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

Gross Area – Specs D3.1 p 16.1.27 Last Time Gross Area Ag: Total Area of Main Body of Member

Net Area – Specs D3.2 p 16.1.27 Last Time Net Area An : Welded Connections An = Ag Bolded Connections An = Ag - Area of Holes

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

Staggered Fasteners Last Time Geometry Constraints Space Limitations

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

Net Area - Gage Distance for an Angle Last Time For holes on different legs

Effective Net Area – Specs D3.3 p 16.1.28 Last Time Ae=AU A = Area that depends on type of connection A=Ag for welded A=An for bolted U = shear lag coefficient (accounts for eccentricities)

Shear Lag Factor Last Time General category for any type of tension member except plates and round HSS with Plates Round HSS with Alternative values for single angles Alternative values for W,M,S and HP shapes

l Length of the connection 1. General category for any type of tension member except plates and round HSS with Last Time Distance from centroid of connected area to the plane of the connection l Length of the connection

1. General category for any type of tension member except plates and round HSS with Last Time

1. General category for any type of tension member except plates and round HSS with Last Time

a. Longitudinal welds on sides only 2. Plates Last Time U=1.0 since cross section has one element and it is connected Special Cases a. Longitudinal welds on sides only

b. Transverse welds only (uncommon) 2. Plates Last Time U=1.0 since cross section has one element and it is connected Special Cases b. Transverse welds only (uncommon) An net area of directly connected members

3. Round HSS with Last Time

4. Alternative values for single angles Last Time 2 or 3 fasteners in direction of loading 4 fasteners in direction of loading

5. Alternative values for W,M,S and HP shapes Last Time Connected through flange with 3 or more fasteners in direction of loading

5. Alternative values for W,M,S and HP shapes Last Time Connected through flange with 3 or more fasteners in direction of loading

5. Alternative values for W,M,S and HP shapes Last Time Connected through web with 4 or more fasteners in direction of loading

Block Shear Last Time

Block Shear Chapter D User Note -> J4.3 (p. 16.1-112) Last Time Anv: net shear area Ant : net tension area For angles and gusset plates

Block Shear Chapter D User Note -> J4.3 (p. 16.1-112) Last Time Anv: net shear area Ant : net tension area AISC Ubs=1 for angles, gusset plates and most coped beams See AISC Commentary J4.3 for other less common cases

Design of Tension Members Tables for the Design TODAY Design of Tension Members Tables for the Design Threaded Rods and Cables

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 ASD etc max ASD min

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

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

Step 1: Required Strength LRFD - 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

Step 3: Plate Selection based on Ag LRFD - 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

OK LRFD - 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

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

Step 1: Required Strength ASD - 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

Step 3: Plate Selection based on Ag - Same as LRFD ASD - 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 - Same as LRFD Try thickness t = 1 in Choose PL 1 X 3-1/2 See Manual pp1-8 for availability of plate products

OK ASD - 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

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

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

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

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

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

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

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

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

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

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

TABLES FOR DESIGN OF TENSION MEMBERS

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

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

NG Angle - Example Step 3: Check Effective Area Length of connection not known 4 – bolts in direction of load U=0.8 NG

Angle - Example Shape did not work because table values are for Ae/Ag=0.75 In this problem Ae/Ag=3.1/4.75 = 0.6526 Enter table with adjusted Pu as

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

OK Angle - Example Step 5: Check Effective Area Length of connection not known 4 – bolts in direction of load U=0.8 OK

HOMEWORK 3.6-3 3.6-6 3.8-1