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**Design of Tension Members**

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

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**Design of Tension Members Tables for the Design **

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

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**Design of Tension Members LAST TIME**

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

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**Design of Tension Members LAST TIME**

Determine required Area LRFD To prevent yielding To avoid fracture Yielding controls if

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**Design of Tension Members LAST TIME**

Determine required Area ASD To prevent yielding To avoid fracture Yielding controls if

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**LRFD - Example LAST TIME**

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

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**LRFD - Example LAST TIME**

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

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**LRFD - Example LAST TIME**

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

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**LRFD - Example LAST TIME**

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

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**Step 1: Required Strength**

ASD - Example LAST TIME 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

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**Step 3: Plate Selection based on Ag - Same as LRFD**

ASD - Example LAST TIME 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

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**OK ASD - Example LAST TIME 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

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**LRFD - Example LAST TIME**

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

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**Angles as Tension Members LAST TIME**

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

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Example LAST TIME 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

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**Angle - Example LAST TIME**

Step 1: Required Strength Step 2: Required Areas

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**Angle - Example LAST TIME**

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

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**Angle - Example LAST TIME**

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

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**Angle - Example LAST TIME**

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

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**Angle - Example LAST TIME**

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

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**Angle - Example LAST TIME**

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

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**Angle - Example LAST TIME**

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

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**TABLES FOR DESIGN OF TENSION MEMBERS**

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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

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**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

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**NG Angle - Example Step 3: Check Effective Area**

Length of connection not known 4 – bolts in direction of load U=0.8 NG

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

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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

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**OK Angle - Example Step 5: Check Effective Area**

Length of connection not known 4 – bolts in direction of load U=0.8 OK

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**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

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**Tension Members in Roof Trussed**

Pin Hinge Supporting walls: reinforced concrete, concrete block, brick or combination

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**Tension Members in Roof Trussed**

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**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

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**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

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**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

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**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

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**Tension Members in Roof Trusses**

Bolted trusses Double Angles for chords Double Angles for web members Single Gusset plate

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**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

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**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

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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

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**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 ……

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**Step 1 – Load Analysis 20ft 130 lb 130 lb …… PURLINS M8x6.5**

Purlin Load = 6.5(20) = 130 lb 20ft 130 lb 130 lb ……

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**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 ……

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**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 ……

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

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

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Step 2 – Required Force Method of Sections

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Step 3 – Required Areas

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**Step 4: T Selection based on Ag**

Choose MT5x A=1.10 in2 See Manual pp1-68

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**Step 5 Check Effective Area**

NG

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

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**Step 7 Check Effective Area**

OK

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**Step 8 – Check Slenderness**

Assume bracing points at panel points OK

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