1. LRFD-Steel Design Dr. Ali Tayeh Second Semester 2010- 2011

2. Steel Design Dr. Ali I. Tayeh Chapter 3 Tension Members “Part B”

3. Tension Members EFFECTIVE AREA : Of the several factors influencing the performance of a tension member, the manner in which is connected is the most important. ◦ Connections almost always weakens the member. ◦ the measure of joints influence is called the joint efficiency ◦ Joint efficiency is a function of the ductility of the material. fastener spacing. stress concentration, and a phenomenon known as "shear lag ". ◦ Shear lag occurs when some elements of the cross section are not connected. ◦ The consequence of the partial connection is that the connected element become loaded and the unconnected part is not fully stressed. ◦ Shear lag be accounted for by using a reduced, or effective. net area because shear lag affects both bolted and welded connections. the effective net area concept applies to both types of connections.

4. Tension Members EFFECTIVE AREA : ◦ For bolted connections, the effective net area. ◦ For welded connections, the effective net area. ◦ Where the reduction factor U is given by ◦ x is the distance from centroid of the connected area to the plane of connection ◦ L is the length of the connection. ◦ For bolted connection : it is measured from the center of the bolt at one end of the connection to the center of the bolt at the other end ◦ For welded connection : it is measured from one end of the end ◦ The longest segment is used if there are segments of different length in the direction of load.

5. Tension Members EFFECTIVE AREA :

6. Tension Members EFFECTIVE AREA : Bolted

7. Welded Tension Members

8. EFFECTIVE AREA : ◦ For Bolted connection: These average value of U classified to two groups:  Values for two fasteners per line in the direction of the applied load.  Values for three fasteners and more per line in the direction of the applied load. ◦ Where the reduction factor U is given by U=0.90  For W, M, and S shapes that have a width to depth ratio of at least 2/3 (and tee shapes cut from them) and are concreted through the flange with at least three fastener per line in the direction of applied load. U=0.85  For all other shape (including built up shapes) with at least three fastener per line. U=0.75  For all member with only two fastener per line.

9. Tension Members EFFECTIVE AREA : ◦ For welded connection: These average value of U :  Where the reduction factor U is given by U=0.90  For W, M, and S shapes that have a width to depth ratio of at least 2/3 (and tee shapes cut from them) and are concreted through the flange with at least three fastener per line in the direction of applied load. U=0.85  For all other shape

10. Tension Members

13. Example 3.4: Determine the effective net area for the tension member shown bellow

14. Tension Members A

15. Example 3.4 cont.: for L6× 6×½

16. Tension Members Example 3.4 cont.: Because this shape is not a W, M, S, or tee and has more than two bolts in the direction of load

17. Tension Members Example 3.5 : if the tension member of this example is welded as shown, Find the effective area

18. Tension Members

19. Failure due to Staggered Holes Staggered fasteners : When a member has staggered bolt holes, a different approach to finding Ae for the fracture limit state is taken. This is because the effective net area (t x w n ) is different as the line of fracture changes due to the stagger in the holes. The test for the yielding limit state remains unchanged (the gross area is still the same). The net width now must account for the change in direction of the line of fracture. First, look at different ways a tension member with staggered holes can fracture. These pictures depict the different lines of failure. When analyzing a member like this, it is important to find all the lines of failure and then determine which line of failure is the weakest cross section. That cross section will be taken as the net width, w n.

22. Tension members Staggered fasteners : ◦ Reduced diameter ◦ Where d: Hole diameter S : Stagger. g: Gage transverse spacing ◦ The net width in the failure line ◦ Where ◦ W n the net width ◦ W g the gross width

23. Tension Members Compute the smallest net area for the plate shown. The holes are for 1-inch- diameter bolts.

24. Tension Members

25. Tension members Block Shear : For tension: A nt and A gt : the net and gross areas along the tension surface bc. F u A nt : the nominal strength in tension for fracture. F y A gt : the nominal strength in tension for yielding. For shear: A nv and A gv : the net and gross areas along the shear surface ba. 0.6 F u A nv : the nominal strength in shear for fracture. 0.6 F y A gv : the nominal strength in shear for yielding.

26. Tension members Block Shear : There are two failure modes: For shear yield and tension fracture the design strength : For shear fracture and tension yield the design strength : In both cases

27. Tension members Block Shear : The block shear strength is given as following:

28. Tension members Block Shear : Example 3.10: check the block-shear design strength of the tension member, the holes are 7/8 inch-diameter, and A36 steel is used.

29. Tension members Block Shear : Example 3.10 Cont.:

30. Tension members Design of tension members : The sum of factored loads not exceed the member strength; that is: For tension members: ◦ To prevent yielding: ◦ To avoid fracture: Radius of gyration

31. Tension members Example 3.11

32. Tension members

33. H.W (2) ONLY Choose 5 questions ONLY from the following questions: Question (1)

34. Question (2)

35. Question (3) For each of the cases shown in Figure P3.3-2, compute the effective area two ways: 1.Use the AI5C Specification equation for U. 2.Use the average value of U as given in the Commentary to the Specification.

36. Question (4)

37. Question (5) Select a single-angle tension member of A36 steel to resist the following service loads: dead load =:50 kips, live load =: 100 kips, and wind load =:45 kips. The member will be connected through one leg with l-inch- diameter bolts in two lines. There will be at least three bolts in each line. The member length is 20 feet.

38. Question (6) Use A36 steel and select a double-angle tension member to resist a service dead load of 20 kips and a service live load of 60 kips. Assume that the member will be connected with a single line of three or more 7/R-inch-diameter bolts to a %-inch-thick gusset plate. The member is 15 feet long.

39. Question (7) What size threaded rod is required for member AB in Figure P3.7-2 The given load is a service live load. (Neglect the weight of member CB.) Use A36 steel.