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. Fracture on Effective Net Area ft=0.75 (Wc=2.00)
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=FyAg Equation 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=FuAe Equation 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 Pu
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
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. 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 Pu
1/3Pu
Pu/6 Pu
Pu/6 Pu
2/3Pu
Pu/6 Pu
Net area reduced by hole area Pu
Cross Section
Bolt line 3 2 1
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 1/3Pu in the plate
Force in plate
Net area reduced by hole area Pu
1/3 Pu
2/3 Pu Pu
Cross Section
Bolt line 3 2 1
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 Pu
Fracture failure across section at lead bolts
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 g s Pu
Additional strength depends on:
Geometric length increase
Combination of tension and shear stresses
Combined effect makes a direct calculation difficult
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) g s Pu
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. Shear Lag Fracture on Effective Net Area
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
Effective Net Area in Tension
Area not Effective in Tension Due to Shear Lag Pu
Shear lag less influential when l is long, or if outstanding leg has minimal area or eccentricity
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
Or value per Table D3.1
= Connection eccentricity
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=FuAe Equation 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≠An Due to Shear Lag 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)
Boundary of force transfer into the plate from each bolt
Tension Theory

30. Fracture on Effective Net AreaPu
At the fracture plane (right bolts) forces have not engaged the entire plate.
Now consider a much wider plate
Portion of member carrying no tension
Fracture Plane
Effective length of fracture plane
Describing this in terms of an extremely wide plate in sheet metal, or tin foil, will allow students to intuitively grasp the concept.
Tension Theory

31. Fracture on Effective Net AreaPu
This concept describes the Whitmore Section
lw= width of Whitmore Section
30o
30o
Whitmore Section applies to bolted or welded sections.
Tension Theory

32. EXAMPLE
Tension Spec 13th Ed

33. Block Shear
Tension Theory

34. Failure Tears Out Block of Steel
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. Typical Examples in Tension Members
Block Shear
Typical Examples in Tension Members
Angle Connected on One Leg
W-Shape Flange Connection
Plate Connection
Tension Theory

36. Block Shear Angle Bolted to Plate Shear plane on Angle Pu
Tension plane on Angle
Shear plane on Plate
Tension plane on Plate
(Shorter Dimension Controls)
Shear plane on Angle Pu Pu
Note that angle tension plane goes towards the free edge rather than up into the other leg, as this would be less resistance.
Similarly the Plate would fail vertically towards the closest edge.
Tension Theory

37. Block Shear Angle Bolted to Plate Pu Block Failure from Angle Pu
Block shear could occur on either the angle or the plate – lowest failure mode strength of all controls
Block Failure From Plate
Tension Theory

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

39. Flange of W-Shape Bolted to Plate
Block Shear
Flange of W-Shape Bolted to Plate 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
Flange of W-Shape Bolted to Plate
Shear planes on Plate
Tension plane on Plate
Tension planes on Plate Pu Pu
Here 2 possible plate block shear modes could occur, the lower strength would control.
Tension Theory

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

42. Angle or Plate Welded to Plate
Block Shear
Angle or Plate Welded to Plate Pu
Weld around the perimeter
Two possible block shear failures can be described by the perimeter of the welds – that with the lower strength would control.
Two Block Shear Failures to Check
Tension Theory

43. Angle or Plate Welded to Plate
Block Shear
Angle or Plate Welded to Plate
Tension plane on Plate
(Shorter Dimension Controls)
Shear planes on Plate
Shear plane on Plate Pu Pu
Two possible block shear failures can be described by the perimeter of the welds – that with the lower strength would control.
Tension Theory

44. Angle or Plate Welded to Plate
Block Shear
Angle or Plate Welded to Plate Pu
Block Failure From Plate Pu
Two possible block shear failures can be described by the perimeter of the welds – that with the lower strength would control.
Tension Theory

45. Block Shear
Block Shear Rupture Strength (Equation J4-5)
Smaller of two values will control
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. Bolts bear into material around hole
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

51. Bearing at Bolt Holes Lc Bolt Pu
When bearing stresses act on bolts that are near the edge of the material (Lc dimension is small)
Tension Theory

52. Bearing at Bolt Holes Pu
A block of material can tear out to the plate edge due to bearing
Note, this is differentiated from block shear since there is no tension plane for the failure.
Tension Theory

53. Bearing at Bolt Holes Lc Bolt Pu
Similarly, when bearing stresses act on bolts that are closely spaced (Lc dimension is small)
Tension Theory

54. Bearing at Bolt Holes Pu
A block of material can tear out between the bolt holes due to bearing stresses
Note, this is differentiated from block shear since there is no tension plane for the failure.
Tension Theory

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

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