Teaching Modules for Steel Instruction TENSION MEMBER Design

Name: Teaching Modules for Steel Instruction TENSION MEMBER Design
Uploaded: 2017-08-02T16:17:17+00:00
Duration: PTM36S54
Channel: Alfred Hart
Description: Teaching Modules for Steel Instruction TENSION MEMBER Design

Teaching Modules for Steel Instruction TENSION MEMBER Design
Developed by Scott Civjan University of Massachusetts, Amherst

Structural member subjected to tensile axial load.
P TENSION MEMBER: Structural member subjected to tensile axial load. Typically hangers, braces, truss members. Also components of connections and other members. Tension Module

Strength design requirements: Pu  Pn (Pa  Pn/Ω)ASD
Where  varies depending on failure mode. Tension Module

Strength Limit States: Yielding on Gross Area Rupture on Net Area
Tensile Strength Strength Limit States: Yielding on Gross Area Rupture on Net Area Block Shear Bearing or Tear-out at Bolts Each of these failure modes will be evaluated individually. The lowest strength will control design strength. Tension Module

Yielding on Gross Area, Ag
Tension Theory

Yield on Gross Area When a member is loaded the strength is limited by the yielding of the entire cross section. P=FyA L0 Note that residual stress does not affect tension member strength, as ultimate load is not affected and loss of stiffness is not a major factor in tension (as opposed to compression where buckling failure modes are affected). eyL0 D Tension Theory

Yield on Gross Area When a member is loaded the strength is limited by the yielding of the entire cross section. P P=FyA D L Note that residual stress does not affect tension member strength, as ultimate load is not affected and loss of stiffness is not a major factor in tension (as opposed to compression where buckling failure modes are affected). P eyL0 D Tension Theory

Yield on Gross Area However, consider how this is affected by the stress-strain conditions. Consider L0=100 inch long tension member. Tension Theory

Yield on Gross Area Stress eu .1 to .2 Strain Fu Esh Fy E ey
er .2 to .3 Strain Tension Theory 9

Yield on Gross Area Stress Δy = 0.0015(100) = 0.15” eu .1 to .2 Strain
Fu Stress Esh Fy Δy = (100) = 0.15” E eu .1 to .2 ey .001 to .002 esh .01 to .03 eu .1 to .2 er .2 to .3 Strain Tension Theory 10

Yield on Gross Area Stress Δsh = 0.02(100) = 2”
Fu Stress Esh Fy Δsh = 0.02(100) = 2” Δy = (100) = 0.15” E eu .1 to .2 ey .001 to .002 esh .01 to .03 eu .1 to .2 er .2 to .3 Strain Tension Theory 11

Yield on Gross Area Δu = 0.15(100) = 15” Stress Δsh = 0.02(100) = 2”
Fu Stress Esh Fy Δsh = 0.02(100) = 2” Δy = (100) = 0.15” E eu .1 to .2 ey .001 to .002 esh .01 to .03 eu .1 to .2 er .2 to .3 Strain Tension Theory 12

Yield on Gross Area Consider L0 = 100 inch long tension member.
ΔYield = approx (100) = 0.172” ΔOnset of Strain Hardening = approx. 0.02(100) = 2” ΔPeak Load = approx. 0.15(100) = 15” Excessive deformations defines “Failure” for tension member yielding. Limit to FyAg. Tension Theory

Rupture on Effective Net Area, Ae
Tension Theory

Rupture on Effective Net Area
If holes are included in the cross section less area resists the tension force. Bolt holes are larger than the bolt diameter. In addition, processes of punching holes can damage the steel around the perimeter. Tension Theory

Design typically uses average stress values. This assumption relies on the inherent ductility of steel. Pn Tension Theory

Design typically uses average stress values. This assumption relies on the inherent ductility of steel. Initial stresses will typically include stress concentrations due to higher strains at these locations. Pn Tension Theory 17 17

Design typically uses average stress values. This assumption relies on the inherent ductility of steel. Highest strain locations yield, then elongate along plastic plateau while adjacent stresses increase with additional strain. Pn Tension Theory 18 18

Design typically uses average stress values. This assumption relies on the inherent ductility of steel. Pn Eventually at very high strains the ductility of steel results in full yielding of the cross section. Tension Theory 19 19

Design typically uses average stress values. This assumption relies on the inherent ductility of steel. Pn Therefore average stresses are typically used in design. Tension Theory 20 20

Similarly, bolts and surrounding material will yield prior to rupture due to the inherent ductility of steel. Therefore assume each bolt transfers equal force . Pn Tension Theory 21 21

Shear Lag affects members where: Only a portion of the cross section is connected, Connection does not have sufficient length. Tension Theory

The plate will fail in the line with the highest force (for similar number of bolts in each line). Each bolt line shown transfers 1/3 of the total force. Net area reduced by hole area Pn Cross Section Bolt line 3 2 1 Tension Theory 23 23

The plate will fail in the line with the highest force (for similar number of bolts in each line). Each bolt line shown transfers 1/3 of the total force. Pn Pn Net area reduced by hole area Pn Cross Section Bolt line 3 2 1 Tension Theory 24 24

The plate will fail in the line with the highest force (for similar number of bolts in each line). Each bolt line shown transfers 1/3 of the total force. Pn/6 Pn 2/3Pn Pn/6 Net area reduced by hole area Pn Cross Section Bolt line 3 2 1 Tension Theory 25 25

The plate will fail in the line with the highest force (for similar number of bolts in each line). Each bolt line shown transfers 1/3 of the total force. Pn/6 Pn/6 Pu Pn 1/3Pn Pn/6 Pn/6 Net area reduced by hole area Pn Cross Section Bolt line 3 2 1 Tension Theory 26 26

The plate will fail in the line with the highest force (for similar number of bolts in each line). Each bolt line shown transfers 1/3 of the total force. Pn Pn/6 Net area reduced by hole area Pn Cross Section Bolt line 3 2 1 Tension Theory 27 27

The plate will fail in the line with the highest force (for similar number of bolts in each line). Each bolt line shown transfers 1/3 of the total force. Bolt line 1 resists Pn in the plate. Bolt line 2 resists 2/3Pn in the plate. Bolt line 3 resists 1/3Pn in the plate. Force in plate Net area reduced by hole area Pn 1/3 Pn 2/3 Pn Pn Cross Section Bolt line 3 2 1 Tension Theory

Consider how this is affected by the stress-strain conditions. Consider L0=1 inch diameter holes. 1 inch Pn Tension Theory

Fu Stress Esh Fy E eu .1 to .2 ey .001 to .002 esh .01 to .03 eu .1 to .2 er .2 to .3 Strain Tension Theory 30

Fu Stress Esh Fy = 50 ksi Δ = (1) = ” E eu .1 to .2 ey .001 to .002 esh .01 to .03 eu .1 to .2 er .2 to .3 Strain Tension Theory 31

Fu Stress Esh Fy Δ = 0.02(1) = 0.02” Δ = (1) = ” E eu .1 to .2 ey .001 to .002 esh .01 to .03 eu .1 to .2 er .2 to .3 Strain Tension Theory 32

Fu Stress Esh Fy Δsh = 0.02(1) = 0.02” Δy = (1) = ” E eu .1 to .2 ey .001 to .002 esh .01 to .03 eu .1 to .2 er .2 to .3 Strain Tension Theory 33

Consider L0=1 inch hole diameter. ΔYield = approx (1) = ” ΔOnset of Strain Hardening = approx. 0.02(1) = 0.02” ΔPeak Load = approx. 0.15(1) = 0.15” Failure at net area can achieve Fu so long as ductility is available. Tension Theory 34 34

For a plate with a typical bolt pattern the rupture plane is shown. Yield on Ag would occur along the length of the member. Both failure modes depend on cross-sectional areas. Rupture failure across section at lead bolts. Pn Yield failure (elongation) occurs along the length of the member. Tension Theory

What if holes are not in a line perpendicular to the load? Need to include additional length/area of failure plane due to non-perpendicular path. Pn g s Additional strength depends on: Geometric length increase Combination of tension and shear stresses Combined effect makes a direct calculation difficult. Tension Theory

Boundary of force transfer into the plate from each bolt. Pn As the force is transferred from each bolt it spreads through the tension member. This is sometimes called the “flow of forces” Note that the forces from the left 4 bolts act on the full cross section at the failure plane (bolt line nearest load application). Tension Theory

Now consider a much wider plate. Pn Describing this in terms of an extremely wide plate in sheet metal, or tin foil, will allow students to intuitively grasp the concept. At the rupture plane (right bolts) forces have not engaged the entire plate. Tension Theory

Now consider a much wider plate. Rupture Plane Pn Describing this in terms of an extremely wide plate in sheet metal, or tin foil, will allow students to intuitively grasp the concept. At rupture plane (right bolts) forces have not engaged the entire plate. Tension Theory 39 39

Now consider a much wider plate. Rupture Plane Portion of member carrying no tension. Pn Describing this in terms of an extremely wide plate in sheet metal, or tin foil, will allow students to intuitively grasp the concept. At the rupture plane (right bolts) forces have not engaged the entire plate. Tension Theory 40 40

Now consider a much wider plate. Rupture Plane Portion of member carrying no tension. Pn Effective length of rupture plane Describing this in terms of an extremely wide plate in sheet metal, or tin foil, will allow students to intuitively grasp the concept. At the rupture plane (right bolts) forces have not engaged the entire plate. Tension Theory 41 41

This concept describes the Whitmore Section. 30o Pn lw= width of Whitmore Section 30o Describing this in terms of an extremely wide plate in sheet metal, or tin foil, will allow students to intuitively grasp the concept. Tension Theory 42 42

Shear Lag Accounts for distance required for stresses to distribute from connectors into the full cross section. Largest influence when Only a portion of the cross section is connected. Connection does not have sufficient length. Tension Theory

Shear Lag Ae = Effective Net Area An = Net Area Ae ≠ An Due to Shear Lag Tension Theory 44 44

Pn l= Length of Connection Tension Theory 45 45

Pn Rupture Plane l= Length of Connection Tension Theory 46 46

Pn Distribution of Forces Through Section RupturePlane l= Length of Connection Tension Theory 47 47

Section Carrying Tension Forces Pn Distribution of Forces Through Section RupturePlane l= Length of Connection Tension Theory 48 48

Pn Area not Effective in Tension Due to Shear Lag Shear lag less influential when l is long, or if outstanding leg has minimal area or eccentricity Effective Net Area in Tension Tension Theory 49 49

Block Shear Tension Theory

Failure Tears Out Block of Steel
Block Shear Failure Tears Out Block of Steel Block defined by: Center line of holes Edge of welds State of Combined Yielding and Rupture Failure Planes At least one each in tension and shear. Tension Theory

Typical Examples in Tension Members:
Block Shear Typical Examples in Tension Members: Angle Connected on One Leg W-Shape Flange Connection Plate Connection Tension Theory

Block Shear Angle Bolted to Plate Pn Pn
Note that angle tension plane goes towards the free edge rather than up into the other leg, as this would be less resistance. Similarly the Plate would fail vertically towards the closest edge. Tension Theory

Block Shear Angle Bolted to Plate Shear plane on Angle Pn
Tension plane on Angle Pn Note that angle tension plane goes towards the free edge rather than up into the other leg, as this would be less resistance. Similarly the Plate would fail vertically towards the closest edge. Shear plane on Plate Tension plane on Plate (Shorter Dimension Controls if Fy and t are the same) Tension Theory 54 54

Block Shear Angle Bolted to Plate Pn Block Failure from Angle
Block Failure From Plate Pn Block shear could occur on either the angle or the plate – lowest failure mode strength of all controls Tension Theory

Flange of W-Shape Bolted to Plate
Block Shear Flange of W-Shape Bolted to Plate Pn First look at the W-Shape, then the plate Tension Theory

Block Shear Flange of W-Shape Bolted to Plate Shear planes on W-Shape Pn Tension planes on W-Shape First look at the W-Shape, then the plate Tension Theory 57 57

Block Shear Flange of W-Shape Bolted to Plate Pn Block Failure in W-Shape First look at the W-Shape, then the plate Tension Theory

Block Shear Flange of W-Shape Bolted to Plate Pn Pn Here 2 possible plate block shear modes could occur, the lower strength would control. Tension Theory

Block Shear Flange of W-Shape Bolted to Plate Pn Shear planes on Plate Tension planes on Plate Pn Here 2 possible plate block shear modes could occur, the lower strength would control. Shear planes on Plate Tension plane on Plate Tension Theory 60 60

Flange of W-Shape Bolted to Plate Block Shear
Pn Block Failure in Plate Pn Block Failure in Plate Tension Theory

Angle or Plate Welded to Plate
Block Shear Angle or Plate Welded to Plate Pn Weld around the perimeter Two possible block shear failures can be described by the perimeter of the welds – that with the lower strength would control. Two Block Shear Failures to Check Tension Theory

Block Shear Angle or Plate Welded to Plate Pn Pn Two possible block shear failures can be described by the perimeter of the welds – that with the lower strength would control. Tension Theory 63 63

Block Shear Angle or Plate Welded to Plate Pn Shear plane on Plate Tension plane on Plate Pn Two possible block shear failures can be described by the perimeter of the welds – that with the lower strength would control. Shear planes on Plate Tension plane on Plate Tension Theory 64 64

Block Shear Angle or Plate Welded to Plate Pn Block Failure From Plate Pn Two possible block shear failures can be described by the perimeter of the welds – that with the lower strength would control. Tension Theory 65 65

Bearing at Bolt Holes Tension Theory

Bolts bear into material around hole.
Bearing at Bolt Holes Bolts bear into material around hole. Direct bearing can deform the bolt hole an excessive amount and be limited by direct bearing capacity. If the clear space to adjacent hole or edge distance is small, capacity may be limited by tearing out a section of base material at the bolt. Tension Theory

Bearing at Bolt Holes Bolt Pn
Bolt induces bearing stresses on the base material. Tension Theory

Bearing at Bolt Holes Bolt Pn
Which can result in excessive deformation of the bolt hole, Tension Theory

Bearing at Bolt Holes Lc Bolt Pn
When bearing stresses act on bolts that are near the edge of the material (Lc dimension is small). Lc= clear distance, in the direction of load, between the edge of the hole and the edge of the adjacent hole or the edge of the material. Tension Theory

Bearing at Bolt Holes Pn
A block of material can tear out to the plate edge due to bearing. Note, this is differentiated from block shear since there is no tension plane for the failure. Tension Theory

Bearing at Bolt Holes Lc Bolt Pn
Similarly, when bearing stresses act on bolts that are closely spaced (Lc dimension is small). Tension Theory

Bearing at Bolt Holes Pn
A block of material can tear out between the bolt holes due to bearing stresses. Note, this is differentiated from block shear since there is no tension plane for the failure. Tension Theory

AISC Manual – 14th Edition
Teaching Modules for Steel Instruction Tension Member AISC Manual – 14th Edition Developed by Scott Civjan University of Massachusetts, Amherst

Tension Members: Chapter B: Gross and Net Areas
Chapter D: Tension Member Strength Chapter J: Block Shear Part 5: Design Charts and Tables Tension - AISC Manual 14th Ed

Gross and Net Areas: Criteria in Section B4.3
Strength criteria in Chapter D: Design of Members for Tension Tension - AISC Manual 14th Ed

Rupture on Effective Net Area Ft = 0.75 (Wt = 2.00)
Yield on Gross Area Ft = 0.90 (Wt = 1.67) Rupture on Effective Net Area Ft = 0.75 (Wt = 2.00) Block Shear Ft = 0.75 (Wt = 2.00) Tension - AISC Manual 14th Ed

Yield on Gross Area Tension - AISC Manual 14th Ed

Yield on Gross Area Pn = FyAg Equation D2-1 Ft = 0.90 (Wt = 1.67)
Ag = Gross Area Total cross-sectional area in the plane perpendicular to tensile stresses. Tension - AISC Manual 14th Ed

Tension - AISC Manual 14th Ed

Pn = FuAe Equation D2-2 ft = 0.75 (Wt = 2.00) Ae = Effective Net Area Accounts for any holes or openings, potential failure planes not perpendicular to the tensile stresses, and effects of shear lag. Tension - AISC Manual 14th Ed

An = Net Area = Net Width x thickness Modify gross area (Ag) to account for the following: Holes or openings Potential failure planes not perpendicular to the tensile stresses. Tension - AISC Manual 14th Ed

Diagonal hole pattern: Net Width = Gross Width + Σs2/4g – width of all holes Section B4.3b and D3.2 s = longitudinal center-to-center spacing of holes (pitch) g = transverse center-to-center spacing between fastener lines (gage) Pu g s Tension - AISC Manual 14th Ed

Holes or openings Section B4.3b Use1/16” greater bolt hole width than nominal hole dimension shown in Table J3.3. Accounts for potential damage in fabrication. Tension - AISC Manual 14th Ed

When considering angles:
Rupture on Effective Net Area When considering angles: Find gage (g) on page 1-48 of Manual, “Workable Gages in Standard Angles” unless otherwise noted. Tension - AISC Manual 14th Ed

An = Net Area An = Ag- ∑(dn+1/16)t + ∑(s2/(4g))t dn = nominal hole diameter t = thickness of tension member Other terms defined on previous slides Tension - AISC Manual 14th Ed

Ae = Effective Net Area Modify net area (An) to account for shear lag. Ae = AnU Equation D3-1 U = shear lag factor reduction Or value per Table D3.1 = eccentricity of connection l = length where force transfer occurs (distance parallel to applied tension force along bolts or weld) Tension - AISC Manual 14th Ed

Block Shear Tension - AISC Manual 14th Ed

Block Shear Block Shear Rupture Strength (Equation J4-3), ft = 0.75 (Wt = 2.00) Agv = gross area subject to shear Anv = net area subject to shear Ant = net area subject to tension Ubs = 1 or 0.5 (1 for most tension members, see Figure C-J4.2) Tension - AISC Manual 14th Ed

Block Shear Block Shear Rupture Strength (Equation J4-5), Smaller of two values will control ft = 0.75 (Wt = 2.00) Agv = gross area subject to shear Anv = net area subject to shear Ant = net area subject to tension Ubs = 1 or 0.5 (1 for most tension members, see Figure C-J4.2) 90 Tension - AISC Manual 14th Ed 90

Bearing at Bolt Holes Tension - AISC Manual 14th Ed

Bearing at Bolt Holes ft = 0.75 (Wt = 2.00)
For standard, oversized, and short-slotted holes, or long slotted holes with slots parallel to the direction of loading: (Equation J3-6a) ft = 0.75 (Wt = 2.00) Lc = clear distance, in the direction of force, between the edge of hole and the edge of adjacent hole or edge of the material. t = thickness of connected material d = nominal bolt diameter Fu = specified minimum tensile strength of the connected material Tension - AISC Manual 14th Ed

Bearing at Bolt Holes ft = 0.75 (Wt = 2.00)
For standard, oversized, and short-slotted holes, or long slotted holes with slots parallel to the direction of loading: (Equation J3-6a) ft = 0.75 (Wt = 2.00) Tearout Limit Bearing Limit Lc = clear distance, in the direction of force, between the edge of hole and the edge of adjacent hole or edge of the material. t = thickness of connected material d = nominal bolt diameter Fu = Specified minimum tensile strength of the connected material 93 Tension - AISC Manual 14th Ed 93

Bearing at Bolt Holes For standard, oversized, and short-slotted holes, or long slotted holes with slots parallel to the direction of loading, but when deformation of the bolt hole is not a design consideration: (Equation J3-6b) For long-slotted holes with slot perpendicular to the direction of force: (Equation J3-6c) Tension - AISC Manual 14th Ed

Design Aids Tension - AISC Manual 14th Ed

Design Aids Tables 5-1 to 5-8
List available yield and rupture strength for typical sections. Use care! These tables assume Ae = 0.700Ag to 0.952Ag. You must check this is met in the member and connections! Tension - AISC Manual 14th Ed

Design Aids Table 7-4 provides bearing strength at bolt holes based on bolt spacing. Table 7-5 provides bearing strength at bolt holes based on edge distance. These tables check bearing and tearout. Note that edge distance, Le and bolt spacing, s are measured to the centers of bolt holes, rather than the edges of the bolt holes. The bearing side of the equation controls when s ≥ sfull or Le ≥ Lefull. sfull and Lefull are the bolt spacing and edge distance, respectively, for full bearing strength. Tension - AISC Manual 14th Ed

Teaching Modules for Steel Instruction TENSION MEMBER Design

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