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1Tension Theory Developed by Scott Civjan University of Massachusetts, Amherst

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Tension Members: Chapter D: Tension Member Strength Chapter B: Gross and Net Areas Chapter J: Block Shear Part 5: Design Charts and Tables Tension Spec 13th Ed2

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Gross and Net Areas: Criteria in Table B3.13 Strength criteria in Chapter D: Design of Members for Tension Tension Spec 13th Ed3

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Yield on Gross Area t =0.90 ( c =1.67) Fracture on Effective Net Area t =0.75 ( c =2.00) Block Shear t =0.75 ( c =2.00) 4 Tension Spec 13th Ed

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Yielding on Gross Area A g 5Tension Theory

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P n =F y A g Equation D2-1 Yield on Gross Area t =0.90 ( c =1.67) A g = Gross Area Total cross-sectional area in the plane perpendicular to tensile stresses 6 Tension Spec 13th Ed

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Fracture on Effective Net Area A e 7Tension Theory

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A e = Effective Net Area Accounts for any holes or openings, potential failure planes not perpendicular to the tensile stresses, and effects of shear lag P n =F u A e Equation D2-2 t =0.75 ( c =2.00) Fracture on Effective Net Area 8 Tension Spec 13th Ed

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If holes are included in the cross section less area resists the tension force Fracture on Effective Net Area Bolt holes are larger than the bolt diameter In addition processes of punching or drilling holes can damage the steel around the perimeter 9Tension Theory

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Fracture on Effective Net Area Holes or openings Section D3.2 Account for 1/16 greater than bolt hole size shown in Table J3.3 Accounts for potential damage in fabrication 10 Tension Spec 13th Ed

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A n = Net Area Modify gross area (A g ) to account for the following: Fracture on Effective Net Area Holes or openings Potential failure planes not perpendicular to the tensile stresses 11 Tension Spec 13th Ed

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Design typically uses average stress values Fracture on Effective Net Area This assumption relies on the inherent ductility of steel PuPu Initial stresses will typically include stress concentrations due to higher strains at these locations Highest strain locations yield, then elongate along plastic plateau while adjacent stresses increase with additional strain Eventually at very high strains the ductility of steel results in full yielding of the cross section Therefore average stresses are typically used in design 12Tension Theory

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PuPu Similarly, bolts and surrounding material will yield prior to fracture due to the inherent ductility of steel Therefore assume each bolt transfers equal force Fracture on Effective Net Area 13Tension Theory

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PuPu PuPu PuPu 2/3P u P u /6 PuPu 1/3P u P u /6 PuPu 0 The plate will fail in the line with the highest force (for similar number of bolts in each line) Fracture on Effective Net Area PuPu Cross Section Net area reduced by hole area Each bolt line shown transfers 1/3 of the total force Bolt line 14Tension Theory

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Fracture on Effective Net Area PuPu PuPu 0 1/3 P u 2/3 P u Cross Section Net area reduced by hole area Force in plate Bolt line 1 resists P u in the plate Bolt line 2 resists 2/3P u in the plate Bolt line 3 resists 1/3P u in the plate Bolt line 15Tension Theory The plate will fail in the line with the highest force (for similar number of bolts in each line) Each bolt line shown transfers 1/3 of the total force

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For a plate with a typical bolt pattern the fracture plane is shown Yield on A g would occur along the length of the member Both failure modes depend on cross-sectional areas Fracture on Effective Net Area PuPu Fracture failure across section at lead bolts 16Tension Theory Yield failure (elongation) occurs along the length of the member

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EXAMPLE Tension Spec 13th Ed17

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What if holes are not in a line perpendicular to the load? Additional strength depends on: Geometric length increase Combination of tension and shear stresses Combined effect makes a direct calculation difficult Need to include additional length/Area of failure plane due to non-perpendicular path Fracture on Effective Net Area 18Tension Theory g s PuPu

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Fracture on Effective Net Area Diagonal hole pattern Additional length of failure plane equal to s 2 /4g Section B3.13 and D3.2 s= longitudinal center-to-center spacing of holes (pitch) g= transverse center-to-center spacing between fastener lines (gage) g s PuPu 19 Tension Spec 13th Ed

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Fracture on Effective Net Area A n =Net Area A n =A g -#(d n )t+(s 2 /(4g))t #= number of holes intersected by failure plane d n = corrected hole diameter per B.3-13 t= thickness of tension member Other terms defined on previous slides 20 Tension Spec 13th Ed

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Fracture on Effective Net Area When considering angles When considering angles: Find gage (g) on page 1-46 Workable Gages in Standard Angles unless otherwise noted 21 Tension Spec 13th Ed

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EXAMPLE Tension Spec 13th Ed22

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Accounts for distance required for stresses to distribute from connectors into the full cross section Fracture on Effective Net Area Only a portion of the cross section is connected Connection does not have sufficient length Largest influence when Shear Lag 23Tension Theory

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Shear Lag affects members where: Only a portion of the cross section is connected Connection does not have sufficient length Fracture on Effective Net Area 24Tension Theory

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Fracture on Effective Net Area Distribution of Forces Through Section PuPu l= Length of Connection Section Carrying Tension Forces Fracture Plane 25Tension Theory

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Fracture on Effective Net Area Effective Net Area in Tension Area not Effective in Tension Due to Shear Lag PuPu Shear lag less influential when l is long, or if outstanding leg has minimal area or eccentricity 26Tension Theory

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A e = Effective Net Area Modify net area (A n ) to account for shear lag Fracture on Effective Net Area Or value per Table D3.1 A e = A n UEquation D3-1 U= Shear Lag Factor Reduction = Connection eccentricity l= length where force transfer occurs (distance parallel to applied tension force along bolts or weld) 27 Tension Spec 13th Ed

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A e = Effective Net Area Accounts for any holes or openings, potential failure planes not perpendicular to the tensile stresses, and effects of shear lag P n =F u A e Equation D2-2 t =0.75 ( c =2.00) Fracture on Effective Net Area 28 Tension Spec 13th Ed

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A e =Effective Net Area A n =Net Area A eA n Due to Shear Lag Fracture on Effective Net Area PuPu As the force is transferred from each bolt it spreads through the tension member. This is sometimes called the flow of forces Note that the forces from the left 4 bolts act on the full cross section at the failure plane (bolt line nearest load application) Boundary of force transfer into the plate from each bolt 29Tension Theory

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Fracture on Effective Net Area PuPu At the fracture plane (right bolts) forces have not engaged the entire plate. Fracture Plane Portion of member carrying no tension Effective length of fracture plane 30Tension Theory Now consider a much wider plate

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This concept describes the Whitmore Section Fracture on Effective Net Area PuPu l w = width of Whitmore Section 30 o 31Tension Theory

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EXAMPLE Tension Spec 13th Ed32

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Block Shear 33Tension Theory

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State of Combined Yielding and Fracture Block Shear Failure Planes Failure Tears Out Block of Steel Block Defined by Center Line of Holes Edge of Welds At Least One Each in Tension and Shear 34Tension Theory

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Block Shear Typical Examples in Tension Members Angle Connected on One Leg W-Shape Flange Connection Plate Connection 35Tension Theory

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Block Shear PuPu Angle Bolted to Plate PuPu Tension plane on Angle Shear plane on Plate Tension plane on Plate (Shorter Dimension Controls) Shear plane on Angle 36Tension Theory

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Block Failure from Angle Block Shear PuPu Angle Bolted to Plate Block Failure From Plate PuPu 37Tension Theory

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Block Shear PuPu Tension planes on W-Shape Shear planes on W-Shape First look at the W-Shape, then the plate 38Tension Theory Flange of W-Shape Bolted to Plate

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Block Shear Flange of W-Shape Bolted to Plate PuPu Block Failure in W-Shape First look at the W-Shape, then the plate 39Tension Theory

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Block Shear Flange of W-Shape Bolted to Plate PuPu PuPu Shear planes on Plate Tension plane on Plate Shear planes on Plate Tension planes on Plate 40Tension Theory

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Block Shear PuPu Block Failure in Plate PuPu 41Tension Theory Flange of W-Shape Bolted to Plate

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Block Shear PuPu Angle or Plate Welded to Plate Weld around the perimeter Two Block Shear Failures to Check 42Tension Theory

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Block Shear PuPu PuPu Tension plane on Plate (Shorter Dimension Controls) Shear planes on Plate Tension plane on Plate Shear plane on Plate 43Tension Theory Angle or Plate Welded to Plate

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Block Shear PuPu PuPu Block Failure From Plate 44Tension Theory Angle or Plate Welded to Plate

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Block Shear Block Shear Rupture Strength (Equation J4-5) t =0.75 ( c =2.00) A gv = Gross area subject to shear A nv = Net area subject to shear A nt = Net area subject to tension U bs = 1 or 0.5 (1 for most tension members, see Figure C-J4.2) Smaller of two values will control 45 Tension Spec 13th Ed

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EXAMPLE Tension Spec 13th Ed46

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Bearing at Bolt Holes 47Tension Theory

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Bolts bear into material around hole Direct bearing can deform the bolt hole an excessive amount and be limited by direct bearing capacity 48Tension Theory If the clear space to adjacent hole or edge distance is small, capacity may be limited by tearing out a section of base material at the bolt Bearing at Bolt Holes

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PuPu Bolt 49Tension Theory Bolt induces bearing stresses on the base material

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Bearing at Bolt Holes PuPu Bolt 50Tension Theory Which can result in excessive deformation of the bolt hole

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Bearing at Bolt Holes PuPu Bolt 51Tension Theory When bearing stresses act on bolts that are near the edge of the material (L c dimension is small) LcLc

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Bearing at Bolt Holes PuPu 52Tension Theory A block of material can tear out to the plate edge due to bearing

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Bearing at Bolt Holes PuPu Bolt 53Tension Theory Similarly, when bearing stresses act on bolts that are closely spaced (L c dimension is small) LcLc

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Bearing at Bolt Holes PuPu 54Tension Theory A block of material can tear out between the bolt holes due to bearing stresses

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Bearing at Bolt Holes For standard, oversized and short-slotted hole or long slotted hole with slot parallel to the direction of loading: (Equation J3-6a) t =0.75 ( c =2.00) L c = Clear distance in the direction of force t= thickness of connected material d= nominal bolt diameter F u = Specified minimum tensile strength of the connected material 55 Tension Spec 13th Ed Bearing Limit Tearout Limit

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Bearing at Bolt Holes For the similar case, but when deformation of the bolt hole is not a design consideration: (Equation J3-6b) 56 Tension Spec 13th Ed For long-slotted hole with slot perpendicular to the direction of force: (Equation J3-6c) Other situations have similar design equations:

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