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

2. Design of Tension Members Tables for the Design
LAST TIME
Design of Tension Members
Tables for the Design
Threaded Rods and Cables

3. Design of Tension Members
Objective
Find a member with adequate gross and net areas
Find a member that satisfies L/r<300
Does not apply to cables and rods
Available Strength
(Nominal Resistance)
Required Strength
LRFD
max
LRFD
min

4. Design of Tension Members
Determine required Area
To prevent yielding
To avoid fracture
Yielding controls if

5. Step 1: Required Strength
Example
Tension member with a length 5’-9” resists D=18 kips and L=52 kips
Select a member with rectangular cross section, A36 steel and one line 7/8” bolts
Step 1: Required Strength
Step 2: Required Areas

6. Step 3: Plate Selection based on Ag
Example
Tension member with a length 5’-9” resists D=18 kips and L=52 kips
Select a member with rectangular cross section, A36 steel and one line 7/8” bolts
Step 3: Plate Selection based on Ag
Try thickness t = 1 in
Choose PL 1 X 3-1/2
See Manual pp1-8 for availability of plate products

7. OK Example Step 4: Check Effective Area
Tension member with a length 5’-9” resists D=18 kips and L=52 kips
Select a member with rectangular cross section, A36 steel and one line 7/8” bolts
Step 4: Check Effective Area OK

8. OK Example Step 4: Check Slenderness
Tension member with a length 5’-9” resists D=18 kips and L=52 kips
Select a member with rectangular cross section, A36 steel and one line 7/8” bolts
Step 4: Check Slenderness OK

9. OK LRFD - Example Step 4: Check Slenderness
Tension member with a length 5’-9” resists D=18 kips and L=52 kips
Select a member with rectangular cross section, A36 steel and one line 7/8” bolts
Step 4: Check Slenderness OK

10. Angles as Tension Members
Must have enough room for bolts
(if bolted connection)
Space is a problem if 2 lines of bolts in a leg
Usual fabrication practice – standard hole location
Manual pp 1-46
Leg 8 7 6 5 4
31/2 3
2-1/2 2
1-3/4
1-1/2
1-3/8
1-1/4 1 g
4-1/2
3-1/2
1-1/8
7/8
3/4
5/8 g1
2-1/4 g2

11. Example
Select and unequal-leg angle tension member 15 feet long to resist a service dead load of 35 kips and a service live load of 70 kips. Use A36

12. Step 1: Required Strength
Angle - Example
Step 1: Required Strength
Step 2: Required Areas

13. Step 3: Angle Selection based on Ag
Angle - Example
Step 3: Angle Selection based on Ag
Two lines of bolts, therefore min. length of one leg = 5 in
see table
Choose L6x4x1/2 A=4.75, rmin=0.864
See Manual pp1-42

14. NG Angle - Example Step 4: Check Effective Area
Length of connection not known
4 – bolts in direction of load U=0.85 NG

15. Step 3: Angle Selection based on Ag – TRY NEXT LARGER
Angle - Example
Step 3: Angle Selection based on Ag – TRY NEXT LARGER
Two lines of bolts, therefore min. length of one leg = 5 in
see table
Choose L5 x 3-1/2 x 5/8 A=4.92, rmin=0.746
See Manual pp1-42

16. NG Angle - Example Step 4: Check Effective Area
Length of connection not known
4 – bolts in direction of load U=0.8 NG

17. Step 3: Angle Selection based on Ag – TRY NEXT LARGER
Angle - Example
Step 3: Angle Selection based on Ag – TRY NEXT LARGER
Two lines of bolts, therefore min. length of one leg = 5 in
see table
Choose L8 x 4 x 1/2 A=5.75, rmin=0.863
See Manual pp1-42

18. OK Angle - Example Step 4: Check Effective Area
Length of connection not known
4 – bolts in direction of load U=0.8 OK

19. TABLES FOR DESIGN OF TENSION MEMBERS

20. Example
Select and unequal-leg angle tension member 15 feet long to resist a service dead load of 35 kips and a service live load of 70 kips. Use A36

21. Step 1: Required Strength Step 2: Choose L based on Pu
Example – Using Tables
Step 1: Required Strength
Step 2: Choose L based on Pu
Choose L6x4x1/2
A=4.75, rmin=0.980
See Manual pp 5-15

22. NG Angle - Example Step 3: Check Effective Area
Length of connection not known
4 – bolts in direction of load U=0.85 NG

23. Angle - Example
Shape did not work because table values are for Ae/Ag=0.75
In this problem Ae/Ag=3.29/4.75 = 0.693
Enter table with adjusted Pu as

24. Example – Using Tables
Step 4: Choose L based on ADJUSTED Pu
Choose L8x4x1/2
A=5.75, rmin=0.863
See Manual pp 5-14

25. OK Angle - Example Step 5: Check Effective Area
Length of connection not known
4 – bolts in direction of load U=0.85 OK

26. Tension Members in Roof Trusses
Main supporting elements of roof systems where long spans are required
Used when the cost and weight of a beam would be prohibitive
Often used in industrial or mill buildings

27. Tension Members in Roof Trussed
Pin
Hinge
Supporting walls: reinforced concrete, concrete block, brick or combination

28. Tension Members in Roof Trussed

29. Tension Members in Roof Trusses
Sag Rods are designed to provide lateral support to purlins and carry the component of the load parallel to the roof
Located at mid-point, third points, or more frequently

30. Tension Members in Roof Trusses
Bottom Chord in tension
Top Chord in compression
Web members: some in compression some in tension
Wind loads may alternate force in some members

31. Tension Members in Roof Trusses
Chord Members are designed as continuous
Joint rigidity introduces small moments that are usually ignored
Bending caused by loads applied directly on members must be taken into account

32. Tension Members in Roof Trusses
Working Lines Intersect at the Working Point in each joint
Bolted Truss: Working Lines are the bolt lines
Welded Truss: Working Lines are the centroidal axes of the welds
For analysis: Member length from working point to working point

33. Tension Members in Roof Trusses
Bolted trusses
Double Angles for chords
Double Angles for web members
Single Gusset plate

34. Tension Members in Roof Trusses
Welded trusses
Structural Tee shapes are used in chords
Angles are used in web members
Angles are usually welded to the stem of the Tee

35. Tension Members in Roof Trusses
Welded trusses
Structural Tee shapes are used in chords
Angles are used in web members
Angles are usually welded to the stem of the Tee

36. Example
Select a structural Tee for the bottom chord of the Warren roof truss. Trusses are welded and spaced at 20 feet. Assume bottom chord connection is made with 9-inch long longitudinal welds at the flange. Use A992 steel and the following load data (wind is not considered)
Purlins M8x6.5
Snow 20 psf horizontal projection
Metal Deck 2 psf
Roofing 4 psf
Insulation 3 psf

37. Step 1 – Load Analysis 20ft 180(2.5)=450 lb 180(5)=900 lb ……
DEAD (excluding purlins)
Deck 2 psf
Roof 4 psf
Insulation 3 psf
Total 9 psf
Total Dead Load = 9(20) = 180 lb/ft
20ft
180(2.5)=450 lb
180(5)=900 lb ……

38. Step 1 – Load Analysis 20ft 130 lb 130 lb …… PURLINS M8x6.5
Purlin Load = 6.5(20) = 130 lb
20ft
130 lb
130 lb ……

39. Step 1 – Load Analysis 20ft 400(2.5)=1000 lb 400(5)=2000 lb …… SNOW
Snow Load = 20(20) = 400 lb/ft
20ft
400(2.5)=1000 lb
400(5)=2000 lb ……

40. Interior Joint 0.1(900+130+2000)=303 lb
Step 1 – Load Analysis
Dead Load of Truss
Assume 10% of all other loads
End Joint 0.1(9(20)(20) )=158 lb
Interior Joint 0.1( )=303 lb
158 lb
303 lb ……

41. Step 1 – Load Analysis
= 738 lb
= 1333 lb …… D
1000 lb
2000 lb S

42. Step 2 – Required Force
1.2(0.74) + 1.6(1) =
2.48 kips
1.2(1.33)+1.6(2)=
4.8 kips ……

43. Step 2 – Required Force
Method of Sections

44. Step 3 – Required Areas

45. Step 4: T Selection based on Ag
Choose MT5x A=1.10 in2
See Manual pp1-68

46. Step 5 Check Effective AreaNG

47. Step 6 TRY NEXT LARGER
Choose MT6X5 A=1.46 in2
See Manual pp1-68

48. Step 7 Check Effective AreaOK

49. Step 8 – Check Slenderness
Assume bracing points at panel points OK