1. Tension Members Structural Elements Subjected to Axial Tensile Forces Cables in Suspension and Cable-Stayed Bridges Trusses Bracing for Buildings and Bridges

2. TENSION MEMBERS - TYPES Wire Ropes and Cables Suspension Bridges, Prestressed Concrete, Guyed towers etc. Strand: wires laid helically about a center Rope: strands laid helically around a central core (fabric or strand) Cable: one or more groups of wires, strands or ropes

3. TENSION MEMBERS - TYPES Rods and Bars Square or Round Rod Difficult to connect to other members Occasional use today - bracing Good practice to produce initial tension to reduce rattling and swaying Bars: Usually rectangular plates eyebars welded bolted Special situations to transfer tensile load from a wire, rope or cable to an assemblage or anchorage

4. Tension Members - Types

5. TENSION MEMBERS - TYPES Structural Shapes & Build Up Members rigidity, small lateral loads, load reversal Slenderness L/r > 300 AISC Spec D1 Does not apply to rods in tension

6. TENSION MEMBERS - LIMIT STATES

8. Limit States STRENGTH Failure at Main Body Failure at Connection etc

9. Tensile Strength Failure in Main Body Failure at Connection AgAg AeAe

10. TENSION MEMBERS - LIMIT STATES AISC Specs Chapter D Failure at main body if connection is strong enough After yielding deformations become too large and member does not serve its design purpose. Failure at yielding nominal strength P n =F y A g F y = Yielding Strength, A g = Gross Area

11. TENSION MEMBERS - LIMIT STATES AISC Specs Chapter D Failure at Connection if connection is weak it will fracture Failure at ultimate strength nominal strength P n =F u A e F u = Ultimate Strength, A e = Effective Area

12. Gross Area – Specs D3.1 p 16.1.27 Gross Area A g : Total Area of Main Body of Member

13. Net Area – Specs D3.2 p 16.1.27 Net Area A n : Welded Connections A n = A g Bolded Connections A n = A g - Area of Holes

14. Net Area Size of hole is larger than size of the bolt d h =d b +1/16” Additional 1/16” of material is damaged during drilling or punchning of holes (Commentary D3.2 p 16.1-250)

15. Net Area – Example (Assume A n =A e ) PL 3/4x10 Bolts  3/4 2 2 3 2 1/4 Based on YieldingBased on Fracture

16. Net Area – Example (Assume A n =A e ) Based on Yielding Based on Fracture LRFD-Design Strength Yielding Fracture ASD-Design Strength Yielding Fracture

17. Net Area – Example (Assume A e =0.85A n ) D=35 kips L=15 kips Investigate Compliance with AISC Specs

18. Net Area – Example (Assume A e =0.85A n ) Based on YieldingBased on Fracture Nominal Strength P n

19. Net Area – Example (Assume A e =0.85A n ) Yielding Fracture LRFD CapacityDemand Yielding Fracture Combination 1 Combination 2 Lowest GOVERNSHighest GOVERNS

20. Net Area – Example (Assume A e =0.85A n ) Yielding Fracture ASD CapacityDemand Yielding Fracture Combination 1 Combination 2 Lowest GOVERNSHighest GOVERNS

21. Staggered Fasteners Space Limitations Geometry Constraints

22. Staggered Fasteners Inclined Fracture Path

23. Net Area - Effect of Staggered Holes AISC Specs D3.1 TT T T Failure paths on net section g s p g = gage s = spacing Reduced diameter

24. Example d=1”

25. Example

26. Smallest w n Controls

27. Example

28. Different failure lines may be subjected to different loads! 11 holes 8/11 of load

29. Net Area - Gage Distance for an Angle Unfold Angle and Visualize as a plate

30. Net Area - Gage Distance for an Angle

31. Example

34. HOMEWORK Study Examples 3.1-3.9 Homework 3.2-1, 3.2-3, 3.4-2, 3.4-4

35. Effective Net Area – Specs D3.3 p 16.1.28 A e =AU A = Area that depends on type of connection U = shear lag coefficient (accounts for eccentricities)