Teaching Modules for Steel Instruction

1. Teaching Modules for Steel Instruction Tension Member THEORY SLIDES Developed by Scott Civjan University of Massachusetts, Amherst Tension Theory

2. 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 Ed

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

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

5. Yielding on Gross Area Ag Tension Theory

6. Yield on Gross Area Pn=FyAgEquation D2-1 ft=0.90 (Wc=1.67) Ag= Gross Area Total cross-sectional area in the plane perpendicular to tensile stresses Tension Spec 13th Ed

7. Fracture on Effective Net Area Ae Tension Theory

8. Fracture on Effective Net Area Pn=FuAeEquation D2-2 ft=0.75 (Wc=2.00) Ae= Effective Net Area Accounts for any holes or openings, potential failure planes not perpendicular to the tensile stresses, and effects of shear lag Tension Spec 13th Ed

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

10. 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 Tension Spec 13th Ed

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

12. Fracture on Effective Net Area Design typically uses average stress values This assumption relies on the inherent ductility of steel 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 Pu Therefore average stresses are typically used in design Eventually at very high strains the ductility of steel results in full yielding of the cross section Tension Theory

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

14. Pu/6 Pu/6 Pu/6 Pu/6 0 Fracture on Effective Net Area Pu/6 Pu/6 Pu/6 Pu/6 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 Pu/6 Pu/6 Pu Pu Pu Pu 1/3Pu 2/3Pu Pu Pu/6 Pu/6 Net area reduced by hole area Pu Cross Section 3 1 Bolt line 2 Tension Theory

15. Fracture on Effective Net Area 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 Bolt line 1 resists Pu in the plate Bolt line 2 resists 2/3Pu in the plate Bolt line 3 resists 1/3Puin the plate Force in plate Net area reduced by hole area Pu 1/3 Pu 2/3 Pu 0 Pu Cross Section 3 1 Bolt line 2 Tension Theory

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

17. EXAMPLE Tension Spec 13th Ed

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

19. Fracture on Effective Net Area Diagonal hole pattern Additional length of failure plane equal to s2/4g 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) Pu g s Tension Spec 13th Ed

20. Fracture on Effective Net Area An=Net Area An=Ag-#(dn)t+(s2/(4g))t #= number of holes intersected by failure plane dn= corrected hole diameter per B.3-13 t= thickness of tension member Other terms defined on previous slides Tension Spec 13th Ed

21. 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 Tension Spec 13th Ed

22. EXAMPLE Tension Spec 13th Ed

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

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

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

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

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

28. Fracture on Effective Net Area Pn=FuAeEquation D2-2 ft=0.75 (Wc=2.00) Ae= Effective Net Area Accounts for any holes or openings, potential failure planes not perpendicular to the tensile stresses, and effects of shear lag Tension Spec 13th Ed

29. Fracture on Effective Net Area Ae=Effective Net Area An=Net Area Ae≠AnDue to Shear Lag Boundary of force transfer into the plate from each bolt Pu 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) Tension Theory

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

31. Fracture on Effective Net Area This concept describes the Whitmore Section 30o lw= width of Whitmore Section 30o Pu Tension Theory

32. EXAMPLE Tension Spec 13th Ed

33. Block Shear Tension Theory

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

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

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

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

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

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

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

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

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

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

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

45. Block Shear Smaller of two values will control Block Shear Rupture Strength (Equation J4-5) ft=0.75 (Wc=2.00) Agv= Gross area subject to shear Anv= Net area subject to shear Ant= Net area subject to tension Ubs= 1 or 0.5 (1 for most tension members, see Figure C-J4.2) Tension Spec 13th Ed

46. EXAMPLE Tension Spec 13th Ed

47. Bearing at Bolt Holes Tension Theory

48. Bearing at Bolt Holes Bolts bear into material around hole Direct bearing can deform the bolt hole an excessive amount and be limited by direct bearing capacity 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 Tension Theory

49. Bearing at Bolt Holes Bolt Pu Bolt induces bearing stresses on the base material Tension Theory

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