler_Fy Le2 := JLe Le2 = in ; Final min. thread length or height of coupler. Conclusion: We have checked the following four parameters and have shown that we exceed the required tension load of the rod.. T = lbf 1) Weld Strength. 2) Coupler Tension Strength. 3) Thread Engagement. WeldCapacity = lbf Le2 = MinCouplerStrength in = lbf ϕrn = lbf ; We will use a much taller coupler that is much longer than Le2. We will use 1:1 height to width ratio to be conservative. The final weld anchor will be a inch dia x inch tall weld anchor tapped for 1.125" dia rod UNC with 5/16" Fillet E70xx. Anchor height includes measurement allocated to the sight (witness) hole and weld fillet height clearance. Earthbound Corporation 8/5/2013 Page 5